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AN ANALYSIS OF THE RELATIONSIPS BETWEEN SOUTH CAROLINA DEPARTMENT OF
EDUCATION ANNUAL SCHOOL REPORT CARD VARIABLES OF PUBLIC ELEMENTARY
SCHOOLS AND STUDENT ACHIEVEMENT AS MEASURED BY 2008 PACT DATA: WITH AN
INITIAL EMPHASIS ON SCHOOL SIZE
by
Salvatore Andrew Minolfo
Bachelor of Arts
University of South Carolina-Aiken, 1994
Master of Education
University of South Carolina, 1998
Educational Specialist
University of South Carolina, 2004
Submitted in Partial Fulfillment of the Requirements
For the Degree of Doctor of Philosophy in
Educational Administration
College of Education
University of South Carolina
2010
Accepted by:
Kenneth Stevenson, Ed. D., Major Professor
Edward Cox, Ed. D., Committee Member
Zach Kelehear, Ed. D., Committee Member
Donna Shannon, Ph. D., Committee Member
Tim Mousseau, Dean of The Graduate School
UMI Number: 3433173
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a note will indicate the deletion.
UMI 3433173
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© Copyright by Salvatore A. Minolfo, 2010
All Rights Reserve
ii
DEDICATION
To Dominick and Andrea Minolfo, my parents. This was your idea. I never thought that I
could accomplish this goal. Through your persistence, encouragement, and support, I
was able to achieve this goal and so much more. Thank you for believing in me. I love
you both.
To my wife and children, Susan, Olivia, Elena, and Isabella. I dedicate this to all of you as
well. Your encouragement, support, and love helped me persevere to “obtain the
prize.” Thank you. I love you all.
iii
ACKNOWLEDGEMENTS
The following individuals deserve far greater recognition and appreciation than I can
describe:
Kenneth Stevenson, Ed.D. – You taught my first graduate level class and now we finish
your career and my doctorate degree together. I am honored to have been your
student these many years. You have taught me so much more than facilities and
whether school size is a predictive variable of student achievement. I truly appreciate
you investing your life in mine. Best wishes in your retirement.
Edward Cox, Ed.D., Zach Kelehear, Ed.D., and Donna Shannon, Ph.D. – thank you for
being a part of my educational career as well as serving on my dissertation committee.
Each of you has had a hand in making me the educator I am today. Truly, I appreciate
each of you.
My family – thank you to each of you for your prayers, support, encouragement, and
love. Thank you for caring enough to ask me and encourage me even when you did not
really know what it was I was doing. That is what makes a family like ours so special.
Jim Hooper and Kevin O’Gorman – my graduate school buddies helped me through each
stage of my graduate career. Thank you, my friends, for pushing me and helping me to
the end.
iv
ABSTRACT
One purpose of this study was to determine whether a relationship exists
between the size of South Carolina PreKindergarten – 5 or Kindergarten – 5 public
elementary schools and student achievement while controlling for the effect of
socioeconomic status. The independent variable school size, or 135-day average daily
membership, the dependent variable student achievement, and the control variable
poverty index were obtained from the 2008 South Carolina Department of Education (SC
DOE) 2008 Annual School Report Card. Utilizing the same variables, a second purpose of
this study was to ascertain if student achievement varied among public elementary
schools in South Carolina when the poverty index was controlled by including schools
with similar poverty indexes in strata.
The third purpose of this study was to determine whether any school variable, or
a combination of these variables, including school size, as reported on the Carolina
Department of Education (SC DOE) 2008 Annual School Report Card, predicted student
achievement. In addition to school size, thirty-nine variables reported on the SC DOE
Report Card were analyzed. The researcher again controlled for poverty by grouping the
public elementary schools in South Carolina into strata based on poverty index
percentages.
v
Descriptive statistics were calculated on all variables. Pearson correlation
analyses, partial correlation analysis, and finally, stepwise regression analyses were
conducted within the poverty index strata to control for poverty to ascertain whether a
relationship existed between school size and student achievement. The researcher also
conducted a stepwise regression analysis with the SC DOE Annual School Report Card
variables and student achievement within the poverty index strata to assess whether a
variable, or a combination of variables, were predictive of student achievement.
When the partial correlation analysis between South Carolina public elementary
school size and 2008 Palmetto Achievement Challenge Test data in English/language arts
and mathematics was calculated, school size was not significantly correlated to student
achievement. The stepwise regression analysis demonstrated the same result: school
size was not found to be significantly related to student achievement. In the stepwise
regression analysis for the SC DOE Annual School Report Card variables, the variable
percent objectives met was the most predictive variable of student achievement.
However, no particular combination of variables was consistently predictive of student
achievement within each poverty index strata.
Finally, this research initially set out to examine the relationship between
elementary school size and student achievement. A few random findings were
identified; however, these outcomes did not lend themselves to predicting student
achievement when poverty was controlled, either across the whole population or within
schools grouped in strata based on poverty index. Subsequent analysis of potential
vi
combinations of predictive variables, including school size, did not identify school size as
a significant combination with other variables in predicting student achievement.
vii
TABLE OF CONTENTS
DEDICATION
iii.
ACKNOWLEDGEMENTS
iv.
ABSTRACT
v.
LIST OF TABLES
xiii.
CHAPTER
I.
PAGE
NATURE OF THE PROBLEM
1
Purpose and Research Questions
6
Poverty
11
School Climate
12
Per Pupil Expenditure
13
Teacher Performance
14
School Size
14
Student Attendance Rate
16
Teacher Attendance Rate
16
Remaining Variables
17
Research Questions
18
Significance of Study
19
viii
II.
Delimitations and Limitations of the Study
21
Overview of the Design of the Study
23
Concepts, Definitions and Source of Evidence
27
Conceptual Framework
31
Summary
32
REVIEW OF THE LITERATURE
33
History of the Research on School Size and Student Achievement
33
National Studies on School Size
38
The Matthew Project: History and Results
44
Summary of Meta-Analyses on School Size
54
South Carolina Studies
55
Variables
72
Poverty
72
School Leadership
74
School Climate
77
Per Pupil Cost
79
Teacher Certification and Professional Development
81
Teacher Attendance Rate
87
Student Attendance Rate
88
Other Variables
89
Summary
90
III. DESIGN OF THE STUDY
92
ix
Purpose of the Study
92
Methodology
97
Instrumentation
102
Sampling Plan
103
Data Gathering
104
Data Analysis
105
Summary
106
IV. RESULTS OF THE STUDY
109
Descriptive Statistics
111
Findings for Research Question One
113
Pearson Correlations
114
Partial Correlation Analysis Controlling for Poverty Index
117
Stepwise Multiple Regression Analysis
120
Findings for Research Question Two
123
Description of Schools within Poverty Index Strata
123
Pearson Correlation Analysis within Poverty Index Strata
139
Partial Correlation Analysis within Poverty Index Strata
143
Stepwise Multiple Regression Analysis within Poverty Index Strata
147
Summary of stepwise multiple regression for poverty index strata
156
Findings for Research Question 3
158
Stepwise Multiple Regression of All Schools by Grade Level and Subject
159
Summary of Stepwise Multiple Regression Analysis for All Schools and All
169
x
Subjects
V.
Stepwise Multiple Regression Analysis Within Poverty Index Strata
170
Stepwise multiple regression for strata 1 (0% - 49%)
171
Stepwise multiple regression for Strata 2 (50% - 59%)
178
Stepwise multiple regression for Strata 3 (60% - 69%)
184
Stepwise multiple regression for Strata 4 (70% - 79%)
190
Stepwise multiple regression for Strata 5 (80% - 89%)
197
Stepwise multiple regression for Strata 6 (90% - 94%)
203
Stepwise multiple regression for Strata 7 (95% - 100%)
208
Summary of stepwise multiple regression for each poverty index strata
214
Summary of stepwise multiple regression for all poverty index strata
230
Summary
233
SUMMARY, DISCUSSION, CONCLUSION AND RECOMMENDATIONS
239
Purpose of the Study and Its Design
239
Findings for the Study
242
Research Question One
243
Research Question Two
244
Research Question Three
247
Summary of Results of Research Question Three
252
Discussion of Findings
254
Conclusions
267
Recommendations
268
xi
Recommendations for Policy Makers
269
Recommendations for Educators
270
Recommendations for Researchers
271
Summary
273
REFERENCES
275
xii
LIST OF TABLES
4.1
Descriptive Statistics for PreKindergarten - 5 and Kindergarten - 5
111
Elementary Schools of 2007-2008 Poverty Index and 135-Day Average
Daily Membership Variables
4.2
Descriptive Statistics for Third Grade PreKindergarten - 5 and Kindergarten
112
- 5 Elementary Schools of 2007-2008 PACT English/Language Arts &
Mathematics Data
4.3
Descriptive Statistics for Fourth Grade PreKindergarten - 5 and
112
Kindergarten - 5 Elementary Schools of 2007-2008 PACT English/Language
Arts & Mathematics Data
4.4
Descriptive Statistics for Fifth Grade PreKindergarten - 5 and Kindergarten
113
- 5 Elementary Schools of 2007-2008 PACT English/Language Arts &
Mathematics Data
4.5
Correlation of Third Grade 2007-2008 PACT English/Language Arts versus
114
135-Day Average Daily Membership
4.6
Correlation of Third Grade 2007-2008 PACT Mathematics versus 135-Day
115
Average Daily Membership
4.7
Correlation of Fourth Grade 2007-2008 PACT English/Language Arts versus
xiii
115
135-Day Average Daily Membership
4.8
Correlation of Fourth Grade 2007-2008 PACT Mathematics versus 135-Day
116
Average Daily Membership
4.9
Correlation of Fifth Grade 2007-2008 PACT English/Language Arts versus
116
135-Day Average Daily Membership
4.10
Correlation of Fifth Grade 2007-2008 PACT Mathematics versus 135-Day
117
Average Daily Membership
4.11
Partial Correlation of Third Grade 2007-2008 PACT English/Language Arts
118
versus 135-Day Average Daily Membership While Controlling for Poverty
Index
4.12
Partial Correlation of Third Grade 2007-2008 PACT Mathematics
118
versus135-Day Average Daily Membership While Controlling for Poverty
Index
4.13
Partial Correlation of Fourth Grade 2007-2008 PACT English/Language Arts
119
versus 135-Day Average Daily Membership While Controlling for Poverty
Index
4.14
Partial Correlation of Fourth Grade 2007-2008 PACT Mathematics
119
versus135-Day Average Daily Membership While Controlling for Poverty
Index
4.15
Partial Correlation of Fifth Grade 2007-2008 PACT English/Language Arts
versus 135-Day Average Daily Membership While Controlling for Poverty
Index
xiv
120
4.16
Partial Correlation of Fifth Grade 2007-2008 PACT Mathematics
120
versus135-Day Average Daily Membership While Controlling for Poverty
Index
4.17
Stepwise Multiple Regression of Third Grade 2007-2008 PACT
121
English/Language Arts versus Poverty Index and 135-Day Average Daily
Membership Variables
4.18
Stepwise Multiple Regression of Third Grade 2007-2008 PACT
121
Mathematics versus Poverty Index and 135-Day Average Daily
Membership Variables
4.19
Stepwise Multiple Regression of Fourth Grade 2007-2008 PACT
122
English/Language Arts versus Poverty Index and 135-Day Average Daily
Membership Variables
4.20
Stepwise Multiple Regression of Fourth Grade 2007-2008 PACT
122
Mathematics versus Poverty Index and 135-Day Average Daily
Membership Variables
4.21
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT
122
English/Language Arts versus Poverty Index and 135-Day Average Daily
Membership Variables
4.22
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT Mathematics 123
versus Poverty Index and 135-Day Average Daily Membership Variables
4.23
Descriptive Statistics for Strata 1 (0% - 49%) PreKindergarten – 5 and
Kindergarten – 5Elementary Schools of 2007-2008 Poverty Index and 135-
xv
124
Day Average Daily Membership Variables
4.24
Descriptive Statistics of Strata 1 (0% - 49%) Third Grade 2007-2008 PACT
125
English/Language Arts and Mathematics Data
4.25
Descriptive Statistics of Strata 1 (0% - 49%) Fourth Grade 2007-2008 PACT
125
English/Language Arts and Mathematics Data
4.26
Descriptive Statistics of Strata 1 (0% - 49%) Fifth Grade 2007-2008 PACT
126
English/Language Arts and Mathematics Data
4.27
Descriptive Statistics for Strata 2 (50% - 59%) PreKindergarten – 5 and
126
Kindergarten – 5Elementary Schools of 2007-2008 Poverty Index and 135Day Average Daily Membership Variables
4.28
Descriptive Statistics of Strata 2 (50% - 59%) Third Grade 2007-2008 PACT
127
English/Language Arts and Mathematics Data
4.29
Descriptive Statistics of Strata 2 (50% - 59%) Fourth Grade 2007-2008
128
PACT English/Language Arts and Mathematics Data
4.30
Descriptive Statistics of Strata 2 (50% - 59%) Fifth Grade 2007-2008 PACT
128
English/Language Arts and Mathematics Data
4.31
Descriptive Statistics for Strata 3 (60% - 69%) PreKindergarten – 5 and
128
Kindergarten – 5Elementary Schools of 2007-2008 Poverty Index and 135Day Average Daily Membership Variables
4.32
Descriptive Statistics of Strata 3 (60% - 69%) Third Grade 2007-2008 PACT
129
English/Language Arts and Mathematics Data
4.33
Descriptive Statistics of Strata 3 (60% - 69%) Fourth Grade 2007-2008
xvi
129
PACT English/Language Arts and Mathematics Data
4.34
Descriptive Statistics of Strata 3 (60% - 69%) Fifth Grade 2007-2008 PACT
130
English/Language Arts and Mathematics Data
4.35
Descriptive Statistics for Strata 4 (70% - 79%) PreKindergarten – 5 and
130
Kindergarten – 5Elementary Schools of 2007-2008 Poverty Index and 135Day Average Daily Membership Variables
4.36
Descriptive Statistics of Strata 4 (70% - 79%) Third Grade 2007-2008 PACT
131
English/Language Arts and Mathematics Data
4.37
Descriptive Statistics of Strata 4 (70% - 79%) Fourth Grade 2007-2008
132
PACT English/Language Arts and Mathematics Data
4.38
Descriptive Statistics of Strata 4 (70% - 79%) Fifth Grade 2007-2008 PACT
132
English/Language Arts and Mathematics Data
4.39
Descriptive Statistics for Strata 5 (80% - 89%) PreKindergarten – 5 and
133
Kindergarten – 5Elementary Schools of 2007-2008 Poverty Index and 135Day Average Daily Membership Variables
4.40
Descriptive Statistics of Strata 5 (80% - 89%) Third Grade 2007-2008 PACT
133
English/Language Arts and Mathematics Data
4.41
Descriptive Statistics of Strata 5 (80% - 89%) Fourth Grade 2007-2008
134
PACT English/Language Arts and Mathematics Data
4.42
Descriptive Statistics of Strata 5 (80% - 89%) Fifth Grade 2007-2008 PACT
134
English/Language Arts and Mathematics Data
4.43
Descriptive Statistics for Strata 6 (90% - 94%) PreKindergarten – 5 and
xvii
135
Kindergarten – 5Elementary Schools of 2007-2008 Poverty Index and 135Day Average Daily Membership Variables
4.44
Descriptive Statistics of Strata 6 (90% - 94%) Third Grade 2007-2008 PACT
136
English/Language Arts and Mathematics Data
4.45
Descriptive Statistics of Strata 6 (90% - 94%) Fourth Grade 2007-2008
136
PACT English/Language Arts and Mathematics Data
4.46
Descriptive Statistics of Strata 6 (90% - 94%) Fifth Grade 2007-2008 PACT
137
English/Language Arts and Mathematics Data
4.47
Descriptive Statistics for Strata 7 (95% - 100%) PreKindergarten – 5 and
137
Kindergarten – 5Elementary Schools of 2007-2008 Poverty Index and 135Day Average Daily Membership Variables
4.48
Descriptive Statistics of Strata 7 (94% - 100%) Third Grade 2007-2008 PACT 138
English/Language Arts and Mathematics Data
4.49
Descriptive Statistics of Strata 7 (94% - 100%) Fourth Grade 2007-2008
138
PACT English/Language Arts and Mathematics Data
4.50
Descriptive Statistics of Strata 7 (94% - 100%) Fifth Grade 2007-2008 PACT
139
English/Language Arts and Mathematics Data
4.51
Correlation of Strata 4 (70% - 79%) Fourth Grade 2007-2008 PACT
140
English/Language Arts versus 135-Day Average Daily Membership
4.52
Correlation of Strata 6 (90% - 95%) Fourth Grade 2007-2008 PACT
141
English/Language Arts versus 135-Day Average Daily Membership
4.53
Correlation of Strata 6 (90% - 95%) Fifth Grade 2007-2008 PACT
xviii
141
Mathematics versus 135-Day Average Daily Membership
4.54
Correlation of Strata 7 (95% - 100%) Third Grade 2007-2008 PACT
142
English/Language Arts versus 135-Day Average Daily Membership
4.55
Correlation of Strata 7 (95% - 100%) Fourth Grade 2007-2008 PACT
142
English/Language Arts versus 135-Day Average Daily Membership
4.56
Correlation of Strata 7 (95% - 100%) Fifth Grade 2007-2008 PACT
143
English/Language Arts versus 135-Day Average Daily Membership
4.57
Partial Correlation of Strata 7 (95% - 100%) Third Grade 2007-2008 PACT
144
English/Language Arts versus 135-Day Average Daily Membership while
controlling for Poverty Index
4.58
Partial Correlation of Strata 1 (0% - 49%) Fourth Grade 2007-2008 PACT
145
Mathematics versus 135-Day Average Daily Membership while controlling
for Poverty Index
4.59
Partial Correlation of Strata 4 (70% - 79%) Fourth Grade 2007-2008 PACT
145
English/Language Arts versus 135-Day Average Daily Membership while
controlling for Poverty Index
4.60
Partial Correlation of Strata 6 (90% - 94%) Fourth Grade 2007-2008 PACT
146
English/Language Arts versus 135-Day Average Daily Membership while
controlling for Poverty Index
4.61
Partial Correlation of Strata 7 (95% - 100%) Fourth Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership while
controlling for Poverty Index
xix
146
4.62
Partial Correlation of Strata 6 (90% - 94%) Fifth Grade 2007-2008 PACT
147
Mathematics versus 135-Day Average Daily Membership while controlling
for Poverty Index
4.63
Stepwise Multiple Regression of Third Grade 2007-2008 PACT
148
English/Language Arts versus Poverty Index and Average Daily
Membership
4.64
Stepwise Multiple Regression of Third Grade 2007-2008 PACT
148
Mathematics versus Poverty Index and Average Daily Membership
4.65
Stepwise Regression of Fourth Grade 2007-2008 PACT English/Language
148
Arts versus Poverty Index and Average Daily Membership
4.66
Stepwise Regression of Fourth Grade 2007-2008 PACT Mathematics versus 149
Poverty Index and Average Daily Membership
4.67
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT
149
English/Language Arts versus Poverty Index and Average Daily
Membership
4.68
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT Mathematics 149
versus Poverty Index and Average Daily Membership
4.69
Stepwise Multiple Regression of Strata 1 (0% - 49%) Third Grade 2007-
150
2008 PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.70
Stepwise Multiple Regression of Strata 1 (0% - 49%) Third Grade 20072008 PACT Mathematics versus Index and Average Daily Membership
xx
150
4.71
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fourth Grade 2007-
151
2008 PACT Mathematics versus Index and Average Daily Membership
4.72
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fifth Grade 2007-2008 151
PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.73
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fifth Grade 2007-2008 151
PACT Mathematics versus Index and Average Daily Membership
4.74
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fourth Grade 2007-
152
2008 PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.75
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fifth Grade 2007-
152
2008 PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.76
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fifth Grade 2007-
152
2008 PACT Mathematics versus Index and Average Daily Membership
4.77
Stepwise Multiple Regression of Strata 4 (70% - 79%) Fourth Grade 2007-
153
2008 PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.78
Stepwise Multiple Regression of Strata 6 (90% - 94%) Fourth Grade 2007-
153
2008 PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.79
Stepwise Multiple Regression of Strata 6 (90% - 94%) Fifth Grade 2007-
xxi
153
2008 PACT Mathematics versus Index and Average Daily Membership
4.80
Stepwise Multiple Regression of Strata 7 (95% - 100%) Third Grade 2007-
154
2008 PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.81
Stepwise Multiple Regression of Strata 7 (95% - 100%) Third Grade 2007-
154
2008 PACT Mathematics versus Index and Average Daily Membership
4.82
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fourth Grade 2007-
154
2008 PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.83
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fourth Grade 2007-
155
2008 PACT Mathematics versus Index and Average Daily Membership
4.84
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fifth Grade 2007-
155
2008 PACT English/Language Arts versus Poverty Index and Average Daily
Membership
4.85
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fifth Grade 2007-
155
2008 PACT Mathematics versus Index and Average Daily Membership
4.86
Stepwise Multiple Regression Summary of PACT English/Language Arts
158
and Mathematics versus Poverty Index and 135-Day Average Daily
Membership (Poverty Index Strata with Significant Relationships Listed
Only)
4.87
Stepwise Multiple Regression of Third Grade 2007-2008 PACT
English/Language Arts versus SC DOE Annual School Report Card Variables
xxii
161
4.88
Stepwise Multiple Regression of Third Grade 2007-2008 PACT
162
Mathematics versus SC DOE Annual School Report Card Variables
4.89
Stepwise Multiple Regression of Fourth Grade 2007-2008 PACT
163
English/Language Arts versus SC DOE Annual School Report Card Variables
4.90
Stepwise Multiple Regression of Fourth Grade 2007-2008 PACT
165
Mathematics versus SC DOE Annual School Report Card Variables
4.91
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT
166
English/Language Arts versus SC DOE Annual School Report Card Variables
4.92
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT Mathematics 168
versus SC DOE Annual School Report Card Variables
4.93
Summary of Stepwise Multiple Regression Analysis for All Schools and All
170
Subjects
4.94
Stepwise Multiple Regression of Strata 1 (0% - 49%) Third Grade 2007-
172
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.95
Stepwise Multiple Regression of Strata 1 (0% - 49%) Third Grade 2007-
173
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.96
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fourth Grade 2007-
174
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.97
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fourth Grade 2007-
xxiii
175
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.98
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fifth Grade 2007-2008 177
PACT English/Language Arts versus SC DOE Annual School Report Card
Variables
4.99
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fifth Grade 2007-2008 178
PACT Mathematics versus SC DOE Annual School Report Card Variables
4.100 Stepwise Multiple Regression of Strata 2 (50% - 59%) Third Grade 2007-
179
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.101 Stepwise Multiple Regression of Strata 2 (50% - 59%) Third Grade 2007-
180
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.102 Stepwise Multiple Regression of Strata 2 (50% - 59%) Fourth Grade 2007-
181
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.103 Stepwise Multiple Regression of Strata 2 (50% - 59%) Fourth Grade 2007-
182
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.104 Stepwise Multiple Regression of Strata 2 (50% - 59%) Fifth Grade 20072008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
xxiv
183
4.105 Stepwise Multiple Regression of Strata 2 (50% - 59%) Fifth Grade 2007-
184
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.106 Stepwise Multiple Regression of Strata 3 (60% - 69%) Third Grade 2007-
185
2008PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.107 Stepwise Multiple Regression of Strata 3 (60% - 69%) Third Grade 2007-
186
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.108 Stepwise Multiple Regression of Strata 3 (60% - 69%) Fourth Grade 2007-
187
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.109 Stepwise Multiple Regression of Strata 3 (60% - 69%) Fourth Grade 2007-
188
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.110 Stepwise Multiple Regression of Strata 3 (60% - 69%) Fifth Grade 2007-
189
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.111 Stepwise Multiple Regression of Strata 3 (60% - 69%) Fifth Grade 2007-
190
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.112 Stepwise Multiple Regression of Strata 4 (70% - 79%) Third Grade 2007-
xxv
191
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.113 Stepwise Multiple Regression of Strata 4 (70% - 79%) Third Grade 2007-
192
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.114 Stepwise Multiple Regression of Strata 4 (70% - 79%) Fourth Grade 2007-
193
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.115 Stepwise Multiple Regression of Strata 4 (70% - 79%) Fourth Grade 2007-
194
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.116 Stepwise Multiple Regression of Strata 4 (70% - 79%) Fifth Grade 2007-
195
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.117 Stepwise Multiple Regression of Strata 4 (70% - 79%) Fifth Grade 2007-
196
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.118 Stepwise Multiple Regression of Strata 5 (80% - 89%) Third Grade 2007-
197
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.119 Stepwise Multiple Regression of Strata 5 (80% - 89%) Third Grade 20072008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
xxvi
198
4.120 Stepwise Multiple Regression of Strata 5 (80% - 89%) Fourth Grade 2007-
199
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.121 Stepwise Multiple Regression of Strata 5 (80% - 89%) Fourth Grade 2007-
200
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.122 Stepwise Multiple Regression of Strata 5 (80% - 89%) Fifth Grade 2007-
201
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.123 Stepwise Multiple Regression of Strata 5 (80% - 89%) Fifth Grade 2007-
202
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.124 Stepwise Multiple Regression of Strata 6 (90% - 94%) Third Grade 2007-
203
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.125 Stepwise Multiple Regression of Strata 6 (90% - 94%) Third Grade 2007-
204
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.126 Stepwise Multiple Regression of Strata 6 (90% - 94%) Fourth Grade 2007-
205
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.127 Stepwise Multiple Regression of Strata 6 (90% - 94%) Fourth Grade 20072008 PACT Mathematics versus SC DOE Annual School Report Card
xxvii
206
Variables
4.128 Stepwise Multiple Regression of Strata 6 (90% - 94%) Fifth Grade 2007-
206
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.129 Stepwise Multiple Regression of Strata 6 (90% - 94%) Fifth Grade 2007-
207
2008PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.130 Stepwise Multiple Regression of Strata 7 (95% - 100%) Third Grade 2007-
209
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.131 Stepwise Multiple Regression of Strata 7 (95% - 100%) Third Grade 2007-
210
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.132 Stepwise Multiple Regression of Strata 7 (95% - 100%) Fourth Grade 2007-
211
2008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
4.133 Stepwise Multiple Regression of Strata 7 (95% - 100%) Fourth Grade 2007-
212
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.134 Stepwise Multiple Regression of Strata 7 (95% - 100%) Fifth Grade 20072008 PACT English/Language Arts versus SC DOE Annual School Report
Card Variables
xxviii
213
4.135 Stepwise Multiple Regression of Strata 7 (95% - 100%) Fifth Grade 2007-
214
2008 PACT Mathematics versus SC DOE Annual School Report Card
Variables
4.136 Summary of the Order of Outcome Variables Produced by Stepwise
216
Multiple Regression for Poverty Index Strata 1 (0% - 49%)
4.137 Summary of the Order of Outcome Variables Produced by Stepwise
217
Multiple Regression for Poverty Index Strata 1 (0% - 49%) by Adjusted R2
4.138 Summary of the Order of Outcome Variables Produced by Stepwise
218
Multiple Regression for Poverty Index Strata 2 (50% - 59%)
4.139 Summary of the Order of Outcome Variables Produced by Stepwise
219
Multiple Regression for Poverty Index Strata 2 (50% - 59%) by Adjusted R2
4.140
Summary of the Order of Outcome Variables Produced by Stepwise
220
Multiple Regression for Index Strata 3 (60% - 69%)
4.141 Summary of the Order of Outcome Variables Produced by Stepwise
221
Multiple Regression for Poverty Index Strata 3 (60% - 69%) by Adjusted R2
4.142 Summary of the Order of Outcome Variables Produced by Stepwise
223
Multiple Regression for Poverty Index Strata 4 (70% - 79%)
4.143 Summary of the Order of Outcome Variables Produced by Stepwise
224
Multiple Regression for Poverty Index Strata 4 (70% - 79%) by Adjusted R2
4.144 Summary of the Order of Outcome Variables Produced by Stepwise
225
Multiple Regression for Poverty Index Strata 5 (80% - 89%)
4.145 Summary of the Order of Outcome Variables Produced by Stepwise
xxix
226
Multiple Regression for Poverty Index Strata 5(80% - 89%) by Adjusted R2
4.146 Summary of the Order of Outcome Variables Produced by Stepwise
227
Multiple Regression for Poverty Index Strata 6 (90% - 94%)
4.147 Summary of the Order of Outcome Variables Produced by Stepwise
228
Multiple Regression for Poverty Index Strata 6 (90% - 94%) y Adjusted R2
4.148 Summary of the Order of Outcome Variables Produced by Stepwise
229
Multiple Regression for Poverty Index Strata 7 (95% - 100%)
4.149 Summary of the Order of Outcome Variables Produced by Stepwise
230
Multiple Regression for Poverty Index Strata 7 (95% - 100%) by Adjusted
R2
4.150 Summary of Stepwise Multiple Regression for Each Poverty Index Strata
xxx
233
CHAPTER I
Nature of the Problem
During the last twenty years educational researchers have conducted numerous
studies to determine the variable or variables that affect student achievement in public
schools (Friedkin & Necochea, 1988; Stevenson, 1996; Howley, 1995; Cushman, 1999;
Durbin, 2001; Stevenson, 2001; McRobbie, 2001; Nathan & Febey, 2001; Roberts, 2002;
Crenshaw, 2003; McCathern, 2004; Carpenter, 2006; and Kaczor, 2006). One variable
that has been a focus is school size in terms of student body population. One prominent
question has been: “What size school positively or negatively affects student
achievement?”
In the late 1950s, James Conant, then president of Harvard University, began the
discussion on school size with the Conant Report (Berry & West, 2005). His report
stated that large high schools resulted in higher student achievement and were
economically advantageous. Conant, and researchers after him, focused on school
inputs such as per pupil expenditures, teacher salaries, and instructional programs,
considered the economies of scale model.
1
Beginning in the 1980s, researchers addressed questions related to school size
that focused on outcome variables such as student achievement, student attendance
rate, and high school completion rate (Berry & West, 2005). The results of this research
showed either no significant relationship between school size and student achievement,
or a significant relationship between school size and student achievement favoring small
schools. The complexity of the issue has increased. Although this topic has become
more complex since the 1980s, recent research indicates that school size and student
achievement may be tied to the affluence of students attending a school (Howley &
Howley, 2004).
One collection of studies on school size that has influenced current research is
The Matthew Project. The basis for The Matthew Project was research begun by Noah
Friedkin and Juan Necochea (1988). These two researchers conducted a study
describing school performance at four grade levels in California. The results of their
study concluded that 1) small schools appeared to positively affect student achievement
for high poverty (low socioeconomic status) populations and 2) large schools with low
poverty (high socioeconomic status) populations positively affected student
achievement. Following this study design, Howley and Bickel replicated the California
research in Alaska, Arkansas, California, Georgia, Ohio, Montana, Texas, and West
Virginia. The findings from each of these studies supported Friedkin and Necochea’s
original results (Howley, Strange & Bickel, 2000).
Howley, as the primary researcher in all of the state studies comprising The
Matthew Project, used the school as the unit of analysis, and tested the concept of the
2
effect of school size on student achievement as influenced by socioeconomic status
(SES). Howley and Bickel (1999) defined student achievement by the overall
standardized test scores on state assessments for each school. School size was defined
as the average number of students per grade in each school. SES was defined as the
percentage of students receiving free and reduced-price lunch.
Howley and Bickel introduced a concept which they refer to as the “excellence
effect.” Excellence effects are defined “as the interaction between school size and SES
level which sought to determine whether students from lower SES backgrounds
benefited more from being at a smaller school than did higher SES students” (Howley &
Bickel, 2000, p. 5). Excellence effect is measured by the correlation between student
achievement within groups of schools divided at the median size of all schools at a given
level within the state (Howley & Bickel, 2000). Excellence effects of size varied
substantially by state, but The Matthew Project studies found that the influence of size
varied by SES level, with size exerting a negative influence on achievement in
impoverished schools, but a positive influence on achievement in affluent schools. That
is, all else equal, larger school size benefits achievement in affluent communities, but it
is detrimental in impoverished communities.
Howley and Bickel (2000) also identified another concept called the “equity
effect,” which also was conceptualized as an outcome of their work in The Matthew
Project. Equity effect is defined as “the negative effect low SES conditions have on
students’ achievement” (Howley & Bickel, 2000, p. 7). The equity effect is measured by
the correlation between achievement and socioeconomic status within groups of
3
schools divided at the median size of all schools at a given level within the state (Howley
& Bickel, 2000). Howley and Bickel found that smaller schools offset the negative
effects of high poverty for students in all grade levels. Larger school size was associated
with higher student achievement in affluent communities, but it was detrimental in
impoverished communities (Howley, Strange, & Bickel, 2000).
In South Carolina, Stevenson has conducted research on school size and student
achievement for more than a decade. In 1996 Stevenson concluded that school size did
not matter in South Carolina elementary schools in relationship to student achievement.
Student achievement was identified as the number of years the school won South
Carolina State Department of Education Incentive Award or Palmetto’s Finest Award.
However, he conducted a subsequent study in 2001 in which he researched the
relationship between the size of elementary school populations and student academic
performance on the South Carolina state assessment entitled the Palmetto Achievement
Challenge Test (PACT). Stevenson’s initial analysis identified a relationship in favor of
larger schools; however, the tendency did not manifest significance when controlling for
SES.
Following Stevenson’s study, ten more studies were conducted on school size
and student achievement in South Carolina. McCathern (2004), White (2005), and
Carpenter (2006) focused on elementary schools in South Carolina. Studies on middle
schools were completed by Roberts (2002), Gettys (2003), and Kaczor (2006). Durbin
(2001), Stevenson (2001), Crenshaw (2003), and Maxey (2008) conducted studies in high
schools to determine whether a relationship existed between school size and student
4
achievement. The summary finding from the studies included in Stevenson’s analysis in
2006 was that SES was the greatest predicator of student achievement or school
climate; accounting for up to (70%) of variation across schools. Maxey’s study was
conducted in 2008, but supported Stevenson’s conclusions, too. Little evidence was
found that size was related to student achievement.
Two of the above studies influenced this study on school size and student
achievement in public elementary schools: McCathern (2004) and Carpenter (2006).
McCathern (2004) examined the relationship between the number of students enrolled
in PreKindergarten – 5 or Kindergarten – 5 elementary schools and student
achievement. McCathern defined student achievement as the mean scaled score of
students on the norm-referenced Metropolitan Achievement Test, Seventh Edition.
McCathern studied student achievement in reading and mathematics while controlling
for several variables: pupil-teacher ratio, percentage of students in the free and
reduced-price lunch program, amount of teacher experience, level of teacher education,
gender of students, racial composition of the school, operating costs of the school, and
community setting (rural, suburban, or urban). His study did not reveal a relationship
between school size and student achievement.
Carpenter (2006) complemented McCathern’s research. However, Carpenter
used the Palmetto Achievement Challenge Test (PACT), the state of South Carolina’s
assessment for students in grades 3 through 8 for English/language arts, mathematics,
science, and social studies. He sought to determine whether a relationship existed
between student achievement in grades 3, 4, and 5 in English/language arts and
5
mathematics and school size while controlling for poverty. Carpenter also studied
whether school size, or any other variable, or set of variables, could predict student
achievement. He utilized the following variables: school size, school per pupil operating
cost, and student body SES. Carpenter controlled for SES by using a partial regression
analysis to isolate the effects of poverty while calculating the effects of school size on
student achievement in English/language arts and mathematics on the PACT.
Carpenter’s study did not reveal a significant relationship between school size
and student achievement in English/language arts or mathematics while controlling for
SES. The study confirmed that SES was a significant predictor of student achievement in
English/language arts (63%) and mathematics (60%). Neither school size nor per pupil
operating cost were found to be statistically significant predictors of student
achievement in English/language arts or mathematics.
In this study, a complementary study to McCathern and Carpenter, the
researcher seeks to determine whether a relationship exists between school size in
public elementary schools in South Carolina and student achievement. The researcher
uses a different methodology to neutralize the effects of SES while measuring whether a
relationship exists between school size and student achievement in English/language
arts and mathematics.
Purpose and Research Questions
In a large number of studies nationally, SES has been demonstrated (Friedkin &
Necochea, 1998; O’Hare, 1988; Howley & Bickel, 2000; McMillen, 2004; Sirin, 2005;
Weber, 2005; Archibald, 2006) to be a predictor of student achievement. Further, in ten
6
South Carolina studies which focused on school size and student achievement, SES was
found to be a significant contributing variable (Stevenson, 1996; Durbin, 2001; Roberts,
2002; Gettys, 2003; Crenshaw, 2003; McCathern, 2004; White, 2005; Carpenter, 2006;
Kaczor, 2006; and Maxey, 2008). In Roberts’ (2002) study, he stated: “Over 70% of the
variation in percentage of students scoring basic or above in English/language arts
(reading) and math on PACT could be related to SES (percent of students in poverty)” (p.
78). Carpenter’s study (2006) similarly found that 63% of the variance in
English/language arts performance and 60% in mathematics performance were
associated with school socioeconomic status (p. 85).
In 2006, Stevenson analyzed multiple South Carolina state-wide studies that
measured school size and student achievement. As a result of his research, Stevenson
ascertained that poverty was such a significant variable related to student achievement
and school success, that he raised two questions: “With poverty level of the student
body accounting for as much as three-fourths of the variability in academic outcomes
and school climate among schools, can the real effects of school size and other variables
be adequately identified at this point in time” and “with student attendance and
teacher performance as possible predictors, would school size be a predictive factor in
student performance and school climate if the effects of poverty could be controlled”
(p. 6)?
One purpose of this study is to complement and add to the research by
Carpenter (2006) on school size and student achievement in South Carolina public
elementary schools while controlling for poverty. The study applies a similar
7
methodology for controlling for the effects of poverty that Kaczor used in her 2006
study. The researcher attempts to answer two questions: One, does a relationship exist
between student achievement and school size while controlling for poverty?
Two, this study seeks to determine does one variable, or a combination of
variables, from the literature predict student achievement? This study utilizes SES and
school size as well as many variables obtained from the South Carolina Department of
Education (SC DOE) 2008 Annual School Report Card. The researcher controls for SES by
grouping the public elementary schools in South Carolina into strata based on poverty
index.
The South Carolina Education Accountability Act of 1998 established a
performance-based accountability system based on academic achievement standards
and the assessment of those standards for schools (South Carolina Education Oversight
Committee, 2008). Additionally, the SC DOE Annual School Report Card was determined
to be the means by which the public would be informed of the effectiveness of each
school in improving student achievement. The purpose of the SC DOE Annual School
Report Card was to assist schools in providing “specific resources to improve student
performance and teacher and staff development and assistance and to provide for the
implementation and oversight [of schools]” (South Carolina Education Oversight
Committee, 2008, p.2). The SC DOE Annual School Report Card includes state
assessment data from the Palmetto Achievement Challenge Test (PACT) for grades 3-8.
The data are presented holistically as well as in disaggregated form. Other demographic
data for each school are provided on the SC DOE Annual School Report Card, such as
8
school size, student attendance rate, teacher attendance rate, retention rate of
students, and per pupil expenditure. The variables are discussed at length in a
subsequent section.
Earlier data provided in the SC DOE Annual School Report Card were used in
Roberts’ (2002) study, which assessed relationships between middle school size and
student achievement. This study was followed by Gettys’ (2003) research, which
utilized the same data to identify the relationships of school size and school climate
factors at middle school level. Kaczor’s study (2006) measured the relationship of
school size on student achievement and school climate, with school climate defined by
nine variables from the 2004 SC DOE Annual School Report Card. Finally, Carpenter’s
study (2006) utilized the variables of school size, poverty, and school per pupil cost
expenditure found on the 2005 SC DOE Annual School Report Card for each school
state-wide.
Since SC DOE Annual School Report Card data are available and deemed
important by both South Carolina legislature and the federal government through No
Child Left Behind Act, this study utilized the 2008 SC DOE Annual School Report Card
data. Student achievement in English/language arts, mathematics, science, social
studies in aggregate and disaggregate form were obtained from the 2008 Elementary
School Performance Data File. The following variables were identified in the 2008
Elementary School Performance Fact File:
1.
2.
3.
4.
Poverty index
School size or average daily membership
First graders that attended full-day kindergarten
Retention rate
9
5. Student attendance rate
6. Eligible for gifted and talented
7. Percent objectives met
8. Students with disabilities other than speech
9. Students older than usual for grade
10. Suspended or expelled
11. Number of teachers with advanced degrees
12. Continuing contract teachers
13. Classes not taught by highly qualified teachers
14. Teachers with emergency or provisional certificates
15. Teachers returning from the previous school year
16. Teacher attendance rate
17. Average teacher salary
18. Professional development days per teacher
19. Principal’s or director’s years at the schools
20. Student-teacher ratio
21. Prime instructional time
22. Dollars spent per student
23. Spent on teacher salaries
24. Opportunities in the arts
25. Parents attending conferences
26. SACS accreditation
27. Portable Classrooms
28. Percent of teachers satisfied with the learning environment
29. Percent of students satisfied with the learning environment
30. Percent of parents satisfied with the learning environment
31. Percent of teachers satisfied with social and physical environment
32. Percent of students satisfied with social and physical environment
33. Percent of parents satisfied with social and physical environment
34. Percent of teachers satisfied with home-school relations
35. Percent of students satisfied with home-school relations
36. Percent of parents satisfied with home-school relations
37. Vacancies for more than nine weeks
38. Character development program
39. Percent of expenditures for instruction
The next section addresses each of the major variables and the research that
supports the inclusion of the variables in this study.
10
Poverty
In research studies measuring the effect of school size on student achievement,
the necessity to control SES is documented by researchers such as Crenshaw (2003);
Durbin (2001); Friedkin and Necochea (1998); Howley, Strange, and Bickel (2000);
Howley and Bickel (1999); O’Hare (1988); Roberts (2002); Howley and Howley (2004);
Kaczor (2006); and Carpenter (2006). Howley and Howley (2004) found: “(1) smaller
school size confers an achievement advantage on all but the highest-SES students, (2)
smaller size mediates the powerful association between SES and achievement, (3) the
relationship between school size and achievement is predominantly linear, and (4) size
effects are at least as robust in rural schools as compared with schools overall”(p. 26).
Carpenter’s (2006) found that poverty accounted for 63% variability in English/language
arts scores and 60% mathematics scores across public elementary schools in South
Carolina.
Archibald (2006) found “at the school level, school size and school-level poverty
had negative, statistically significant impacts on both math and reading” (p. 34). Further,
Archibald (2006) stated:
After accounting for all of the socioeconomic and prior achievement indicators at
the student level, and controlling for teacher background characteristics, the
results show that other factors at the school level play a significant role in
determining how a student performs on a standardized test. These contextual
effects, strongest for school-level poverty, have a statistically significant,
negative effect of similar magnitude for both reading and math. This provides
11
further evidence that school poverty concentration affects students’
opportunities to learn. (p. 34)
Sirin (2005) conducted a meta-analysis of studies conducted on SES and student
achievement published between 1990 and 2000. Sirin determined that a “medium level
of association between SES and academic achievement at the student level and a large
degree of association at the school level” (p. 447). His research also concluded, “of all
the factors examined in the meta-analytic literature, family SES at the student level is
one of the strongest correlates of academic performance. At the school level, the
correlations were even stronger” (p. 447). Since SES is such a high predictor of student
achievement, it is necessary to include SES as a variable and attempt to neutralize its
affect.
School Climate
School climate is defined as a cluster of variables presented on the SC DOE
Annual School Report Card. Kaczor (2006) utilized the following variables as school
climate indicators in her study: teachers satisfied with the learning environment;
students satisfied with the learning environment; parents satisfied with the learning
environment; teachers satisfied with social and physical environment; students satisfied
with social and physical environment; parents satisfied with social and physical
environment; teachers satisfied with home-school relations; students satisfied with
home-school relations; and parents satisfied with home-school relations.
Three different but similar definitions exist regarding school climate. Hoy and
Miskel (2004) define school climate as “the set of internal characteristics that
12
distinguishes one school from another and influences the behavior of its members is the
organizational climate of the school” (p. 221). Owens (2001) defines school climate as
the “perceptions of persons in the organization that reflect those norms, assumptions,
and beliefs” (p. 81). Finally, Johnson (2003) defines school climate as related to the SC
DOE Annual School Report Card indicators of school performance. He identifies student
and teacher morale, attendance, school environment, and educational programs as
those indicators.
MacIntosh (1988) researched the dimensions and determinants of the social
climate at schools with grades, 7, 8, and 9. He determined that school climate and
satisfaction were positively affected if students felt they were supported academically.
School climate variables are considered an outcome of other variables; however, as a
set of variables, school climate may be a predictor of student achievement. Thus,
climate is included.
Per Pupil Expenditure
Conant (1967) sought to determine whether the size of the school makes it
profitable as well as academically successful. In school size research conducted in South
Carolina by Durbin (2001) and Carpenter (2006), the variables of percent of expenditure
and per pupil operating costs derived from the SC DOE Annual School Report Card did
not prove to be predictors of student achievement. Durbin’s study measured high
school size, student achievement, and per pupil expenditure in South Carolina. In
Carpenter’s study, he measured elementary school size, student achievement, and per
pupil expenditure. Both researchers concluded that there was no statistically significant
13
relationship when measuring student achievement and the cost of instruction per child.
The variables of percent of expenditure for instruction and per pupil cost or dollars
spent per student are available for this study and may act as a predictor of student
achievement.
Teacher Performance
Archibald’s study (2006) concluded that “teacher performance as measured in a
standards-based teacher evaluation system is positively related to student
achievement” (p. 35). Since the variable is identified in the literature, it is used in this
study. For the purposes of this study, the researcher uses the following variables
considered teacher performance variables to measure if one or more are a predictor of
student achievement: number of teachers with advanced degrees, continuing contract
teachers, classes not taught by highly qualified teachers, teachers with emergency or
provisional certificates, teachers returning from the previous school year, and
professional development days per teacher.
School Size
Numerous studies have been conducted on school size and student achievement
with regard to output variables beginning with Friedkin and Necochea’s study in
California in 1988. Howley and Bickel (1999) followed Friedkin and Necochea’s study
with their own studies on school size and student achievement in Alaska and California.
Following these two studies, they conducted further studies in West Virginia, Montana,
Georgia, Ohio, and Texas, collectively known as The Matthew Project. The researchers
14
concluded that a strong equity effect of small size existed, which was consistent with
the research done by Friedkin and Necochea.
McMillen (2004) analyzed North Carolina grades 2 through 11. The results of the
researcher were:
At the elementary and middle school levels, school size was related to
achievement but only through interactions with students’ prior level of
achievement. Students who were scoring on grade level in reading and
mathematics in the baseline year tended to score higher two years later if they
attended larger schools, whereas students who were scoring below grade level
in the baseline year demonstrated slightly lower performance two years later if
they attended larger schools. These effects were somewhat stronger in middle
school than in elementary school. At the high school level, size was positively
related to both reading and mathematics achievement in the overall sample. (p.
18)
Weber (2005) studied class size, student achievement, and poverty in California.
Weber’s research demonstrated that as class size increased, student achievement
decreased. In rural schools, this occurred at an increased rate.
In South Carolina, ten studies have been conducted on school size and student
achievement by Stevenson and his doctoral students (Durbin, 2001; Stevenson, 2001;
Roberts, 2002; Gettys, 2003; Crenshaw, 2003; McCathern, 2004; White, 2005;
Carpenter, 2006; Kaczor, 2006 and Maxey, 2008). Each of the studies revealed that
school size showed a limited relationship or no relationship to student achievement
15
when neutralizing for the effects of SES. Since school size continues to be studied as a
possible predictor, this study includes it as well.
Student Attendance Rate
Student attendance rate is a variable identified on the SC DOE Annual School
Report Card. This variable has been utilized in research to ascertain whether it is a
variable that predicts student achievement. In a study conducted by Caldas in 1993, the
researcher concluded that student attendance rate was the single most significant
variable which schools could manipulate to affect student achievement in a positive
manner. The results of Daugherty’s study (2008) showed that:
The higher the percentage average of absenteeism the lower the student
performance average. Eighth and tenth grade math mean scale scores fall below
the state proficiency level when students miss sixteen or more days of school. In
reading, both eighth and tenth grades mean scale scores fall below the state
proficiency levels when students miss seventeen or more days of school. This
study also indicated student categories had a relationship with student
achievement, scale scores and daily attendance. (p. 109)
Based on this research, student attendance rate is found to be a variable that
may be a predictor of student achievement and is included in this study.
Teacher Attendance Rate
Miller, Murnane, and Willett (2008) conducted a study on teacher attendance
rate. Their research found that:
16
10 additional days of teacher absence reduced student achievement in fourthgrade mathematics by at least 3.2% of a standard deviation, which is large
enough to be of policy relevance. This is especially the case in today’s
accountability system, in which even small differences in achievement will
influence whether schools satisfy the annual yearly progress requirements of the
No Child Left Behind legislation. Moreover, our estimates indicate that 10
additional days of unexpected absences reduce student achievement in
mathematics by more than 10% of a standard deviation. (p. 196)
Since teacher attendance rate has been identified as a possible predictor of student
success, the researcher utilizes this variable in the research.
Remaining Variables
A survey of the literature did not produce prominent research studies that
measure the relationship of student achievement and the following variables: first
graders that attended full-day kindergarten, retention rate, eligible for gifted and
talented, academic plans, students with disabilities other than speech, students older
than usual for grade, suspended or expelled, average teacher salary, principal’s or
director’s years at the school, prime instructional time, spent on teacher salaries, and
parents attending conferences. However, these variables are utilized because these
variables were required on the SC DOE Annual School Report Card and, therefore, may
be potential factors of student achievement.
17
Research Questions
Using Stevenson’s questions (2006), McCathern’s research (2004), and Carpenter’s
research (2006) as a basis for this study, the research questions are as follows:
1. Does a relationship exist between the enrollment of South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and student
achievement in English/language arts and mathematics? Achievement is defined
by the percentage of the third, fourth, and fifth grade students scoring Proficient
and Advanced on the 2007-2008 Palmetto Achievement Challenge Test. Do
results vary when controlling for poverty?
2. Does a relationship exist between the enrollment in South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and student
achievement in English/language arts and mathematics as defined by the results
of the third, fourth, and fifth grade 2007-2008 Palmetto Achievement Challenge
Test scores when schools are grouped by poverty index of schools?
Achievement is defined as the percentage of students scoring Proficient and
Advanced.
3. Can student achievement in South Carolina’s PreKindergarten – 5 or
Kindergarten – 5 public elementary schools in English/language arts and
mathematics as measured by the third, fourth, and fifth grade 2008 Palmetto
Achievement Challenge Test be predicted by at least one, and possibly a
combination, of the following variables:
1. Poverty index
2. School size or average daily membership
18
3. First graders that attended full-day kindergarten
4. Retention rate
5. Student attendance rate
6. Eligible for gifted and talented
7. Percent objectives met
8. Students with disabilities other than speech
9. Students older than usual for grade
10. Suspended or expelled
11. Number of teachers with advanced degrees
12. Continuing contract teachers
13. Classes not taught by highly qualified teachers
14. Teachers with emergency or provisional certificates
15. Teachers returning from the previous school year
16. Teacher attendance rate
17. Average teacher salary
18. Professional development days per teacher
19. Principal’s or director’s years at the schools
20. Student-teacher ratio
21. Prime instructional time
22. Dollars spent per student
23. Spent on teacher salaries
24. Opportunities in the arts
25. Parents attending conferences
26. SACS accreditation
27. Portable classrooms
28. Percent of teachers satisfied with the learning environment
29. Percent of students satisfied with the learning environment
30. Percent of parents satisfied with the learning environment
31. Percent of teachers satisfied with social and physical environment
32. Percent of students satisfied with social and physical environment
33. Percent of parents satisfied with social and physical environment
34. Percent of teachers satisfied with home-school relations
35. Percent of students satisfied with home-school relations
36. Percent of parents satisfied with home-school relations
37. Vacancies for more than nine weeks
38. Character development program
39. Percent of expenditures for instruction
Significance of Study
In an effort to add to the growing body of knowledge of the relationship of
school size and student achievement in elementary schools in South Carolina, this study
19
seeks to complement studies conducted by McCathern (2004) and Carpenter (2006).
The significance and uniqueness of this study are that it measures the effects of size
within bands of schools, with sets being determined by SES of the schools.
A body of contrasting evidence on the effects of school size and student
achievement exists. Hoagland (1995) determined that high schools beyond a certain
size demonstrated a negative relationship in reading achievement, but that school size
did not matter in mathematics or writing. He also determined that students in smaller
schools performed better in reading achievement. The current study seeks to determine
if a relationship exists with one variable or a combination of variables, including school
size and student achievement, when controlling for the effects of SES.
Cotton’s meta-analysis in 1996 and 2001 determined that smaller schools
demonstrated higher academic achievement and better school climates. In 1997, Lee
and Smith conducted at study on school size and student achievement. A major
conclusion of their study is that schools larger than 1,500 or 1,800 have a negative effect
on student achievement. That study helped educators in urban school districts with
large high schools argue that big is not better. Coupled with the evidence provided by
the College Board (2005) that found that “low-income students are significantly less
likely to enter college than students from high-income backgrounds and significantly
less likely to graduate if they do enter” (p. 10), the effect of school size on student
achievement continues to be an important area to research.
A second reason this study is significant is that South Carolina studies at the
elementary level have not examined the effect of school size on student achievement
20
while controlling for SES by banding schools with like poverty indexes. This information
is necessary because policymakers should know what variable or combination of
variables effect student achievement the most to ensure that every student has the
opportunity to succeed. The next section discusses the study’s delimitations by
addressing the variables or factors not addressed in this study.
Delimitations and Limitations of the Study
Delimitations and limitations of the study are as follows. A delimitation of the
study is the researcher used only public elementary schools in South Carolina in 20072008 with grade spans of PreKindergarten – 5 or Kindergarten – 5. Additionally, the use
of only these grade spans reduces the possibility of uncontrolled variables, which may
occur in the limited public elementary school grade spans found in South Carolina like K
– 3, 4 – 6, or other less traditional grade span configurations. The data set were used
because the data are provided by the South Carolina Department of Education, which
assumes it to be reliable and valid. The data are also available to the public, which
allows ease of access. The results of the study may not generalize elsewhere. Schools
were not excluded if they had students with Individualized Education Plans.
The Palmetto Achievement Challenge Test (PACT) data utilized is the most recent
data from the 2007-2008 school year and other measures might produce different
results. PACT is a norm-referenced and a criterion-referenced test created for students
in South Carolina based on the South Carolina Curriculum Standards. The data are
required by state law to be publicly made available because they are used to report
21
adequate yearly progress on the South Carolina Department of Education Annual School
Report Card.
One method for controlling the effects of poverty index for each of the
PreKindergarten – 5 and Kindergarten – 5 public elementary schools in South Carolina in
this study was through the utilization of “banding” the schools by the SC DOE variable
poverty index. A delimitation utilizing the poverty index strata is no natural groupings
developed when the variables poverty index and school size were applied to a
scatterplot. Therefore, the schools were arbitrarily placed into strata with
approximately the same number of schools within each strata. Seven poverty index
bands were created; however, it may be argued that any number of poverty index
bands could have been utilized in this study.
Schools were sorted by poverty index into bands, or strata, of 0% - 49%, 50% 59%, 60% - 69%, 70% - 79%, 80% - 89%, 90% - 94%, and 95% - 100%. For the statistical
purposes of ensuring a valid sample size, each poverty index band contains
approximately the same number of schools. The number of schools in each band is as
follows: 0% - 49% (63 schools); 50% - 59% (48 schools); 60% - 69% (73 schools); 70% 79% (71 school); 80% - 89% (75 schools); 90% - 94% (54 schools); 95% - 100% (57
schools).
The arbitrary placement caused three unique poverty index strata: one poverty
index strata with schools ranging from 0% to 49%, one poverty index strata with schools
ranging from 90% - 94%, and finally, one poverty index strata with schools ranging from
95% - 100%. A delimitation of this study due to the three unique poverty index strata, it
22
may be argued that a school with a poverty index of 0% may be significantly different
from a school with a poverty index of 49%, while in contrast, it may be argued that a
school with a poverty index of 90% is not significantly different from a school with a
poverty index of 100%.
Another delimitation the three unique poverty index strata created is an inability
by the researcher to compare the schools with the lowest and highest poverty indexes.
As a result, the researcher cannot ascertain whether any patterns exist that may have
an impact on the results of this study between the schools with a poverty index range of
0% - 10% and 90% - 100%.
A limitation of this study is PACT data are used to measure academic success.
Since PACT is specific to South Carolina, the results of this study may not be
generalizable to other states. Other assessment measures may produce different
results in different states or in different grades.
Another limitation of the study is that there are statistical and design problems
inherent with correlation studies (Garson, 2002). As a result, the reader should
understand that the outcomes from this study are not causal in nature. That is, the
results indicate relationships, but the cause and/or effect cannot be determined.
Overview of the Design of the Study
This study examines the relationship of PreKindergarten – 5 or Kindergarten – 5
public elementary schools size and the academic achievement of students. Many school
districts continue to close small schools and create larger ones for the sake of alleged
cost efficiency and curricular breadth (Howley, 1996). Common justifications for
23
building larger schools and closing smaller ones are administrative and instructional.
The administrative motive is based on the principle of the economy of scale, or the idea
that larger units can use staff and other resources more efficiently.
In research question one, a quantitative format was used to examine the
relationship between the size of public PreKindergarten – 5 or Kindergarten – 5
elementary schools in South Carolina and the third, fourth, and fifth grade achievement
scores of students in English/language arts and mathematics. The 2008 Palmetto
Achievement Challenge Test was used as the basis to measure academic achievement
among students. The independent variable was school size as measured by the total
school enrollment and reported on the 2008 SC DOE Annual School Report Card as
average daily membership on the 135th day of school. The dependent variable was
student achievement as measured by the third, fourth, and fifth grade scores on the
2008 Palmetto Achievement Challenge Test and defined as the percent of students
scoring Proficient and Advanced. The control variable was socioeconomic status (SES) as
determined by the 2008 SC DOE Annual School Report Card and reported as the poverty
index.
In research question two, a quantitative format was used to examine the
relationship between the public PreKindergarten – 5 or Kindergarten – 5 elementary
schools in South Carolina and the third, fourth, and fifth grade achievement scores of
pupils in English/language arts and mathematics. The 2008 Palmetto Achievement
Challenge Test was used as the basis to measure academic achievement among
students, while controlling for the effects of socioeconomic status or poverty.
24
Socioeconomic status, or poverty, was controlled by “banding” the schools by the SC
DOE variable poverty index. Schools were sorted by poverty index into bands of 0% 49%, 50% - 59%, 60% - 69%, 70% - 79%, 80% - 89%, 90% - 94%, and 95% - 100%. Each
poverty index band contains approximately the same number of schools. The number
of schools in each band is as follows: 0% - 49% (63 schools); 50% - 59% (48 schools); 60%
- 69% (73 schools); 70% - 79% (71 school); 80% - 89% (75 schools); 90% - 94% (54
schools); 95% - 100% (57 schools). The poverty index band 0% - 49% contains the 63
schools with a poverty index percentile from 0% to 49%. The poverty index band 50% 59% contains the 48 schools with poverty index percentiles from 50% to 59.9%. The
remaining poverty index bands are sorted similarly.
The independent variable was school size as measured by the total school
enrollment and reported on the 2008 SC DOE Annual School Report Card as average
daily membership on the 135th day of school. The dependent variable was student
achievement as measured by the third, fourth, and fifth grade scores on the 2008
Palmetto Achievement Challenge Test in English/language arts and mathematics and
defined as the percent of students scoring Proficient and Advanced.
In research question three, a quantitative format was used to determine
whether student achievement in public PreKindergarten – 5 or Kindergarten – 5
elementary schools in South Carolina in English/language arts and mathematics as
measured by the third, fourth, and fifth grade 2008 Palmetto Achievement Challenge
Test can be predicted by one, or a multitude, of the following independent variables:
student achievement in English/language arts, mathematics, poverty index, school size
25
or average daily membership, first graders that attended full-day kindergarten,
retention rate, student attendance rate, eligible for gifted and talented, percent
objectives met, students with disabilities other than speech, students older than usual
for grade, suspended or expelled, number of teachers with advanced degrees,
continuing contract teachers, classes not taught by highly qualified teachers, teachers
with emergency or provisional certificates, teachers returning from the previous school
year, teacher attendance rate, average teacher salary, professional development days
per teacher, principal’s or director’s years at the schools, student-teacher ratio, prime
instructional time, dollars spent per student, spent on teacher salaries, opportunities in
the arts, parents attending conferences, SACS accreditation, portable classrooms,
percent of teachers satisfied with the learning environment, percent of students
satisfied with the learning environment, percent of parents satisfied with the learning
environment, percent of teachers satisfied with social and physical environment,
percent of students satisfied with social and physical environment, percent of parents
satisfied with social and physical environment, percent of teachers satisfied with homeschool relations, percent of students satisfied with home-school relations, percent of
parents satisfied with home-school relations, vacancies for more than nine weeks,
character development program, and percent of expenditures for instruction.
The dependent variable was student achievement as measured by the 2008
Palmetto Achievement Challenge Test data. Student achievement is defined as the
percentage of students scoring Proficient and Advanced on PACT in English/language
26
arts and mathematics during the 2007-2008 school year. The next section addresses
each of the major variables supported by research.
Concepts, Definitions and Source of Evidence
The following operational terms are defined for the reader.
1. South Carolina public elementary schools: For this study, the researcher defined
South Carolina public elementary schools as elementary schools with grade spans of
PreKindergarten – 5 or Kindergarten – 5.
2. Student achievement: For this study, the researcher defined student achievement as
the Palmetto Achievement Challenge Test (PACT) 2007-2008. The Palmetto
Achievement Challenge Tests (PACT) is a standards-based accountability
measurement of student achievement in four core academic areas –
English/language arts (ELA), mathematics, science, and social studies. The PACT
items are aligned to the South Carolina academic standards developed for each
discipline. An accountability system and a statewide test, such as the PACT, are
mandated by the South Carolina Education Accountability Act of 1998 and the
federal No Child Left Behind Act of 2001 (NCLB). For the purposes of this study, only
PACT English/language arts and mathematics data were used.
3. Poverty bands – For this study, the researcher sorted public elementary schools in
South Carolina into poverty index bands or strata based upon each school’s SC DOE
poverty index. Schools were placed in percentile bands of 0% - 49%, 50% - 59%, 60%
- 69%, 70% - 79%, 80% - 89%, 90% - 94%, and 95% - 100%. Each percentile band
contains approximately the same number of schools. The number of schools in each
band is as follows: 0% - 49% (63 schools); 50% - 59% (48 schools); 60% - 69% (73
schools); 70% - 79% (71 school); 80% - 89% (75 schools); 90% - 94% (54 schools);
95% - 100% (57 schools).
4. Poverty Index (PI) – For this study, the researcher uses the SC DOE definition for
Poverty Index or socioeconomic status (SES): “The poverty index includes both the
student participation of free and reduced-price lunch and the student participation
of Medicaid benefits” (SCSDE, 2004).
5. School size: For this study, the researcher uses the SC DOE definition of school size,
which is the average daily membership (ADM) of the students in a school on 135th
day of the 2007-2008 school year (SCSDE, 2008). This definition was used to assure
consistency determining school size in the sample.
6. First graders that attended full-day kindergarten: For this study, the researcher uses
the SC DOE definition of this variable: “This fact reports the percentage of first
27
graders at the school who participated in full-day kindergarten programs” (SC EOC,
2008, p. C-17).
7. Retention rate: For this study, the researcher uses the SC DOE definition of this
variable: “This indicator reports the percentage of students required to repeat grade
levels because of poor grades, low test scores, and/or teacher judgment in the last
completed school year” (SC EOC, 2008, p. C-27).
8. Student attendance rate: For this study, the researcher uses the SC DOE definition of
this variable: “This indicator reports the average number of students present on
each day” (SC EOC, 2008, p. C-9).
9. Eligible for gifted and talented: For this study, the researcher uses the SC DOE
definition of this variable: “This fact reports the percentage of students who meet
the state guidelines for receiving gifted and talented services” (SC EOC, 2008, p. C17).
10. Percent Objectives Met: For this study, the researcher uses the SC DOE definition of
this variable: “This indicator reports the percentage of the No Child Left Behind Act
adequate yearly progress objectives for the school that were met” (SC EOC, 2008, p.
A-9).
11. Students with disabilities other than speech: For this study, the researcher uses the
SC DOE definition of this variable: “The percentage of students qualifying under the
Individuals with Disabilities Education Act (IDEA) and receiving services in programs
for students with disabilities (excluding students receiving speech services only)” (SC
EOC, 2008, p. C-12).
12. Students older than usual for grade: For this study, the researcher uses the SC DOE
definition of this variable: “This fact provides information on the percentage of
students who are two or more years over age for grade” (SC EOC, 2008, p. C-21).
13. Suspended or expelled: For this study, the researcher uses the SC DOE definition of
this variable: “This fact provides information on the percentage of out-of-school
suspensions and expulsions for physical violence and/or criminal offenses” (SC EOC,
2008, p. C-28).
14. Teachers with advanced degrees: For this study, the researcher uses the SC DOE
definition of this variable: “This indicator reports the percentage of teachers with
earned degrees above the bachelor’s” (SC EOC, 2008, p. C-7).
15. Continuing contract teachers: For this study, the researcher uses the SC DOE
definition of this variable: “This indicator reports on the percentage of teachers in
the school/district with continuing contract status” (SC EOC, 2008, p. C-12).
28
16. Classes not taught by highly qualified teachers: For this study, the researcher uses
the SC DOE definition of this variable: “This indicator reports on the percentage of
teachers in the school/district that do not have highly qualified status” (SC EOC,
2008, p. C-12).
17. Teachers with emergency or provisional certificates: For this study, the researcher
uses the SC DOE definition of this variable: “This indicator reports the percentage of
teachers who do not have full teaching certification” (SC EOC, 2008, p. C-30).
18. Teachers returning from the previous school year: For this study, the researcher uses
the SC DOE definition of this variable: “This indicator provides information on the
percentage of classroom teachers returning to the school/district from the previous
school year for a three-year period” (SC EOC, 2008, p. C-30).
19. Teacher attendance rate: For this study, the researcher uses the SC DOE definition of
this variable: “This indicator reports the average percentage of teachers present on
each school day” (SC EOC, 2008, p. C-9).
20. Average teacher salary: For this study, the researcher uses the SC DOE definition of
this variable: “This indicator reports the average salary of teachers at the school.
This average is compared to the state average teacher salary on the school report
card” (SC EOC, 2008, p. C-10).
21. Professional development days per teacher: For this study, the researcher uses the
SC DOE definition of this variable: “This indicator reports the average number of
professional development days per teacher” (SC EOC, 2008, p. C-25).
22. Principal’s or director’s years at the schools: For this study, the researcher uses the
SC DOE definition of this variable: “This fact reports the length of time that the
principal or director has been assigned to the school or center as a principal or
director” (SC EOC, 2008, p. C-24).
23. Student-Teacher Ratio: For this study, the researcher uses the SC DOE definition of
this variable: “This fact reports the average student-teacher ratio for /language arts
and mathematics” (SC EOC, 2008, p. C-24).
24. Prime instructional time: For this study, the researcher uses the SC DOE definition of
this variable: “This indicator provides information on the percentage of instructional
time available when both teachers and students are present” (SC EOC, 2008, p. C24).
25. Dollars spent per student: For this study, the researcher uses the SC DOE definition
of this variable: “This indicator reports the federal, state, and district funds spent for
29
the education of each student during the most recent school year” (SC EOC, 2008, p.
C-13).
26. Spent on teacher salaries: For this study, the researcher uses the SC DOE definition
of this variable: “This fact provides information on the percentage of per student
expenditures spent on teacher, instructional assistant, and substitute salaries” (SC
EOC, 2008, p. C-16).
27. Opportunities in the Arts: For this study, the researcher uses the SC DOE definition
of this variable: “The number of arts disciplines offered in a school and the
percentage of arts classes taught by teachers certified in the arts discipline (music,
visual art, drama, dance)” (SC EOC, 2008, C-8).
28. Parents attending conferences: For this study, the researcher uses the SC DOE
definition of this variable: “The percentage of students in the school whose
parents/guardians participate in or attended an individual parent conference and/or
an academic plan conference. Conferences include face-to-face, telephone, and
two-way e-mail conferences” (SC EOC, 2008, p. C-22).
29. Southern Association of Colleges and Schools (SACS) Accreditation: For this study,
the researcher uses the SC DOE definition of this variable: “School Report Card:
School is/is not accredited by the Southern Association of Colleges and Schools” (SC
EOC, 2008, p. C-4).
30. Portable Classrooms: For this study, the researcher uses the SC DOE definition of this
variable: “This fact reports the number of portable (relocatable units) classrooms
(shown as a percentage of the total classrooms)” (SC EOC, 2008, p. C-26).
31. Percent of teachers satisfied with the learning environment: For this study, the
researcher uses the SC DOE definition of this variable: “survey response taken from
the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
32. Percent of students satisfied with the learning environment: For this study, the
researcher uses the SC DOE definition of this variable: “survey response taken from
the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
33. Percent of parents satisfied with the learning environment: For this study, the
researcher uses the SC DOE definition of this variable: “survey response taken from
the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
34. Percent of teachers satisfied with social and physical environment: For this study,
the researcher uses the SC DOE definition of this variable: “survey response taken
from the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
30
35. Percent of students satisfied with social and physical environment: For this study,
the researcher uses the SC DOE definition of this variable: “survey response taken
from the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
36. Percent of parents satisfied with social and physical environment: For this study, the
researcher uses the SC DOE definition of this variable: “survey response taken from
the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
37. Percent of teachers satisfied with home-school relations: For this study, the
researcher uses the SC DOE definition of this variable: “survey response taken from
the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
38. Percent of students satisfied with home-school relations: For this study, the
researcher uses the SC DOE definition of this variable: “survey response taken from
the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
39. Percent of parents satisfied with home-school relations: For this study, the
researcher uses the SC DOE definition of this variable: “survey response taken from
the 2008 SCSDE Annual School Report Card” (SC SDE, 2008).
40. Vacancies for more than nine weeks: For this study, the researcher uses the SC DOE
definition of this variable: “This indicator reports the percentage of teaching
positions that remain unfilled for more than nine weeks” (SC EOC, 2008, p. C-26).
41. Character Development Program: For this study, the researcher uses the SC DOE
definition of this variable: “The character development of students and staff in the
school is measured using a rubric developed by the S.C. Character Education
Partnership Team” (SC EOC, 2008, p. C-10).
42. Percent of expenditures for instruction: For this study, the researcher uses the SC
DOE definition of this variable: “This fact reports the percentage of school district
funding expended on classroom instruction” (SC EOC, 2008, p. C-22).
Conceptual Framework
Howley and Bickel (2000) postulate that school size influence varies by SES level,
with school size exerting a negative influence on student achievement in impoverished
schools, but a positive influence on student achievement in affluent schools. All else
equal, larger school size benefits student achievement in affluent communities, but it is
detrimental in impoverished communities. The current study is intended to test that
31
theory using a sample of schools in South Carolina divided into poverty index strata. At
the same time, the current study seeks to determine whether a single explanatory
variable, or a combination of variables, may explain the complex task of improving
student achievement.
Summary
The purpose of this study is to add to the body of knowledge regarding school
size and student achievement. The study seeks to determine if a relationship exists
between student achievement and school size while controlling for SES. The study also
seeks to determine whether a variable or combination of variables predicts student
achievement when controlling for SES.
Chapter I of this study has provided the foundation for the nature and scope of
student achievement and school size in PreKindergarten – 5 or Kindergarten – 5 public
elementary schools in South Carolina. Chapter II consists of the review of the literature.
It is presented in two parts: the history of the school size debate nationally and in the
state of South Carolina and the most recent literature on student achievement and
school size. Chapter III presents an overview of the design of the study. Chapter IV
defines the research questions and presents the outcome of the statistical analyses.
Chapter V offers a summary of the study and recommendations.
32
CHAPTER II
Review of the Literature
Various researchers began to publish opposing positions on school size and
student achievement in the early 1900’s and it continues today. This chapter provides a
comprehensive review of the history of the research on school size and student
achievement from a national perspective. A historical review of research on school size
and student achievement conducted in South Carolina follows. The chapter concludes
with research studies conducted on variables found in the South Carolina Department of
Education Annual School Report Card.
History of the Research on School Size and Student Achievement
Schooling during the mid-1800s was typically in a one-room, one-teacher, multigrade level format operated in rural settings (Tyack, 1974). Often, the schoolhouse was
the center for the community activities: school, church, political forums, and social
gatherings (Hampel, 2002a). Attendance was voluntary and largely depended on the
weather, or the season, with students staying home and working on the farms as
needed (Tyack, 1974).
In 1848, John Philbrick initiated a reform movement for the consolidation of
small, one room schools into larger schools with multiple grade levels. Also, he
33
developed a grading system for student work that still is largely used in most schools in
the nation. By consolidating the one-room, multi-grade level schools into one larger
school, teachers could teach a grade level, decrease the amount of subject preparations
and potentially increase the proficiency for students academically (Tyack, 1974).
In 1911, Frank Spaulding, a school superintendent, applied an efficiency model
that suggested that a school’s effectiveness could be determined based on measurable
products exemplified by available data (Callahan, 1962). During this time, many
associated the productivity of school systems and businesses as the same. The
efficiency model was applied to determine school effectiveness. The measure of
efficiency was based on cost-benefit analyses. The result of applying the efficiency
model to schools using cost-benefit analysis was the determination that small schools
were costly and inefficient (Tyack, 1974). As a result, educational reformers became
consumed with the idea of schools becoming more efficient. The one-room, multigrade level schools came under scrutiny and criticism became rampant that the schools
were too small to be cost-effective; equipment and supplies were too expensive, and it
would be difficult to provide adequate salaries and benefits to hire and retain good
teachers (Howley & Eckman, 1997).
Spaulding’s efficiency model stimulated a greater reform effort to
professionalize education. Reformers supported the notion that professional educators
were the more logical leaders of the management of the consolidated schools and
subsequent school district. The reformers still based their school management beliefs
on the business principles of economy of scale. This belief was resisted in the rural
34
areas where schools were still the hub of the community (Tyack, 1974). State
governments, in an effort to entice rural schools to consolidate, offered fiscal incentives
or unilaterally mandated consolidation by redrawing district boundaries (Hooker &
Mueller, 1970; Strang, 1987).
The number of public schools peaked at 217,000 in 1920 and then declined in
number rapidly until slowing in the 1970s (Berry & West, 2005). Cotton (1996)
attributes the decline to the following:
(a) a commitment to efficiency, progress, and modernization, (b) a belief that
larger schools can produce the U.S. scientists needed to surpass the Soviet space
satellite Sputnik, (c) that the 1960s desegregation and entitlement programs
resulted in school mergers, and (d) that James Conant argued in his 1959 book,
The American High School, that secondary schools needed at least 100 students
in a class to allow the school to offer a sufficiently varied and large curriculum
and to be cost effective. (p. 27)
Allen (2002) argues that successive waves of immigration, especially after World
War II, led to larger urban schools being created to accommodate the increasing
population. Hampel (2002a) identified five beliefs held to be true by educators during
the 20th century:
Larger schools were better able to provide the organization necessary to track
students appropriately to maximize their education. Space and equipment are
more readily available in larger schools which allows for greater curricular and
extracurricular opportunities. Larger schools are more professionally attractive,
35
drawing in better teachers and administrators. The association made between
small schools and rural schools led most to infer that small school reflected the
same provincial values considered out-dated in rural schools. And, class size
mattered more than school size because that is where the learning actually
occurred. (p. 28)
Howley and Bickel (2002) and Wasley (2002) assert the economy of scale model
in which more ‘units’ produced in a single ‘house’ leads to cost efficiency was applied to
public schools. James Conant (1959) believed that putting more students in each school
would put less of a drain on community resources. He made this assertion in his book
The American High School, in which the former Harvard University president reported
on a nationwide survey of 2,000 high schools (Allen, 2002).
Conant’s influence, and the growing emphasis on the economy of scale model
for schooling, caused a national movement of consolidation of schools and districts. The
number of students attending public schools from 1929 to 1969 doubled, rising from
approximately 21 to 42 million students (Berry &West, 2005). By 1970, the average
daily attendance per school increased from 87 to 440 students (Berry &West, 2005).
School consolidation was part of a greater school reform movement. From 1930 to
1970, the school year grew longer, class sizes decrease, and teacher salaries increased.
The average cost for funding public education increased by more than 100% from 1920
to 1950. By the 1970s, schools had been transformed from one-room, multi-grade level
entities to business-like organizations, which emphasized cost-effectiveness and
curricular variety in large schools (Berry &West, 2005).
36
Research on larger school size and economies of scale began to provide
contradictory and inconclusive results. For example, Coleman conducted a study in
1966 in which he found that as school size increased, student achievement increased.
However, Riew (1966), using operating expenditure data on districts with a single high
school, concluded that beyond an enrollment of 900, the existence of economies of
scale is unclear (Stiefel, Schwartz, Iatorola, & Chellman, 2008). Further, Kiesling (1967)
found that as school size increases, student achievement decreases. At the same time,
Burkehead, Fox, and Holland (1967) found no statistically significant relationship
between school size and student test scores.
A significant study was conducted by Turner and Thrasher in 1970. Their
research indicated that increasing school size initially results in a decrease in per pupil
expenditures, which supports the economy of scale principles. However, Turner and
Thrasher found that increases beyond 1,000 students were unlikely to result in further
gains. Their research concluded that optimal school size for the economy of scale was
at 1,000 students. The researchers also discovered that other outcome measures
appeared to demonstrate school size optimization between 300 and 500 students.
These outcome variables were affected by the socioeconomic status (SES) of the student
body. Turner and Thrasher summarized that optimal school size could not be
determined by one number, but must be determined by the range in which increased
school size has a beneficial effect on both expenditures and educational outcomes for a
particular school (Turner & Thrasher, 1970).
37
Though research conducted during the late 1960s and early 1970s demonstrated
no clear indication that the economy of scale model was the best system for educating
students, the business principles were firmly entrenched as the correct way to run
schools. The idea of efficiency became ensconced in the notion that funds were not
being used effectively if the product was not up to par. Howley (1989) summarized the
history of research into school size from the early 20th century to the beginning of the
21st century: “Research from the 1960s, 1970s, and 1980s generally favored increasing
school size when the research was based on input variables and concentrated on
economies of scale” (p. 2). However, the focus on school size changed to output
variables such as student achievement in the early 1980s. Once this occurred, the
recommendation to increase school size was not justified (Howley, 1994).
The next section provides a chronological review of national studies that focused
on school size and student achievement beginning in the early 1980s. Howley (1994)
suggests, as noted above, that during this time period, researchers’ studies on school
size and student achievement transitions from a focus on input variables to output
variables.
National Studies on School Size
Research conducted on school size and student achievement focused primarily
on input variables prior to 1988. The measure of effectiveness of schools was based on
the economy of scales principles utilized by businesses (Callahan, 1962). During the
1980s, the focus of research studies on school size and student achievement shifted
from input variables to output variables. The following section presents studies on
38
school size and student achievement in chronological order which demonstrates the
change in focus by researchers towards output variables.
Riew conducted a study on schools focused on the economies of scale principle
in 1966. This researcher found declining costs in middle schools with enrollments as
large as 1,024. However, in a twist from previous studies which focused on economies
of scale, the elementary school level portion of the study produced the lowest costs in
schools with 200-400 enrolled students.
Eberts, Kehoe, and Stone conducted a study in 1984 on a nationwide sample of
more than 300 elementary schools. The researchers found that the differences in
student achievement in mathematics between small schools (less than 200 students)
and medium schools (200-800 students) are not significant. The significant difference
was apparent between small schools and large schools (more than 800 students) with
large schools demonstrating higher student achievement than the small schools.
A study that had a major effect on the school size debate was one conducted by
Friedkin and Necochea in 1988. Friedkin and Necochea studied students in the 3rd, 6th,
8th, and 12th grades in all California schools. The researchers discovered that large
schools were associated with greater achievement for 12th grade students, but small
schools were associated with greater achievement for students in the 3rd, 6th, and 8th
grades. This study was the first truly comprehensive study of school size as it related to
student achievement. On a statewide data sample of 6th, 8th, and 12th grade scores on
the 1983-84 California Assessment Program the researchers’ examination was
significant because the researchers found that both school size and school district size
39
were important for student achievement. Specifically, students from economically
disadvantaged families benefited from education in a small school, especially if that
small school was in a small school district. Further discussion on the importance of this
study will follow in the section entitled “The Matthew Project.”
Plecki (1991) conducted a study that utilized data from 4,337 California
elementary schools in grade level formats of Kindergarten through 6. Plecki conducted
the study to test the relationship among school size, student socioeconomic status,
school setting, student characteristics, and performance as measured by the California
Assessment Program. The researcher grouped schools into five size categories based on
total school population. Plecki found a negative linear relationship between school size
and student achievement when the school’s population had a high poverty rate. An
important conclusion of her study was that she found no support for increasing school
size for any population of students. Plecki’s study supported Friedkin and Necochea’s
1988 study that school size and poverty affected student achievement.
Fowler and Walberg (1991) studied 293 public high schools in New Jersey to
analyze the relationships between high school size and eighteen different school
outcomes, including student performance on state tests of basic skills and high school
proficiency. The researchers concluded that the economies of scale principle when
applied to large high schools did not work where it mattered most – academic
achievement: “The empirical evidence for cost savings applies only if achievement and
other positive student outcomes are not considered, and the empirical evidence for
curricular offering suggests that small schools are at least competitive, and possibly
40
superior to larger schools” (Fowler & Walberg, 1991, p. 33). This study was important
because it significantly negated the argument that the economies of scale principle
should be the primary focus of school leadership.
Caldas (1993), utilizing student performance data collected by the Louisiana
Department of Education, set out to determine the impact that input and process
factors had on student achievement in Louisiana by using multiple regression analysis
techniques on his data. Caldas’ sample consisted of all 1,301 public schools in Louisiana,
including all elementary, middle, and secondary schools. The performance data, along
with the input and process variables, were collected for the 1989 school year. ACHIEVE
scores for Louisiana public schools, based upon the calculation of z-scores for criterionreferenced tests (administered to students in grades 3, 5, 7, 10, and 11) and normreferenced tests (administered to students in grades 4, 6, and 10), produced one
composite measure of academic achievement for Louisiana public schools.
Caldas (1993) described input factors as those elements affecting student
outcomes over which the school has virtually no control. The input factors he identified
in his study included student ethnicity, socioeconomic status, size of the community
served by the school, and mandatory school attendance laws. Caldas’ results showed
that the process variables having the most significant impact on student achievement
were student attendance rates and small school size, as evidenced in the central city
schools, thus emphasizing that school leaders in urban areas may enhance achievement
by addressing these process factors. For schools in non-central cities, class size had the
most significant impact on student achievement.
41
Still, Caldas (1993) concluded that student attendance rate was the single most
significant variable which schools could manipulate to affect student achievement in a
positive manner. Caldas (1993) stated:
Of those factors examined in this study over which schools and districts do have
some control, the most important by a significant margin was percent student
attendance. This is an encouraging finding because even vigorous efforts to
increase school attendance likely require far fewer resources than either
reducing school sizes (which often require new building construction) or class
sizes (which usually means hiring new teachers). (p. 214)
One of the first efforts by Howley in researching school size and its effect on
student achievement was in 1993, when he and Huang found a positive relationship
between student achievement and school size in Alaskan schools. The researchers
discovered that small schools had lower student achievement success. These results are
consistent with the general trend in the research that the effects of school size are
mediated by SES because small Alaskan secondary schools have very high poverty levels.
Alspaugh (1994) examined the relationship between school size and student
achievement in Missouri. Alspaugh concluded that the critical element for achievement
was the lower student-to-teacher ratio prevalent in the smaller schools. He did note
that smaller schools demonstrated significantly better student achievement.
Lamdin (1995) examined the relationship between school size and student
achievement in Baltimore, Maryland. Using data collected from the 1989 administration
of the California Achievement test (CAT) to all first through fifth grade students in
42
ninety-seven Baltimore, Maryland elementary schools, Lamdin found no statistically
significant contribution of school size to student achievement. The relationship was
always negative, with smaller schools slightly outperforming larger ones.
Socioeconomic status was found to be a significant contributor to student achievement
for each test at every grade level. Lamdin found that the differences in student
achievement between small schools and larger schools favored small schools, but the
difference was not statistically significant.
Hoagland (1995) conducted a study in California in which he controlled for the
effects of socioeconomic status while studying the relationships among reading,
mathematics, and writing performance and school size. The study concluded a negative
relationship between school size and the academic achievement of low income
students. The negative relationship was greatest for reading scores. Hoagland’s
research identified a concern about school size range:
This study clearly suggests concern about relative effectiveness of the very large
high school. Statistically inferior in two-of-nine differential measures, the very
large high school was last or next to last in every achievement measure.
Combined with the cumulative evidence of decades of affective studies, it can be
concluded that the upper end of high school sizes should be seriously
questioned. (For purposes of this study, very large high schools had over five
hundred ‘seniors to be tested’ suggesting a four-year enrollment in excess of
2,500.). (p. 89)
43
The Matthew Project: History and Results
(Researcher’s note: The Matthew Project is a multi-state research study on school size
and student achievement conducted over several years. To assist the reader, the
researcher chose to present The Matthew Project collectively and not in the order the
studies chronologically were conducted.)
As noted earlier, Friedkin and Necochea conducted research in 1988 in which
they studied students in the 3rd, 6th, 8th and 12th grades in all California schools. The
study was a comprehensive study of school size as it related to student achievement.
The researchers examined the 1983-84 California Assessment Program through a
sample of student achievement scores from the 6th, 8th and 12th grades. As a result of
their study, Friedkin and Necochea determined small schools were associated with
greater achievement for students in the 3rd, 6th, and 8th grades. This study was
significant because the researchers found that both school size and school district size
were important for student achievement. Also, the results of the study demonstrated
that low socioeconomic status (SES) students appeared to benefit from education in a
small school, especially if that small school was in a small school district.
Following the Friedkin and Necochea study, Howley and Huang published a study
in 1993. The researchers used data from the fall 1989 administration of the Iowa Test of
Basic Skills statewide in Alaska in grades 4, 6, and 8. They examined the relationships
among district size, school size, and five conditions of disadvantage. They found that
“small schools in Alaska appear to mitigate the effects of disadvantage, whereas large
schools tend to compound those effects” (p. 143). Disadvantaged students attending
44
small schools achieved better than equally disadvantaged students attending large
schools.
From this study, Howley (1995) conducted research in West Virginia which
replicated Friedkin and Nocochea’s (1988) study. In the study, Howley cited Matthew
13:12 from the King James Version of the Bible: “For whosoever hath, to him shall be
given, and he shall have more abundance: but whosoever hath not, from him shall be
taken away even that he hath.” Howley then tied the study to the verse with the
following statement:
This epigraph, revealed two thousand years ago, captures something of how the
world works, the social world certainly, but perhaps also the natural world. For
instance, Jesus’ remarks may allude to the principles related to iterative
processes that are now understood to account for much that natural science
previously found obscure. In these "chaotic" processes small differences in initial
states lead to great differences in final states. But when the differences in initial
social states are great, it should come as no surprise that differences in final
social states can be dramatic. After two millennia, we can say with more
certainty than ever that it takes money to make money, and also, that in this
chaotic process of making money, the rich get richer and the poor get poorer.
(p. 3-4)
The outcome of the West Virginia study produced similar results to the California
study by Friedkin and Necochea (1988). Howley and his colleague Bickel (1999) then
conducted studies in Georgia, Montana, Ohio, and Texas—with nearly identical results.
45
These studies became known at The Matthew Project because of Howley’s reference to
Matthew 13:12.
Howley and Bickel (2000) summarized each study’s findings:
In Ohio:
Between 41% and 90% of schools (depending on grade level tested) would likely
produce "lower" average scores if the schools were larger, or (in these schools)
higher scores if they were smaller. At the ninth grade level, 90% of schools are
too big to maximize achievement. These schools serve 89% of Ohio's ninth
graders. (p. 3)
In Texas:
Between 26% and 57% of schools (depending on grade level tested) would likely
produce lower average student scores if the schools were larger, or higher
scores, if smaller. At the 10th grade level, 57% of the schools are too big to
maximize achievement. These schools serve almost half (46%) of Texas' 10th
graders. (p. 3)
In Georgia:
Between 36 and 68 percent of the schools (depending on grade level tested)
would likely produce lower scores if the schools were larger, or higher scores if
the schools were smaller. At the eighth grade level, 52% of the schools serving
48% of the students are too big to maximize achievement. The percentage of
schools "at risk" in this way (i.e., too large to maximize achievement) is even
greater at the elementary level. (p. 3)
In Montana:
In Montana there is only weak evidence that the effect of school size on the
average academic achievement of students depends on the level of poverty
among the students in the school. The effect was statistically significant only in
grade 4. Montana's unique results are probably due to the fact that its schools
are more uniformly small and income is more evenly distributed than in any of
the other three states. (p. 3-4)
In every state studied, the higher the SES of the community served by a school,
the more student achievement was benefited by smaller schools. Racial composition of
the school had no bearing on this determination; however, schools with higher minority
compositions had higher poverty (Howley & Bickel, 2000).
46
As a result The Matthew Project, Howley and Bickel (2000) hypothesized equity
effects of size as well as excellence effects. Excellence effects of size varied substantially
by state, but like Friedkin and Necochea (1988) and Howley (1996), The Matthew
Project studies found that the influence of size varied by SES level, with size exerting a
negative influence on achievement in impoverished schools, but a positive influence on
achievement in affluent schools. That is, all else equal, larger school size benefits
achievement in affluent communities, but it is detrimental in impoverished
communities.
One outcome of The Matthew Project is that in 48 of the 49 areas of comparison
between small and large schools, the small schools decreased the influence of poverty
over student achievement by between 24% and 90%. In some cases, this left the
student achievement gap at nearly zero. As a result, the results of The Matthew Project
demonstrate the importance of recognizing the effects of poverty on student
achievement. It also creates the need to control for student socioeconomic status in an
effort to determine whether school size is a predictor of student achievement (Howley
& Bickel, 2000).
Lee and Smith's 1997 study of high school size is referenced often in reviews of
school-size literature. Their findings are consistent with those reported in the Friedkin
and Nocechea’s study (1988) and Howley and Bickel’s (1999) The Matthew Project. Lee
and Smith found that in schools with fewer than 301 students, the influence of poverty
was reduced. Lee and Smith also determined that for high schools enrolling 601-900
students, the aggregate achievement (with all else being equal) was highest.
47
The Texas Education Agency (1999) conducted a study that reviewed school size
research conducted nationally, the school size trends in Texas, and the relationship
between school size and student academic performance in Texas. Student academic
performance data obtained from the Texas Assessment of Academic Skills (TAAS).
Analysis of TASS elementary school data revealed that reading and mathematics
performance declined as school size increased. In the middle schools, attendance rates
and TAAS mathematics performance declined as school size increased. When high
school data were analyzed, retention rates increased as school size increased, and
attendance rates and TAAS mathematics performance declined.
Lee and Loeb (2000) studied 6th and 8th graders in 246 Kindergarten-8 schools in
Chicago, Illinois. The sample studied was roughly 5,000 teachers and 23,000 students.
The researchers defined small schools as schools with enrollments under 400, large
schools were defined as schools with enrollments over 750, and middle-sized schools as
those with enrollments between 400 and 750. The researchers concluded that students
from the small schools achieved at levels significantly better statistically than students
from either large or middle-sized schools on the Iowa Test of Basic Skills assessment
administered in 1997. The Iowa Test of Basic Skills is a norm-referenced assessment
that assesses general skills rather than knowledge of specific material.
Roeder (2002) conducted a study of schools in the two largest school districts in
Kentucky. The researcher concluded that school size had no significant relationship to
achievement, when variables for school level (elementary, middle or high) were added
into the prediction equation. The variables the researcher used were school size,
48
poverty, race, and student achievement. Roeder also found that smaller schools did not
negate the negative effects of poverty on student achievement. An important finding
from the study was that for elementary schools, the interaction between socioeconomic
status and grade configuration was significant on three of four measures of
achievement. For elementary students, poverty remained the most significant predictor
of student academic achievement. Roeder (2002) stated the following: “if an important
question for education officials is how to improve performance in large and mediumsized urban/suburban school districts, focusing on school size does not appear to offer
answers” (p. 17). The researcher emphasized the focus on improving student
achievement should be on equity issues and instructional practice.
Abbott, Joireman, and Stroh (2002) conducted a study using data from all 4th and
7th grade students on the Washington Assessment of Student Learning (WASL). The
researchers examined the interactions between and among school size, district size,
WASL scores, and socioeconomic status. While no statistically significant results were
noted in the analysis, the data did indicate some advantage of smaller schools for
students living in poverty. Abbott, Joireman, and Stroh did find statistically significant
relationships among school district size, school size, socioeconomic status, and student
achievement. Student WASL data in small school districts and schools, when analyzed,
revealed less variance than in larger districts and schools. This indicated greater equity
for students from low socioeconomic backgrounds.
McMillen (2004) examined the relationship between school size and
achievement in which he conducted a study using longitudinal achievement data from
49
North Carolina for three separate cohorts of public school students (one elementary,
one middle, and one high school). The study revealed several interactions between size
and student characteristics. These interactions indicated that the achievement gaps
that typically exist between certain subgroups were larger in larger schools. The results
of the study varied across the three grade level cohorts as well as across content areas.
The research did support findings by Howley and his colleagues that the school-level
“equity effects” of size may also translate down to student subgroups within schools
(Howley & Bickel, 2000).
Weber (2005) conducted a study that investigated the association between
grade-level enrollment and student outcomes for all students, economically
disadvantaged students, and English learners. Weber also studied the effects of input
variables like student demographics, teacher qualifications, school characteristics, and
the impact of enrollments on student achievement in schools with increasing
percentages of students receiving free or reduced price lunch. The researcher
attempted to determine the range of grade-level enrollments in California schools in
which achievement may be maximized. The study indicated that size was negatively
associated with achievement in grades six through ten for all students, disadvantaged
students, and English learners. In each school, as the poverty level increased, the
negative effect of size on achievement became greater in the high school grades.
Further, the data revealed that both advantaged and disadvantaged students’
achievement was higher in smaller settings and lower in larger settings in grades five
through eleven.
50
Berry and West (2005) conducted a study using data from the Public-Use MicroSample of the 1980 U.S. census to “estimate the effects of changes in school and district
size on students’ labor market outcomes and educational attainment” (p. 15). The
results of their study indicated:
Students born in states with smaller schools obtained higher returns to
education and completed more years of schooling. While larger districts were
associated with somewhat higher returns to education and increased
educational attainment in most specifications, any gains from consolidation were
outweighed by the harmful effects of larger schools. (p. 18)
Berry and West (2005) concluded that an increase of one standard deviation in
average school size is associated with a decrease of 1.23 standard deviations in the rate
of return to education. For example, increasing a state’s average school size by 145
students, equivalent to the difference in average school size between the median state
in the 1920–29 cohort and the median state in the 1940–49 cohort, is associated with
about a 9% decline in earnings for high school graduates (those with exactly twelve
years of education).
In the same analysis, Berry and West also found:
…a positive effect of large district sizes on students’ adult wages. In other words,
the results suggest that larger schools were detrimental—whereas larger
districts were beneficial—to the return to education. An increase of district size
by 947 students, again the difference in average size between the 1920–29 and
1940–49 median states, is associated with a 2.1 percent increase in earnings for
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high school graduates. However, the findings on district size were not robust
enough to further analytical checks, so we are cautious about putting much
weight on the positive effect of larger districts. (p. 18)
Cartner (2005) conducted a study on the relationship between elementary
school enrollment and fifth-grade achievement data from a large urban Missouri school
district. Thirty-nine elementary schools received uniform allocations of resources from
the district and used the same instructional materials. The schools varied in their
enrollment, socioeconomic status (SES), and student achievement. The thirty-nine
schools were placed into five enrollment groups: less than 200, 200-299, 300-399, 400499, and 500 or more. Stanford 9 NCE reading, mathematics, language, science, and
social science achievement scores were compared for schools within the enrollment
groups. The researcher controlled for SES by using a hierarchical regression analysis.
Cartner found statistically significant differences among the mean levels of achievement
of students in the five school enrollment groups. There was a general decline in
achievement as school enrollments increased, for both the inner-city and suburban
schools. Pearson correlation and hierarchical regression analyses revealed statistically
significant results indicating that 3rd grade students made greater gains in both math
and reading in smaller schools. Though the relationships between the variables
indicated an advantage for 5th grade students in smaller schools, the results were not
statistically significant.
Gilmore (2007) examined whether school size in Texas middle schools bears a
relationship with student academic performance. This study analyzed all ethnic groups
52
combined and discretely for White, African-American, Hispanic, Asian-American, and
Native-American students. The data used were reading and math scores from the Texas
Assessment of Knowledge and Skills (TAKS). The relationships were examined
separately for the 2003, 2004, and 2005 school years. According to the ANOVA results,
in all 3 school years, the data revealed significant differences among the ethnic groups.
The researcher determined that regardless of ethnicity or socioeconomic status,
students earned higher achievement at very large schools when compared to small
schools.
Stiefel, Schwartz, Iatorola, and Chellman (2008) studied New York City schools to
determine the economy of scale. The study revealed that small schools operationally
cost almost 15% less than very small schools; medium size schools were slightly
cheaper; large size schools were nearly 20% cheaper than very small schools and very
large schools were 28% cheaper to operate than very small schools. The researchers’
analysis of their data suggested that direct costs per pupil generally decline with size for
all types of high schools. Based on the researchers’ data, they concluded that it would
cost less per pupil as outputs increase, for example, student achievement.
A summary of these major studies reveals that school size does impact student
achievement and that poverty is a significant variable in this field of research, but
impact varies across studies. The next section is a review of three meta-analyses related
to school size and student achievement which contributes relevant information and
adds to the body of literature reviewed by the researcher.
53
Summary of Meta-Analyses on School Size
Greenwood, Hedges, and Laine (1996) conducted a meta-analysis of sixty
primary studies. The researchers found across the studies that student achievement
was negatively related to school size. Because many of the studies in this analysis had
been conducted in the 1960s, Greenwood, Hedges, and Laine performed a second metaanalysis including only the twenty-six studies that had been conducted since 1970. The
results of this analysis again demonstrated greater student achievement in smaller
schools. The researchers concluded that per student expenditure was positively related
to student achievement. They also determined that a 10% increase in per pupil
expenditures was related to an increase in student achievement of one standard
deviation over twelve years of schooling.
Cotton (2001) conducted an empirical literature review about the effect of small
schools. She determined that students in smaller schools performed at least as well as
students in larger schools. Cotton also found no studies that supported the theory that
students in general perform better in large schools. Cotton reported that many studies
indicated that students of low socioeconomic status (high poverty) and minority
students appeared to benefit from the effects of small school due to the benefits
associated with small schools.
Karen Irmsher (1997) conducted a literature review on the affective reasons
small schools appear to support greater achievement for students of low socioeconomic
status (high poverty). Irmsher found the structure of large schools most effective for
increasing the achievement of high socioeconomic status students. However, the
54
outcome of her literature review found inconsistencies in the student achievement of
large schools with high socioeconomic status that she concluded was due to the
bureaucratic nature of large schools.
The following section of this literature review considers studies conducted in
South Carolina related to school size and its effect on student achievement. Included
are studies that were conducted on elementary schools, middle schools, and high
schools in South Carolina. Some of the studies attempted to ascertain a variable or set
of variables that were predictors of student achievement as well.
South Carolina Studies
In South Carolina, Stevenson initiated a series of studies on school size and its
effect on student achievement. The first study by Stevenson in 1996 concluded that
school size did not matter in South Carolina elementary schools in relationship to
student achievement. Specifically, Stevenson studied South Carolina’s 598 public
elementary schools. To neutralize the effect of poverty, he assigned each of the
elementary schools to one of five categories based upon socioeconomic status.
Category 5 schools were identified as the wealthiest student populations and Category 1
schools were identified as the poorest. Stevenson utilized data provided by the South
Carolina Department of Education as well as the list of South Carolina Association of
Elementary and Middle School Principals (SCAEMSP) Palmetto’s Finest Award winning
schools to ascertain whether a relationship existed between school size and student
achievement.
55
Stevenson’s (1996) research questions focused on the following: 1) the
relationship between elementary school size and the number of times an elementary
school earned a state academic Incentive Award between 1985-1994; 2) the relationship
between the averaged-sized South Carolina elementary school and the size of the
Palmetto’s Finest Award winners; and 3) the relationship between the average-sized
South Carolina elementary school, the size of the Palmetto’s Finest Award winners, and
the size of elementary schools designated by the State Department as “dysfunctional” in
1995 due to their poor performance on standardized achievement tests.
For the first research question, Stevenson (1996) observed an advantage for
wealthier Category 5 schools: “schools serving students in the highest socioeconomic
category tend to win the award slightly more often than schools serving students from
the lowest socioeconomic category” (p. 12). Further, his research determined that the
seven schools that won state Incentive Awards for all ten years were significantly larger
in enrollment than the schools that had never won the award. Stevenson also
concluded that the same seven schools were equally distributed over the five
socioeconomic categories.
The second research question revealed that the Palmetto’s Finest Award winning
schools were larger than the average-sized South Carolina elementary school
(Stevenson, 1996). The mean school size of the Palmetto’s Finest Award winners was
720 students, which was more than 200 students on average greater than the average
enrollment for a South Carolina elementary school. The outcome of the research
conducted for the second research question, Stevenson (1996) determined that
56
“Palmetto’s Finest schools served a substantially larger student population than the
average school in the state. They also have won the state Incentive Award significantly
more often than the typical school” (p. 13).
Stevenson’s third research question revealed that elementary schools classified
by the state as “dysfunctional,” due to their standardized test scores, had mean student
enrollments smaller than the state’s average-sized elementary school. When compared
to the Palmetto’s Finest Award winners’ mean enrollment, the “dysfunctional” schools
were significantly smaller. The summary of Stevenson’s study (1996) is smaller schools
tended to be labeled as “dysfunctional” and the larger schools, in contrast, won more
South Carolina State Incentive Awards and/or Palmetto’s Finest Awards.
Following his 1996 study, Stevenson conducted another study in 2001 for the
South Carolina Education Oversight Committee. In his study, Stevenson (2001)
researched the relationship between size of elementary school populations and student
academic performance. The data Stevenson utilized for this study were the Palmetto
Achievement Challenge Test (PACT) results for the 1999-2000 school year in
English/language arts and mathematics for elementary schools. Stevenson’s purpose
was to determine if a relationship existed between the dependent variables (PACT
scores) and the independent variables of school age, school size, pupil attendance,
teacher attendance, and the principal’s rating of the physical condition and adequacy of
his/her school.
Stevenson (2001) analyzed the data twice. The first analysis demonstrated a
relationship in favor of larger schools, which supported his 1996 study. When
57
Stevenson analyzed the data a second time controlling for poverty, no significant
relationship resulted (Stevenson, 2001). Socioeconomic status was repeatedly a
significant determinant of student academic performance, accounting for almost a 70%
variance in school performance on PACT among fourth and fifth graders in both reading
and math. Student attendance was a factor. However, it was not as significant.
Stevenson noted that the larger percent of children in poverty served by a school, the
fewer the percentage of students who scored proficient or advanced on PACT. In
summary, Stevenson (2001) stated: “The effects of socio-economic status, social class if
you will, are so great and so intertwined with other variables that distinguishing the
impact of facilities factors (like school size) from a strictly statistical perspective is
challenging” (p. 71).
Following Stevenson’s research, several South Carolina studies on school size
and its effect on student achievement ensued. The first of those studies was by Durbin
in 2001. Durbin (2001) explored the relationships among high school size, student
achievement, and per pupil expenditure. Durbin’s study intended to determine if a
relationship existed between the size of South Carolina’s public high schools and
student achievement. Durbin analyzed the data in reading, mathematics, and writing
from 11th graders’ performance on the spring 1998 administration of the Metropolitan
Achievement Test, Seventh Edition (MAT-7). The second focus of Durbin’s research was
whether a relationship existed between the size of South Carolina public high schools
and per pupil expenditure. The last question Durbin examined was whether a
relationship existed among the size of South Carolina public high schools, per pupil
58
expenditure, and student achievement. Due to the large percentage of variance poverty
demonstrated in Stevenson’s (1996, 2001) studies, Durbin controlled for the
socioeconomic status of students in her analysis in each of these three relationships.
The sample for Durbin’s study was 193 South Carolina public high schools.
Durbin (2001) concluded a strong negative relationship existed between the
socioeconomic status of students and academic achievement. Durbin (2001) stated that
her study “yielded results that indicated that more than 74% of the variation of
outcomes was a result of socioeconomic status” (p. 77). Her research also supported
Stevenson’s conclusions in his 1996 study that larger schools in South Carolina tended to
be associated with higher levels of student achievement. This was the case even when
the researcher controlled for socioeconomic status. The final question supported the
data as well, and revealed that the larger schools cost less to operate. An interesting
note is that Durbin determined from her data that the optimum size for a public high
school in South Carolina would be in the range of 1,431 – 2,019 students.
Roberts (2002) conducted his study of middle schools in South Carolina in which
he attempted to determine if a relationship existed between the size of public middle
schools and student academic achievement as evidenced by student performance levels
on the language arts and mathematics portions of the 2001 Palmetto Achievement
Challenge Test (PACT). Second, Roberts explored the relationship between per pupil
expenditures and public middle school size while controlling for the socioeconomic
status of students. Roberts took into account the percentage of students with
disabilities other than speech when he analyzed the data for this research question. The
59
final question examined by Roberts was whether student academic achievement levels
could be predicted by the middle school size and per pupil expenditures while
controlling for the socioeconomic status of students and the percentage of students
with disabilities other than speech. Roberts’ (2002) sample for this study was 156 South
Carolina public middle schools with a grades 6-8 configuration.
As a result of his study, Roberts (2002) discovered that the socioeconomic status
of students accounted for over 70% of the variance in the levels of student achievement
on PACT on the English/language arts and mathematics portions for the 2001 data. He
also found a small negative relationship between the size of public middle schools in
South Carolina and student achievement levels when controlling for socioeconomic
status of students. When Roberts’ analyzed the school size and per pupil expenditures
data, the results revealed that a negative relationship existed. He determined that as
the size of the middle school increased, the level of spending per student decreased
with the socioeconomic status of students. This also was produced when the
percentage of students with disabilities other than speech was controlled.
For the final question regarding academic achievement on PACT for middle
school students based on school size and per pupil expenditures, Roberts found that
middle school size nor per pupil expenditures were a predictor of student achievement.
Important to note, Roberts’ (2002) analysis indicated that larger schools were less
expensive to operate, but smaller schools demonstrated higher levels of student
academic performance. As a result of this finding, Roberts (2002) stated: “Smaller
schools cost more but produce better achievement results (p. 79).”
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A complementary study to Roberts’ (2002) research was conducted by Gettys in
2003. Gettys examined whether a relationship existed between the size of middle
schools and school climate by analyzing the South Carolina Department Of Education (SC
DOE) Annual School Report Card data from 2001. Gettys analyzed the data for the 156
public South Carolina middle schools with a grade configuration of 6-8. The 135th-day
average daily membership figure was the representation for each middle school’s size;
this number served as the independent variable for the study. All of the data were
provided by the South Carolina Department of Education. The dependent variable of
school climate was divided into three areas that included the following:
1) the percent of teachers and students satisfied with the learning environment,
social and physical environment, and home-school relations, 2) the percent of
students who are identified as gifted and talented, on academic plans, suspended or
expelled, and the student level of attendance, and 3) the percent of teacher
returning from the previous year, and the teacher level of attendance. (p. 51-52)
Gettys (2003) controlled for the socioeconomic status in each of the analyses
conducted. Gettys also ran data to determine the relationship of student achievement
to socioeconomic status, the percentage of students with disabilities other than speech,
and per pupil expenditures.
Gettys (2003) concluded from the data that the socioeconomic status (SES) of
the students had the greatest impact on school climate factors. Gettys stated, “At this
time, because of the strong relationship between SES and each of the school climate
variables, as defined in this study, no relationship was found between school size and
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school climate in the public middle schools serving grades 6-8 of South Carolina”
(p.128). Gettys’ study supported Roberts’ (2002) determinations that socioeconomic
status is a significant predictor that affects the outcomes of student achievement in
middle schools in South Carolina.
The results of a study conducted by Crenshaw in 2003 concluded the same as
Roberts (2002) and Gettys (2003) regarding socioeconomic status and its effect as a
predictor of student achievement in schools in South Carolina. Crenshaw’s study was
conducted on high schools in South Carolina. Crenshaw (2003) studied the relationships
among high school size, student achievement, and school climate. Crenshaw, like
Gettys (2003), used SC DOE Annual School Report Card data from 2001. The researcher
analyzed student achievement data for 178 public high schools based upon absolute
report card ratings. Crenshaw examined multiple dependent variables from the SC DOE
Annual School Report Card data to determine school climate: student attendance;
student dropout rates; teacher attendance; teacher stability; and student and teacher
perception of climate. For the independent variable of poverty, or socioeconomic
status, Crenshaw used the South Carolina Department of Education’s poverty index.
She then grouped the high schools by poverty index into two groups: high schools that
fell within the upper 50% of the poverty index, i.e. having less poverty, were classified as
“higher socioeconomic level” schools, while those schools falling in the lower fifth
percent, i.e., having more poverty, were designated as the “lower socioeconomic level”
schools (p. 59).
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The outcome of Crenshaw’s (2003) study revealed no significant relationships
between school size and student achievement. As stated previously, Crenshaw’s results
supported Roberts’ (2002) and Gettys’ (2003) conclusions that socioeconomic status had
significant impact on both student achievement and school climate. Crenshaw (2003)
stated: “Within the low socioeconomic schools grouping, when socioeconomic level was
lower, achievement ratings were lower; teacher perception of school climate was less
positive; and teachers did not stay as long” (p. 89).
In contrast, Crenshaw (2003) observed that the higher socioeconomic levels had
a positive impact on school climate variables. Crenshaw stated:
…the higher socioeconomic schools had higher teacher attendance and student
attendance; teachers that stayed longer at the same school; fewer students that
drop out; and more positive perceptions of the learning environment, social and
physical environment, and home school relations by teachers and students. (p.
91)
In 2004, McCathern continued the examination of school size in South Carolina
schools, but he focused on the public elementary schools (334 PreKindergarten – 5 and
Kindergarten – 5 schools in 1996-1997 and 348 in PreKindergarten – 5 and Kindergarten
– 5 in 1997-1998). McCathern studied whether a relationship could be determined
between the size of South Carolina public elementary schools and student achievement
through an analysis of fifth graders’ mean scaled scores in reading and mathematics on
the Metropolitan Achievement Tests, Seventh Edition, (MAT-7) for the years 1996-97
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and 1997-98. McCathern divided the 334 public elementary schools into five size
categories and into three community groups – urban, suburban, and rural.
McCathern (2004) used the input variables of school operating costs, pupilteacher ratio, level of teacher experience, level of teacher education, gender, ethnicity,
socioeconomic status, and community setting, which he obtained from the South
Carolina Department of Education. McCathern analyzed the data without controlling for
the input variables, then with the input variables controlled. He used the mean scaled
scores in mathematics and reading for the 1996-1997 and 1997-1998 school years.
McCathern (2004) concluded from his study that a significant relationship did
not exist between the size of South Carolina public elementary schools and student
achievement. He did, like previous researchers in South Carolina (Stevenson, 1996,
2001; Roberts, 2002; Gettys, 2003; and Crenshaw, 2003), determine that socioeconomic
status, i.e., the percentage of students receiving free-reduced lunch within a school, was
a strong predictor of an elementary school’s student academic achievement.
McCathern’s research ascertained that per pupil expenditures and teacher
experiences had significant, positive correlations with student achievement in two
samples, but not throughout the whole study. In the two samples cited, schools which
spent more funds on classroom instruction and schools with more experienced teachers
demonstrated significantly higher achievement (2004).
The one input variable that had a small but statistically significant relationship to
student academic performance in both math and reading in each year studied was
average years of professional experience of the teaching corps (McCathern, 2004).
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McCathern found that school size was one of the least predictive of student academic
outcomes. He stated that through his study he concluded that “the concept of school
size is somewhat nebulous” (p. 208).
White (2005) conducted a study of the relationships between public elementary
school size and school climate in South Carolina using data from the 2001 SC DOE
Annual School Report Card. Data utilized in the study were the list of the 271 public
elementary schools with grades PreKindergarten – 5th, 135-day average daily
membership, socioeconomic status (SES), percent of students with disabilities other
than speech (%SDA), and per pupil expenditure (PPE). Also used were data identified as
the school climate indicators: the percentage of teachers and student satisfied with the
learning environment, social/physical environment, and home-school relations within
the schools, the percentage of students identified as gifted and talented, percentage on
academic plans, academic probation, suspended or expelled, retained, and student
attendance, the percentage of teachers returning from the previous year, holding
advanced degrees, and teacher attendance as defined in the study.
White’s (2005) study revealed a significant negative correlation between school
size and both the percentage of students retained and the percentage of students
suspended/expelled when controlling for SES, %SDA, and PPE. The researcher
determined that no significant correlations were found between school size and school
climate as measured by the percentage of students on academic plans, on academic
probation, gifted and talented, student attendance, percentage of teachers returning
from the previous year, teachers with advanced degrees, or teacher attendance.
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Two significant correlations were identified by White (2005). She concluded that
as elementary school size increased, the percentage of students retained increased as
well. Additionally, White (2005) found that schools with larger student enrollments
were associated with higher percentage of students being suspended/expelled.
As with the Stevenson (2001) and McCathern (2004) South Carolina public
elementary school studies, White concluded that student SES was the most significant
factor in predicting school results. She stated: “The intent of this study was not to
investigate the effect of SES on school climate; however, the findings reaffirm the
negative impact of poverty. The statistical results of this investigation revealed SES had
the greatest impact on all of the school climate variables” (p. 159).
A third South Carolina middle school size study was conducted in 2006 by Kaczor.
She examined the relationship between the size of middle schools and student
achievement as well as school climate. Kaczor identified 173 South Carolina public
middle schools with the grade configuration of 6-8 for the school year 2003-2004.
Kaczor’s study focused on 1) the relationship between the size of South Carolina middle
schools with similar poverty levels and academic achievement as represented by the
percentage of students scoring either proficient or advanced on the English/language
arts and mathematics portions of PACT, and 2) the relationship between the size of
South Carolina middle schools with similar poverty levels and school climate. The data
used in her study were obtained from the South Carolina Department of Education for
the 2004 SC DOE Annual School Report Card. Variables utilized were the percentages of
students performing both proficient and advanced on the English/language arts and
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mathematics portions of the Palmetto Academic Challenge Test (PACT). Additionally,
Kaczor used variable data on school size, socioeconomic status of middle school student
populations, and school climate from the SC DOE Annual School Report Card for 2004.
She then categorized the schools into one of four poverty groupings: group one’s
poverty index ranged from 11.34% to 39.0%; group two’s poverty index ranged from
39.1% to 60.0%; group three’s poverty index ranged from 60.1% to 80.0%; and group
four’s poverty index ranged from 80.1% to 97.2%. During the study, Kaczor controlled
for per pupil expenditure, poverty levels, and then controlled for both of these variables
combined.
The data from Kaczor’s (2006) study revealed a strong negative correlation
between school size and student achievement in 6th grade PACT mathematics results,
while controlling for poverty and per pupil expenditure. In effect, she concluded that as
the size of the middle school increased, the percentage of students scoring proficient or
advanced on 6th grade PACT mathematics decreased. A second finding of the study was
a strong negative correlation between school size and school climate when Kaczor
controlled for per pupil expenditure and poverty index. Kaczor determined that
“smaller schools were associated with a more positive response about learning
environment, social and physical environment, and home and school relations” (p. 93).
Finally, Kaczor’s analysis of the schools was that “in approximately 75% of the instances
analyzed, more positive school climate was associated with smaller school size” (p. 93).
White (2005) and Kaczor (2006) both found similar results in their research on
school size and climate: smaller schools tend to be associated with more positive
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learning environments. This notion supports sentiments that Cotton (1996) and Howley
and Bickel (2001) concluded in their research. However, larger schools were associated
with higher achievement.
Following Stevenson’s (1996) study and McCathern’s (2004) study on school size
and student achievement in elementary schools in South Carolina, Carpenter (2006)
examined three questions in his research:
1. Does a relationship exists between South Carolina PreKindergarten – 5 or
Kindergarten – 5 public elementary schools as measured by student
enrollment and student achievement in English/language arts and
mathematics as defined by the results of the third, fourth, and fifth grade
2004-2005 Palmetto Achievement Challenge Test (PACT)? Do the results
differ when controlling for the effects of student socioeconomic status?
2. Does a relationship exists between South Carolina PreKindergarten – 5 or
Kindergarten – 5 public elementary schools as measured by student
enrollment and per pupil operating costs? Do the results differ when
controlling for the effects of student socioeconomic status?
3. Can student achievement in South Carolina’s PreKindergarten – 5 or
Kindergarten – 5 public elementary schools in English/language arts and
mathematics as measured by the third, fourth, and fifth grade 2004-2005
Palmetto Achievement Challenge Test be predicted by at least one, or a
combination, of the following variables: school size, school per pupil
operating cost, and school study body socioeconomic status? (p. 10)
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As did previous researchers of school size in South Carolina, Carpenter (2006)
collected data from the SC DOE Annual School Report Card data for the 2004-2005
academic year. Carpenter collected data on the 400 public elementary schools with
either a PreKindergarten – 5 or Kindergarten – 5 grade configuration. These data
included “the percentage of third, fourth, and fifth grade students performing either
proficient or advanced on the English/language arts and mathematic portions of PACT,
the 135th-day ADM for these schools, and the percentage of students eligible for free
and reduced lunch/Medicaid” (p. 38).
Carpenter (2006) concluded from his study that no statistically significant
relationship existed between school size and student achievement as evidenced by
student performance on the English/language arts and mathematics portions of PACT
when controlling for socioeconomic status. He did note that a statistically significant
negative relationship was apparent between school size and per pupil expenditure.
Carpenter (2006) stated, “This relationship indicated that as the size of South Carolina
public elementary schools increased, the per pupil operating costs became lower, even
when controlling for socioeconomic status” (p. 78).
In summary of his study, Carpenter (2006) drew the same conclusions regarding
the impact that socioeconomic status had on student achievement as previous studies
of public schools in South Carolina made: socioeconomic status of students was a
significant predictor of student achievement (Durbin, 2001; Stevenson, 2001; Roberts,
2002; Crenshaw, 2003; Gettys, 2003; McCathern, 2004). Carpenter (2006) noted that
poverty was a significant predictor of student achievement. In his study, Carpenter
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found that 63% of the variance in English/language arts performance and 60% in
mathematics performance was associated with school socioeconomic status.
The most recent study on school size in South Carolina was conducted by Maxey
in 2008. Maxey’s research sought to determine whether a relationship existed between
the size of South Carolina’s public high schools and student achievement. As in other
studies, Maxey used the SC DOE Annual School Report Card data. For the 2006-2007
school year, Maxey used the variable of school size as determined by the average daily
membership (ADM) of students as calculated on the 135th-day of the school year,
student achievement as measured by the 2007 ACT and SAT Reasoning Test (SAT) mean
composite scores and class members’ ACT and SAT mean scores for reading and
mathematics, and school poverty level. Maxey identified 167 South Carolina’s public
high schools for inclusion in his investigation.
Maxey’s (2008) research questions examined the relationship between the size
of South Carolina public high schools and student achievement while controlling for the
effects of poverty. He concluded that on the surface, high school size was positively
related to student achievement, but, when the influence of poverty was controlled
statistically, high school size was not found to be significantly related to student
achievement. In fact, Maxey’s (2008) study found no significant relationship between
the size of South Carolina public high schools and student achievement when the effect
of poverty was controlled. The summary conclusion of Maxey’s (2008) study again
supported previous empirical studies on school size nationally (Friedkin & Necochea,
1988; and Hoagland, 1995) and in South Carolina (Stevenson, 1996; Howley, 1995;
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Durbin, 2001; Stevenson, 2001; Roberts, 2002; Crenshaw, 2003; McCathern, 2004;
Carpenter, 2006; and Kaczor, 2006). His study affirmed that poverty is a powerful
predictor of student achievement.
Stevenson (2006) noted in a review of the South Carolina state-wide studies, that
the socioeconomic status of students was the greatest predictor of student
achievement. However, he also notes, and McCathern concurs, that other variables
may be predictors of student achievement as well:
The first relates to “masking.” With poverty level of the student body accounting
for as much as three-fourths of the variability in academic outcomes and school
climate among schools, can the real effects of school size and other variables be
adequately identified at this point in time? The 2001 findings by Stevenson
(student attendance) and McCathern in 2004 (teacher experience) indicate that
other factors periodically do emerge along with poverty as predictors school
success. With this in mind, would school size actually emerge as a predictive
factor in student performance and school climate if the exceedingly harsh, huge
effects of poverty could be fully controlled? (p. 6)
Stevenson’s question summarizes what researchers nationally and state-wide
have attempted to determine in their studies: is there a variable or a set of variables
that may be predictors of student achievement, when poverty is controlled? The next
section of this literature review considers prominent literature on variables that may
predictor student achievement in isolation or as a set of variables.
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Variables
The following section of this literature review presents variables that are
prominent in current literature on school size. Each of the variables may be predictors
of student achievement in isolation or as a set of variables.
Poverty
Based on the findings of The Matthew Project and many other studies’, the
school size debate cannot continue without the acknowledgement of the effects of
poverty. This determination is documented by researchers such as Friedkin and
Necochea (1998); Howley, Strange, and Bickel (2000); Howley & Bickel (1999); O’Hare
(1988); Abbott, Joireman, & Stroh (2002); Howley & Howley (2004); McMillen (2004);
Weber, 2005; Berry and West (2005); and Cartner (2005). In fact, Howley and Howley
(2004) concluded from their research: “(1) smaller school size confers an achievement
advantage on all but the highest-SES students, (2) smaller size mediates the powerful
association between SES and achievement, (3) the relationship between school size and
achievement is predominantly linear, and (4) size effects are at least as robust in rural
schools as compared with schools overall” (p. 26).
In the literature, poverty often is defined differently and with different
synonyms. Typically, poverty is defined in research studies as socioeconomic status
(SES). The United States Bureau of the Census (2005) defines poverty is: “a family is
considered to be poor if its income for a particular year is below the amount deemed
necessary to support a family of a certain size. For example, $15,219 was the poverty
threshold for a single parent with two children in 2004” (Burney & Beilke, 2008, p. 297).
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The definition provided by the National School Lunch Program (2009) states that the
Free and Reduced Price Lunch Program is for
Children from families with incomes at or below 130% of the poverty level are
eligible for free meals. Those with incomes between 130% and 185% of the
poverty level are eligible for reduced‐price meals, for which students can be
charged no more than 40 cents. (p. 2)
Frequently, the Free and Reduced Price Lunch program is used in research studies as the
poverty index or socioeconomic status of the schools (Friedkin & Necochea, 1988;
Cushman, 1999; Stevenson, 2001; McRobbie, 2001; Nathan & Febey, 2001; Roberts,
2002; Crenshaw, 2003; McCathern, 2004; Carpenter, 2006; and Kaczor, 2006).
Four major studies emphasized the impact poverty has on student achievement
specifically. The summary of each study follows:
Howley (1995) argued that the association between school size and academic
achievement is governed entirely by SES. He estimated that increased school size
produced an effect equivalent to an extra .25 years of school for middle and upper class
students, but for low social class students the effect was equivalent to a loss of .67 years
of school.
Abbott and Joireman (2001) used multiple regression analysis to study group
differences in school achievement according to ethnic population as well as income
levels of student families: "Across a variety of grades and tests, our results support the
conclusion that low income explains a much larger percentage of the variance in
academic achievement than ethnicity" (p. 13).
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Fermanich (2003) conducted a study in which he concluded that the poverty
index and the student achievement level emerged as the only two variables with a
significant relationship. The correlation was a negative relationship, which showed that
as the poverty index level for a school district increased, the student achievement levels
decreased. Fermanich concluded that poverty constituted 77% variability in student
achievement as a result of his study.
In 2005, Sirin conducted a meta-analysis of studies conducted on poverty and
student achievement published between 1990 and 2000. Sirin concluded that poverty
had a high degree of association at the school level for student achievement and “of all
the factors examined in the meta-analytic literature, family SES at the student level is
one of the strongest correlates of academic performance. At the school level, the
correlations were even stronger” (p. 447).
A review of school size literature as it relates to poverty reinforces what has
previously been stated: poverty has a significant effect on student achievement and
must be considered when conducting a study to determine whether school size has an
effect on student achievement. A discussion of the literature of variables that might
also effect student achievement will be reviewed in the next section.
School Leadership
School leadership is a variable that has a significant amount of research done in
recent years. One of the first major studies on school leadership and its effect on
student achievement was Murphy’s study in 1988. Murphy determined that the
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research previously conducted failed to offer proof that educational leadership had a
positive or negative relationship on student achievement.
Following Murphy’s study, Hallinger and Heck (1996) determined from their
study on school leadership and student achievement that “despite the traditional
rhetoric concerning principal effects, the actual results of empirical studies in the U.S.
and U.K. are not altogether consistent in size or direction” (p. 1).
In 2001, Cotton reviewed eighty-one leadership studies conducted between
1979 and 2000. She determined that school leadership did have a positive effect on
student achievement. She also identified twenty-six administrative behaviors that she
determined contributed substantially to student achievement. She classified the
behaviors into five thematic categories including establishing a clear focus on student
learning, establishing and maintaining quality interactions and relationships, shaping
school culture, serving as an instructional leader, and ensuring accountability. Cotton
concluded that each of these behaviors had a positive effect on increasing student
achievement.
Following Cotton’s 2001 study, Waters, Marzano, and McNulty (2003) conducted
a meta-analysis on studies from 1970 to the 2003 involving Kindergarten-12 students in
the U.S. or similar culture. The study examined the relationships between the
leadership of the school-level principal and student academic achievement. The
researchers utilized standardized achievement tests, state tests or a composite index
based on one or both. The results of the analysis concluded that studies produced an
average correlation of 0.25 between principal leadership and student achievement.
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From the data, the researchers calculated a 10% increase in student test scores on
average when a principal improved his or her “demonstrated abilities in all twenty-one
responsibilities by one standard deviation” (Waters, Marzano, and McNulty, 2003, p. 3).
A follow-up empirical research study conducted by Leithwood, Louis, Anderson,
and Wahlstrom (2004) sought to identify the links between school-level leadership and
student learning. The researchers determined that educational leadership comes from
many different sources within the school, but that school leaders specifically are still the
most influential. Leithwood et al (2004) stressed the importance of improved
recruitment, training, evaluation, and successful school improvement. The emphasis on
these areas would translate into more productive schools and increased student
achievement.
Finally, Gentilucci and Muto (2007) studied student perceptions of the influence
of school principals at the elementary, middle, and high school levels. The researchers
found that students at all three levels perceived that effective principals can and do
directly influence learning and academic achievement in their schools by engaging in
certain student- and instructionally-focused behaviors. That perception of principal
influence was further supported by positive assessments of school climate by staff,
parent, and students.
Based on these studies, principal influence on student achievement is a variable
that the researcher felt was demonstrated through the literature as an important
variable to consider in this study.
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School Climate
A third variable reviewed is school climate. Hoy and Miskel (2004) define school
climate as “the set of internal characteristics that distinguishes one school from another
and influences the behavior of its members is the organizational climate of the school”
(p. 221). McRobbie (2001) defined the school climate as the personal bonds between
the school and community that allow the school to work with parents and area leaders
to focus on the educational needs of students. Owens’ (2001) definition of school
climate is the “perceptions of persons in the organization that reflect those norms,
assumptions, and beliefs” (p. 81). Johnson’s (2003) definition of school climate was
defined as it related to the School Report Cards indicators of school performance. He
identifies student and teacher morale, student and teacher attendance, school
environment, and educational programs as those indicators.
With the consideration of the previously mentioned definitions of school
climate, Kaczor (2006) defined school climate variables in her study on the effects of
school size on student achievement in middle schools from the South Carolina Annual
School Report Card. The variables she defined in her study were: teachers satisfied with
the learning environment; students satisfied with the learning environment; parents
satisfied with the learning environment; teachers satisfied with social and physical
environment; satisfied with social and physical environment; parents satisfied with
social and physical environment; teachers satisfied with home-school relations; students
satisfied with home-school relations; and parents satisfied with home-school relations.
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MacIntosh (1988), Cotton (1996), Abbott et al (2002), Cushman (1999) Kennedy,
(2001), Langdon (2000) and Nathan and Febey (2001) conducted studies on school
climate and student achievement. All of the studies found similar results: positive
school climate and high student achievement correlated. Further, small schools had
higher positive school climates. Several reasons were presented as to why small schools
had higher school climate results.
MacIntosh (1988) determined that school climate and satisfaction were
positively affected if students felt they were supported academically. Cotton’s (1996)
research showed that small schools had lower incidences of negative social behavior,
however measured, than do large schools. Her research also demonstrated that the
social behavior of ethnic minority and low-SES students is even more positively
impacted by small schools than that of other students. Cushman (1999), McRobbie
(2001), and Nathan and Febey (2001) each conducted research on school climate and
found that small schools were less expensive due to their tendency to have lower
dropout and higher graduation rates. Cushman (1999) also concluded that small schools
were safer. Cushman stated that “rates of truancy, classroom disruptions, vandalism,
theft, substance abuse and gang participation all are reduced in small schools” (1999, p.
38). Howley (1989, 1994, 1996, 2001), Raywid (1996, 1998, 1999), Cotton (1996, 2001),
and Irmsher (1997) each report that smaller schools better serve students, especially
students from low income and minority families.
In summary, the improvement in achievement is derived not just from the
smallness of the school, but the conditions that occur in small schools. From the
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research presented, the researcher will utilize the variable of school climate from
Kaczor’s (2006) study cited previously.
Per Pupil Cost
The question economy of scale represents a major topic in the literature on small
schools. In fact, Conant in 1959 was a primary instigator of the debate when he
contended that “The enrollment of many American public high schools is too small to
allow a diversified curriculum except at exorbitant cost” (P. 77). For many years, district
and school consolidation was the focus of state and district educational leadership. This
line of thinking was supported in research studies for many years. Currently, most
researchers of school size admit that larger schools can offer more courses at lower perpupil costs, but the definition of cost has changed considerably over the years. The cost
definition changed as a result of the Friedkin and Necochea study of California schools in
1988 because the focus changed from economy of scale to student achievement.
McKenzie (1983) and Haller (1992) argued that additional administrative costs in
large schools can undermine economies of scale just as they do in the business world.
Both researchers supported the theory that large schools, just like large businesses, can
become too big and create inequities as well as get bogged down with bureaucracy,
thereby nullifying the economy of scale theory.
Sergiovanni (1995) argued in support of small schools. He recognized that small
schools do cost slightly more per student than do large schools, but his argument that
small schools could still be more efficient if they were more productive demonstrates
some validity. In his literature, he urged educational decision-makers to go beyond
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simple per student cost and consider the ratio of productivity to cost, which falls in line
with Friedkin and Necochea (1988) and Howley and Bickel (2001).
In 2006, Archibald conducted a study that produce the finding that per-pupil
spending at the school level is positively related to student achievement in math and
reading, and the result was statistically significant for reading achievement. This is an
important study because it substantiates that per-pupil expenditure may be a variable
that is a predictor of student achievement.
Stiefel, Schwartz, Iatorola, and Chellman (2008) studied New York City schools to
determine the economy of scale. Their study revealed that small schools cost almost
15% less than very small schools; medium size schools were slightly cheaper; large size
schools were nearly 20% cheaper than very small schools and very large schools were
28% cheaper than very small schools. The researchers’ analysis of their data suggested
that direct costs per pupil generally decline with size for all types of high schools.
Further, Stiefel, Schwartz, Iatorola, and Chellman supported schools moving to small
themed schools and moving away from large comprehensive schools. This suggestion is
based on the conclusion that it would cost less per pupil as outputs increase.
In research conducted in South Carolina by Durbin (2001) and Carpenter (2006),
per pupil expenditure did not prove to be a predictor of student achievement. Durbin
examined high school size, student achievement, and per pupil expenditure in South
Carolina, while Carpenter measured elementary school size, student achievement and
per pupil expenditure. As a result of their studies, both researchers concluded that
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there was no statistically significant relationship when measuring student achievement
and the cost of instruction per child.
A review of the literature presented in this section suggests that it is
undetermined whether per pupil expenditure is a predictor of student achievement.
The researcher will use the variable of per pupil expenditure and percent of expenditure
for instruction.
Teacher Certification and Professional Development
Two variables considered to be predictors of student achievement are linked due
to the nature of the variables. These are teacher certification and teacher professional
development.
Strauss and Sawyer (1986) found that North Carolina’s teachers’ average scores
on the National Teacher Examinations (NTE) had a strong influence on average school
district test performance. The researchers concluded from their research: “Of the inputs
which are potentially policy-controllable (teacher quality, teacher numbers via the pupilteacher ratio and capital stock), our analysis indicates quite clearly that improving the
quality of teachers in the classroom will do more for students who are most
educationally at risk, those prone to fail, than reducing the class size or improving the
capital stock by any reasonable margin which would be available to policy makers” (p.
47).
In a study by Armour-Thomas, Clay, Domanico, Bruno, and Allen in 1989, the
researchers found that when student characteristics were held constant, the
relationship of teachers’ qualifications to student achievement was significant. The
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researchers studied high and low-achieving schools with demographically similar
student populations in New York City. The determination was that differences in
teacher qualifications (educational degrees, certification status, and experience)
accounted for approximately 90% of the total variation in average school-level student
achievement in reading and mathematics at all grade levels tested.
Ferguson’s (1991) study of almost 900 Texas school districts found that
combined measures of teachers’ expertise—scores on a licensing examination, master’s
degrees, and experience—accounted for more of the inter-district variation in students’
reading and mathematics achievement (and achievement gains) in grades 1 through 11.
Ferguson evaluated the effects of many school input variables and controlled for
student background and district characteristics in the study.
Following Ferguson’s study (1991), Ferguson and Womack (1993) conducted a
study of more than 200 graduates of a single teacher education program. They
examined the influences on thirteen dimensions of teaching performance of education
and subject matter coursework, National Teachers Exam (NTE) subject matter test
scores, and grade point average(GPA) in the student’s major. The results of the study
found that the amount of education coursework completed by teachers explained more
than four times the variance in teacher performance than did measures of content
knowledge (NTE scores and GPA in the major).
Ferguson and Ladd (1996) then conducted an analysis in Alabama similar to the
Texas study conducted in 1991. The researchers used the variables of master’s degrees
and American College Testing (ACT) scores instead of teacher licensing examination
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scores. When they combined the variables of teachers’ academic ability, education, and
experience were combined with class sizes, the variance accounted for 31.5% of the
predicted difference in reading and mathematics student achievement gains between
districts scoring in the top and bottom quartiles in mathematics.
A study that demonstrated a positive effect of teacher education coursework on
student learning was Monk’s (1994) study of student’s mathematics and science
achievement. Monk also found that teacher education coursework was sometimes
more influential than additional subject matter preparation.
Greenwald, Hedges, and Laine (1996) completed a review of studies that further
supported Monk’s (1994) study. These researchers found that teacher education,
ability, experience, small schools and lower teacher-pupil ratios were associated with
increases in student achievement across schools and districts.
Darling-Hammond and Sykes (1999) examined data from a fifty-state survey of
policies, state case study analyses, the 1993-94 Schools and Staffing Surveys (SASS), and
the National Assessment of Educational Progress (NAEP) to conduct her study. The
purpose for the study was to examine the ways in which teacher qualifications and
other school inputs were related to student achievement across states. DarlingHammond and Sykes concluded that both the qualitative and quantitative analyses
implied that policy investments in the quality of teachers may be related to
improvements in student performance. Further, the quantitative analyses indicated
that measures of teacher preparation and certification are the strongest correlates of
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student achievement in reading and mathematics. This was demonstrated before and
after controlling for student poverty and language status.
Another Texas study, this one by Fuller in 1999, found that students in districts
with greater proportions of licensed teachers were significantly more likely to pass the
Texas state achievement tests, particularly when controlling for student socioeconomic
status, school wealth, and teacher experience. Additionally, teacher licensing was
especially influential on the test performance of elementary students.
Fetler (1999) examined school level analysis of mathematics test performance in
California high schools. The researcher found a strong negative relationship between
average student scores and the percentage of teachers on emergency certificates, as
well as a smaller positive relationship between student scores and teacher experience
levels, after controlling for student poverty rates.
Finally, Goldhaber and Brewer conducted a study of high school students’
performance in mathematics and science in 1999. They utilized data from the National
Educational Longitudinal Studies (NELS) of 1988. The researchers found that fully
certified teachers had a statistically significant positive impact on student test scores
when compared to teachers who are not certified in their subject area.
These studies, when considered as a body of evidence, support the theory that
teacher certification and/or licensure was a predictor of student achievement. Several
studies follow that provide research on teacher professional development and its effect
on student achievement.
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Marchant (2002) conducted a study that intended to evaluate the effect that an
association with the Teachers College of a midwestern university had on student
achievement at schools designated as Professional Development Schools (PDS). The
results of the study concluded that PDS sites with higher ratings in staff development
had students that achieved more in a number of areas (especially noteworthy were the
predicted achievement scores). In effect, the research determined that the more
focused and relevant the staff development, the better students achieved. The
researcher did acknowledge that correlations do not indicate causation, but evidence
did support a significant connection between professional development and student
achievement in PDSs.
In a synthesis of available research on teacher professional development and its
effect on student achievement, Wilson, Floden, and Ferrini-Mundy (2002) provided a
detailed summary of various studies concluding that subject area certification makes a
difference in student outcomes. Rivkin, Hanushek, and Kain (2005) found that there is
minimal variation in teacher quality, as evidenced by student achievement gains, due to
teacher characteristics such as certification, pre-service education and even experience.
Rivkin et al (2005) determined through a study on professional development that quality
professional development could be a powerful tool for promoting teacher learning
which, in turn, could lead to reforming structures for effective teaching. The outcome
of the reformation of teaching structures could lead to increased student learning.
However, Rivkin et al (2005) could not produce evidence in support of this theory.
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Penuel, Fishman, Yamaguchi, and Gallagher (2007) conducted a study that
utilized 454 teachers who participated in an inquiry science program. The purpose of
the study was to examine the effects of different characteristics of professional
development on teachers’ knowledge and their ability to implement the program. The
researchers found consistent findings from earlier studies of effective professional
development: teachers’ perceptions about the professional development experiences
played a significant role in teacher learning and program implementation. The
researchers also concluded that the incorporation of time for teachers to plan for
implementation and the provision of technical support were significant for promoting
program implementation in the program, which ultimately may lead to increased
student achievement.
Tabernik’s (2008) study examined the relationship between teacher participation
in sustained, targeted professional development and student performance on the Ohio
Achievement Test for Mathematics (OATM). Tabernik compiled and reviewed data for
sixty-nine mathematics teachers in grades 4 through 8 during the 2006-2007 school
year. This sample consisted of teachers in forty-six schools across eleven Northeast
Ohio school districts. The input variables were demographic information, hours of
participation in professional development provided through the SMART Consortium,
and additional information obtained through a survey instrument. The results of the
study found that student outcomes, expressed as standard scores, were predicted to be
higher for students assigned to teachers who participated in ninety or more hours of
professional development, and for teachers who were certified specifically to teach
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mathematics. Tabernik also found that increased years of teaching experience was
associated with higher standard scores for students on the 2007 OATM.
Considering the evidence of the studies presented, it is appropriate to consider
teacher certification/licensure and teacher professional development at input variables
for this study. For the purposes of this study, the researcher will use the following
variables to measure if one or more are a predictor of student achievement: number of
teachers with advanced degrees; continuing contract teachers; classes not taught by
highly qualified teachers; teachers with emergency or provisional certificates; teachers
returning from the previous school year; and professional development days per
teacher.
Teacher Attendance Rate
In 2008, Miller, Murnane, and Willett conducted a study on teacher attendance
rate and its effect on student achievement. The results of their study determined that
“10 additional days of teacher absence reduce student achievement in fourth-grade
mathematics by at least 3.2% of a standard deviation is large enough to be of policy
relevance…[the researchers’] estimates indicate that 10 additional days of unexpected
absences reduce student achievement in mathematics by more than 10% of a standard
deviation” (p. 196). Utilizing Miller, Murnane, and Willett’s study results as support for
teacher attendance as a possible predictor of student achievement, the researcher will
use this variable in the research.
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Student Attendance Rate
The next variable considered as an input variable for this study is student
attendance rate. Two significant studies have been conducted on student attendance
rate and its effect on student achievement.
In 1993, Caldas conducted a study in Louisiana to determine the impact of input
and process factors on student achievement. Caldas utilized student performance data
collected by the Louisiana Department of Education from all 1,301 public schools in
Louisiana, including all elementary, middle and secondary schools for the 1989 school
year. Caldas described input factors as those elements affecting student outcomes over
which the school has virtually no control. The input factors he identified in his study
included student ethnicity, socioeconomic status, size of the community served by the
school, and mandatory school attendance laws.
As a result of Caldas’ study, he determined that the process variables that had
the most significant impact on student achievement were student attendance rates and
school size. This was particularly true in the central city schools. By contrast, noncentral city schools revealed class size as the most significant impact on student
achievement. Nonetheless, Caldas concluded that student attendance rate was the
single most significant variable for student achievement gains because schools could
improve the attendance rates of schools. Caldas states (1993):
Of those factors examined in this study over which schools and districts do have
some control, the most important by a significant margin was percent student
attendance. This is an encouraging finding because even vigorous efforts to
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increase school attendance likely require far fewer resources than either
reducing school sizes (which often require new building construction) or class
sizes (which usually means hiring new teachers). (p. 214)
A study that complemented Caldas’ (1993) research was conducted by
Daugherty in 2008. Daugherty’s study showed that:
…the higher the percentage average of absenteeism the lower the student
performance average. Eighth and tenth grade math mean scale scores fall below
the state proficiency level when students miss sixteen or more days of school. In
reading, both eighth and tenth grades mean scale scores fall below the state
proficiency levels when students miss seventeen or more days of school. This
study also indicated student categories had a relationship with student
achievement, scale scores and daily attendance. (p. 109)
Utilizing the evidence supported by the studies presented, student attendance
rate is a variable that may show to be a predictor of student achievement and will be an
input variable used.
Other Variables
A survey of the literature did not reveal research on the breadth and depth of
the following potential variables: first graders that attended full-day kindergarten,
retention rate, eligible for gifted and talented, percent objectives met, students with
disabilities other than speech, students older than usual for grade, suspended or
expelled, number of teachers with advanced degrees, continuing contract teachers,
classes not taught by highly qualified teachers, teachers with emergency or provisional
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certificates, teachers returning from the previous school year, teacher attendance rate,
average teacher salary, professional development days per teacher, principal’s or
director’s years at the schools, student-teacher ratio, prime instructional time,
opportunities in the arts, parents attending conferences, SACS accreditation, portable
classrooms, percent of teachers satisfied with the learning environment, percent of
students satisfied with the learning environment, percent of parents satisfied with the
learning environment, percent of teachers satisfied with social and physical
environment, percent of students satisfied with social and physical environment,
percent of parents satisfied with social and physical environment, percent of teachers
satisfied with home-school relations, percent of students satisfied with home-school
relations, percent of parents satisfied with home-school relations, vacancies for more
than nine weeks, and character development program. However, these variables are
utilized because these variables are part of the SC DOE Annual School Report Card.
Therefore, the variables are potential factors of student achievement.
Summary
A review of historical and recent empirical studies which focused on the
relationship between school size and student achievement nationally was conducted. In
South Carolina specifically, the relationship between the size of South Carolina public
elementary schools and student achievement has been examined previously in four
studies: Stevenson (1996), McCathern (2004), White (2005), and Carpenter (2006).
Studies conducted of South Carolina public middle schools (Roberts, 2002; Gettys, 2003;
and Kaczor, 2006) and public high schools (Durbin, 2001; Crenshaw, 2003; and Maxey,
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2008), were analyzed to ascertain the relationship between school size and student
achievement. The researcher concluded that in South Carolina studies, school size has
not demonstrated a significant relationship to student achievement. The researchers
acknowledged that poverty index was a significant influence on student achievement
despite researchers’ efforts to neutralize the effects of this variable. Further, in
empirical studies of school size and student achievement nationally (Friedkin &
Necochea, 1988; Howley, 1995; and Hoagland, 1995) and in South Carolina (Stevenson,
1996; Durbin, 2001; Stevenson, 2001; Roberts, 2002; Crenshaw, 2003; McCathern, 2004;
Carpenter, 2006; and Kaczor, 2006), researchers have affirmed that poverty is a
powerful predictor of student achievement.
This study, like the earlier South Carolina studies, seeks to identify the impact of
school size on student achievement through the statistical control of SES. The
researcher uses a different statistical method to control for SES than those utilized by
previous researchers in South Carolina. The researcher also includes a significantly
larger number of variables to see if a particular factor or combination of factors may
best predict student achievement.
Chapter II has provided a review of the literature concerning empirical studies
that have examined the relationship between school size and student achievement.
Chapter III presents a discussion of the methods used to collect and analyze data for this
study.
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CHAPTER III
Design of the Study
Chapter III presents the design of the study. This chapter begins by explaining
the purpose of the study. Next, the methodology utilized to conduct the study is
reviewed. The sample and sampling plan, data collection and preparation, and analysis
of data related to the research questions are presented. The chapter concludes with a
summary.
Purpose of the Study
The first purpose of this study was to determine whether there is a relationship
between the size of South Carolina public elementary schools and student achievement
while controlling for the effect of socioeconomic status. For this part of the study, the
independent variable was school size or 135-day average daily membership. The
control variable was poverty index and the dependent variable was student
achievement. School size was determined for each elementary school based upon the
average daily membership (ADM) of students as calculated on the 135th – day of the
school year. The socioeconomic status (SES) of each school was identified as the
poverty index of each PreKindergarten – 5 or Kindergarten – 5 public South Carolina
elementary school in 2007-2008.
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Further, poverty index was defined as the percentage of a school’s student
enrollment that is eligible for Medicaid and/or participation in the free or reduced lunch
program (SC DOE, 2008). The ADM and poverty index for each public elementary school
in South Carolina were obtained from the South Carolina Department of Education via
its 2008 Elementary School Fact File. Student achievement, the dependent variable of
this study, was identified as the 2008 Palmetto Achievement Challenge Test (PACT) data
from the third, fourth, and fifth grades in English/language arts and mathematics. The
PACT data were retrieved from the South Carolina Department of Education in the 2008
Elementary School Performance Data File. To measure student achievement the
percentages of students scoring Proficient and Advanced on PACT in English/language
arts and mathematics were utilized.
A second purpose of this study was to ascertain if student achievement varies
among public elementary schools in South Carolina. SES was controlled by including
schools with similar poverty indexes in strata.
The third purpose of this study was to determine whether one variable, or a
combination of variables, from the literature and the South Carolina Department of
Education Annual School Report Card predicts student achievement. This study utilized
SES and school size as well as many variables obtained from the South Carolina
Department of Education (SC DOE) 2008 Annual School Report Card. The researcher
controlled for SES by grouping the public elementary schools in South Carolina into
strata based on poverty index percentages.
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Thirty-nine independent variables were obtained from the South Carolina
Department of Education via its 2008 Elementary School Fact File. These variables were
used to analyze whether one factor or a combination of factors predict student
achievement. The variables used for the third analysis are:
1. Poverty index
2. School size or average daily membership
3. First graders that attended full-day kindergarten
4. Retention rate
5. Student attendance rate
6. Eligible for gifted and talented
7. Percent objectives met
8. Students with disabilities other than speech
9. Students older than usual for grade
10. Suspended or expelled
11. Number of teachers with advanced degrees
12. Continuing contract teachers
13. Classes not taught by highly qualified teachers
14. Teachers with emergency or provisional certificates
15. Teachers returning from the previous school year
16. Teacher attendance rate
17. Average teacher salary
18. Professional development days per teacher
19. Principal’s or director’s years at the schools
20. Student-teacher ratio
21. Prime instructional time
22. Dollars spent per student
23. Spent on teacher salaries
24. Opportunities in the arts
25. Parents attending conferences
26. SACS accreditation
27. Portable classrooms
28. Percent of teachers satisfied with the learning environment
29. Percent of students satisfied with the learning environment
30. Percent of parents satisfied with the learning environment
31. Percent of teachers satisfied with social and physical environment
32. Percent of students satisfied with social and physical environment
33. Percent of parents satisfied with social and physical environment
34. Percent of teachers satisfied with home-school relations
35. Percent of students satisfied with home-school relations
36. Percent of parents satisfied with home-school relations
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37. Vacancies for more than nine weeks
38. Character development program
39. Percent of expenditures for instruction
This study sought to expand the body of research that had previously examined
the relationship between school size and student achievement in South Carolina and
across the national, while controlling for the powerful effects of poverty index.
Additionally, the study sought to identify a variable or combination of variables that may
predict student success. The variables used in the study are obtained from the SC DOE
2008 Annual School Report card.
From the outcome of this study, policy makers, school boards, and educators
may have a more substantial body of knowledge when making decisions related to
elementary school size. This knowledge may prove to be helpful when deciding
whether to begin new school construction, propose school consolidations, or
reconfigure school grade structures.
Given these purposes, three research questions were investigated in this study:
1. Does a relationship exist between the enrollment of South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and
student achievement in English/language arts and mathematics?
Achievement is defined by the percentage of the third, fourth, and fifth
grade students scoring Proficient and Advanced on the 2007-2008 Palmetto
Achievement Challenge Test. Do results vary when controlling for poverty?
2. Does a relationship exist between the enrollment in South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and
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student achievement in English/language arts and mathematics as defined by
the results of the third, fourth, and fifth grade 2007-2008 Palmetto
Achievement Challenge Test scores when schools are grouped by poverty
index of schools? Achievement is defined as the percentage of students
scoring Proficient and Advanced.
3. Can student achievement in South Carolina’s PreKindergarten – 5 or
Kindergarten – 5 public elementary schools in English/language arts and
mathematics as measured by the third, fourth, and fifth grade 2007-2008
Palmetto Achievement Challenge Test be predicted by at least one, and
possibly a combination, of the following variables:
1. Poverty index
2. School size or average daily membership
3. First graders that attended full-day kindergarten
4. Retention rate
5. Student attendance rate
6. Eligible for gifted and talented
7. Percent objectives met
8. Students with disabilities other than speech
9. Students older than usual for grade
10. Suspended or expelled
11. Number of teachers with advanced degrees
12. Continuing contract teachers
13. Classes not taught by highly qualified teachers
14. Teachers with emergency or provisional certificates
15. Teachers returning from the previous school year
16. Teacher attendance rate
17. Average teacher salary
18. Professional development days per teacher
19. Principal’s or director’s years at the schools
20. Student-teacher ratio
21. Prime instructional time
22. Dollars spent per student
23. Spent on teacher salaries
24. Opportunities in the arts
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25. Parents attending conferences
26. SACS accreditation
27. Portable classrooms
28. Percent of teachers satisfied with the learning environment
29. Percent of students satisfied with the learning environment
30. Percent of parents satisfied with the learning environment
31. Percent of teachers satisfied with social and physical environment
32. Percent of students satisfied with social and physical environment
33. Percent of parents satisfied with social and physical environment
34. Percent of teachers satisfied with home-school relations
35. Percent of students satisfied with home-school relations
36. Percent of parents satisfied with home-school relations
37. Vacancies for more than nine weeks
38. Character development program
39. Percent of expenditures for instruction
Methodology
This study sought to determine the relationship between school size and student
achievement among public elementary schools with grade span configurations of
PreKindergarten – 5 or Kindergarten – 5, using the Palmetto Achievement Challenge Test
(PACT) data. The study also attempted to conclude whether a relationship exists
between school size and student achievement data among public elementary schools
with similar poverty indexes with the grade spans PreKindergarten – 5 or Kindergarten –
5 while controlling for poverty index or SES. It further sought to determine whether
student achievement could be predicted by at least one, and possibly a combination, of
the SC DOE Annual School Report Card variables. The study utilizes PACT data for
English/language arts and mathematics for the third, fourth, and fifth grade students
from the 2007-2008 school year. The PACT data were obtained for public elementary
schools in South Carolina with a grade span of PreKindergarten – 5 or Kindergarten – 5.
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Poverty index or SES is a significant control variable because of the effects it has
on student achievement in South Carolina. For the purposes of this study, poverty
index, as defined by the South Carolina Department of Education (SC DOE), was used.
The SC DOE defines poverty index (PI) as poverty or socioeconomic status (SES) (SC DOE,
2004). The SC DOE states that the poverty index includes both the student participant
of free and reduced-price lunch and the student participant of Medicaid benefits.
For the first research question, the researcher examined whether a relationship
existed between the size of South Carolina’s PreKindergarten – 5 or Kindergarten – 5
public elementary schools and as measured by student enrollment and student
achievement in English/language arts and mathematics as defined by the results of the
third, fourth, and fifth grade 2007-2008 Palmetto Achievement Challenge Test scores.
Data used were the percentile of students scoring Proficient and Advanced for each
grade level and for each subject. A Pearson correlation analysis was used to make an
initial analysis. The researcher repeated the statistical analysis utilizing the same data,
however, the second analysis controlled for SES, using a stepwise multiple regression.
For question two, a Pearson correlation analysis was conducted to examine
whether a relationship existed between the size of South Carolina’s PreKindergarten – 5
or Kindergarten – 5 public elementary schools with similar poverty indexes as measured
by student enrollment and student achievement in English/language arts and
mathematics as defined by the results of the third, fourth, and fifth grade 2007-2008
Palmetto Achievement Challenge Test scores meeting Standard and Above.
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Since SES is a variable that significantly influences student achievement (Roberts,
2002; Carpenter, 2006) this researcher sought to neutralize the effects of SES.
Stevenson (1996) and Kaczor (2006) utilized the methodology of grouping schools in
South Carolina to measure whether school size has an effect on student achievement.
Stevenson (1996) conducted his study within the five elementary school levels created
by the South Carolina Department of Education. Kaczor (2006) created “strata” based
on poverty index of the middle schools she studied. By banding the schools into strata
based on the poverty index of the schools, the researcher controls for the effects of
poverty while measuring whether school size has an effect on student achievement in
English/language arts and mathematics in public elementary schools with grade spans
of PreKindergarten – 5 and Kindergarten – 5.
The elementary schools were placed into poverty index bands based on each
school’s poverty index. The poverty index bands are as follows: 0% - 49%, 50% - 59%,
60% - 69%, 70% - 79%, 80% - 89%, 90% - 94%, and 95% - 100%. Each poverty index
band contains approximately the same number of schools. The number of schools in
each band is as follows: 0% - 49% (63 schools); 50% - 59% (48 schools); 60% - 69% (73
schools); 70% - 79% (71 school); 80% - 89% (75 schools); 90% - 94% (54 schools); 95% 100% (57 schools). Each school’s poverty index was obtained from the South Carolina
Department of Education in the 2008 Elementary School Fact File. Within each group,
statistical analysis was conducted utilizing a stepwise multiple regression. The poverty
index variable was included in the stepwise regression to increase the possibility of
ascertaining the affect of poverty on student achievement.
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For research question three, a stepwise regression model was employed to
determine if student achievement in South Carolina PreKindergarten – 5 or Kindergarten
– 5 schools in English/language arts and mathematics as measured by the third, fourth,
and fifth grade 2007-2008 Palmetto Achievement Challenge Test could be predicted by
at least one, or a set, of the following independent variables as reported on the SC DOE
Annual School Report Card data:
Student achievement in English/language arts , mathematics, poverty index,
school size or average daily membership, first graders that attended full-day
kindergarten, retention rate, student attendance rate, eligible for gifted and
talented, percent objectives met, students with disabilities other than speech,
students older than usual for grade, suspended or expelled, number of teachers
with advanced degrees, continuing contract teachers, classes not taught by
highly qualified teachers, teachers with emergency or provisional certificates,
teachers returning from the previous school year, teacher attendance rate,
average teacher salary, professional development days per teacher, principal’s or
director’s years at the schools, student-teacher ratio, prime instructional time,
dollars spent per student, spent on teacher salaries, opportunities in the arts,
parents attending conferences, SACS accreditation, portable classrooms, percent
of teachers satisfied with the learning environment, percent of students satisfied
with the learning environment, percent of parents satisfied with the learning
environment, percent of teachers satisfied with social and physical environment,
percent of students satisfied with social and physical environment, percent of
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parents satisfied with social and physical environment, percent of teachers
satisfied with home-school relations, percent of students satisfied with
home-school relations, percent of parents satisfied with home-school relations,
vacancies for more than nine weeks, character development program, and
percent of expenditures for instruction.
The researcher conducted two separate stepwise regressions for research
question three. The first stepwise regression was conducted on the total population of
PreKindergarten – 5 and Kindergarten - 5 public elementary schools, using third grade,
fourth grade, and fifth grade PACT English/language arts and mathematics data. The
independent variables noted previously were used.
A second stepwise regression was conducted which utilized the poverty index
bands. The poverty index bands are as follows: 0% - 49%, 50% - 59%, 60% - 69%, 70% 79%, 80% - 89%, 90% - 94%, and 95% - 100%. Third grade, fourth grade, and fifth grade
PACT English/language arts and mathematics data were analyzed by poverty index band.
The 2008 SC DOE Annual School Report Card variables were the independent factors.
The poverty index variable was included in the stepwise regression to increase the
possibility of ascertaining the effect of poverty on student achievement.
Data sets for this research investigation were taken from the South Carolina
Department of Education and analyzed using the PASW Statistics Base 18 software
program. The p<0.05 significance criterion was used in all inferential analyses. Since
this is a complementary study to Carpenter’s (2006), the significance criterion of p<0.05
was maintained for the purposes of consistency.
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Instrumentation
Third, fourth, and fifth grade test scores from the South Carolina Palmetto
Achievement Challenge Test (PACT) were used to measure English/language arts and
mathematics student achievement in this study. The PACT was developed by teachers,
college and university faculty, and professional test writers (SC SDE, 2001). A sample
group of students took a field test version of PACT in grades 1 through 8 and 10 in the
spring of 1998. The new tests in English/language arts and mathematics were
administered for the first time in grades 3 through 8 in South Carolina during the spring
of 1999 (SC SDE, 2001). The PACT was designed to be a more accurate measure of the
academic achievement levels of students in South Carolina. Moreover, legislators
wanted a more rigorous test, and the Basic Skills of Academic Progress (BSAP) only
measured the ability of students to meet minimum levels of achievement (SC SDE,
2001).
The process for formulating PACT started when the state began developing
frameworks for each academic area. These frameworks established broad goals for
what students should know and be able to do as they progress through school. Based
on these frameworks, standards were developed to describe specifically what students
in South Carolina should learn (SC SDE, 2001). PACT is separated into four categories for
scoring academic achievement of students. The four categories consist of Below Basic,
Basic, Proficient, and Advanced. Students who score at the Below Basic level have not
met the minimum requirements for academic achievement and, therefore, are not
prepared to enter the next grade level. Students scoring at the Basic level have met the
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minimum state standards and are prepared to enter the next grade. Students who
score in the Proficient and/or Advanced range on PACT, which is the range the
researcher used to measure academic achievement, have met the qualifications for
promotion and are identified as well prepared for the next grade level. In addition,
students scoring at the Advanced level are highly prepared for the next grade level and
exhibit skills that are academically exceptional. The PACT is based on South Carolina
Curriculum Standards and is considered to be a greater indicator of academic
achievement of the standards taught in South Carolina classrooms than other measures
used in the past such as BSAP or the MAT7 (SC SDE, 2001).
Sampling Plan
The study population for the portion of the research examining the relationship
between elementary school size and student achievement consisted of 441 public
elementary schools with grade spans of PreKindergarten – 5 or Kindergarten – 5 in the
state of South Carolina. The PreKindergarten – 5 or Kindergarten – 5 enrollment at each
elementary school was the 135-day average daily membership (ADM) in 2007-2008.
This number represented the best indicator of actual enrollment, or school size, during
the spring 2008 administration of the Palmetto Achievement Challenge Test, which was
the sample size used.
For the study, the whole population of public PreKindergarten – 5 or
Kindergarten – 5 elementary schools in South Carolina was used for the three research
questions. For research question two and three, the whole sample data sets were run
initially. For the second analysis of the data, the sample population of elementary
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schools was placed into poverty index bands based on each school’s poverty index. The
poverty index bands are as follows: 0% - 49%, 50% - 59%, 60% - 69%, 70% - 79%, 80% 89%, 90% - 94%, and 95% - 100%. Each poverty index band contained approximately
the same number of schools. The number of schools in each band is as follows: 0% 49% (63 schools); 50% - 59% (48 schools); 60% - 69% (73 schools); 70% - 79% (71
school); 80% - 89% (75 schools); 90% - 94% (54 schools); 95% - 100% (57 schools). Each
school’s poverty index was obtained from the South Carolina Department of Education
in the 2008 Elementary School Fact File.
Data Gathering
The SC DOE Annual School Report Card data for the academic school year of
2007-2008 were obtained from the South Carolina State Department of Education
website (SC DOE, 2008) in the form of a Microsoft Excel document. This information is
collected and distributed each year and provides a variety of information about schools
and school districts in the state. Data specifically used for this research included: (a) the
percentage of third, fourth and fifth grade students scoring proficient or advanced on
the English/language arts and mathematics portions of PACT; (b) student enrollment as
reported by the 135 average daily membership at each school; and (c) the percentage of
PreKindergarten – 5 or Kindergarten – 5 students who were eligible to receive free and
reduced-price lunch and Medicaid benefits as measured by the poverty index. The data
contained in the Excel document was imported into the PASW Statistics Base 18
software program. The 2008 SC DOE Annual School Report Card data was then
formatted for statistical analysis in the PASW Statistics Base 18 software program.
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Data Analysis
This design of this study was intended to complement research conducted in
South Carolina on school size by McCathern (2004) and Carpenter (2006). Each research
question was answered utilizing descriptive and inferential statistical formulas. To
address the three research questions, data were obtained from the SC DOE Annual
School Report Card in the 2008 Elementary School Fact File.
For research question one, the researcher imported the data from the Excel
spreadsheet 2008 Elementary School Fact File into PASW Statistics Base 18 software
program. A simple Pearson correlation was run to determine if any relationship existed
that supported the use of the control variable of SES and/or identified interactions
between the variable of school size and student achievement that might affect
generalization from the outcome of the study. Then a partial correlation was used on all
441 schools to control for the possible effects of socioeconomic status while
ascertaining if the PACT data were related to school size. This was done separately for
the English/language arts and mathematics data. Analysis was performed for each
grade level (3, 4, and 5). The outcome measure was defined as the percentage of
students scoring Proficient and Advanced on the tests.
For the second research question, the researcher followed the same
methodology, but each data set used was from the elementary schools within the
poverty index bands of 0% - 49%, 50% - 59%, 60% - 69%, 70% - 79%, 80% - 89%, 90% 94%, and 95% - 100%. Analysis was performed for the third, fourth, and fifth grades
individually. The percentage of students scoring Proficient and Advanced were the
105
outcome measures used. The tables were created within the PASW Statistics Base 18
software program to conduct the analysis for this study.
For the last research question, the researcher did the following: A simple
Pearson correlation was run across all the variables for the whole sample of 441 public
elementary schools in South Carolina. This was conducted to determine whether any
relationships existed that supported the use of the control variables and/or identified
any relationships between variables that might affect the generalizability of this study.
The variables identified previously within the chapter were obtained from the 2008
Elementary School Fact File provided by the SC DOE Annual School Report Card. Using
the total 441 elementary schools, a stepwise multiple regression analysis was run to
ascertain whether any of the variables were related to student achievement. A
stepwise multiple regression analysis was used to control for the possible effect of SES.
The stepwise multiple regression was conducted a second time within the poverty index
bands to determine whether a variable or set of variables were related to student
achievement. The tables were created from the PASW Statistics Base 18 software
program were used to conduct the analysis for this study.
Summary
This study was designed to examine the relationship among the size of South
Carolina PreKindergarten – 5 or Kindergarten – 5 schools and student achievement in
English/language arts and mathematics. Initially, the foundation of the study was based
on Howley and Bickel’s (2000) postulation that school size influence varies by poverty
index level, with school size exerting a negative influence on student achievement in
106
impoverished schools, but had a positive influence on student achievement in affluent
schools. Howley and Bickel (2000) also ascertained through their research that poverty
index had to be controlled in an effort to determine whether school size was a predictor
of student achievement. In South Carolina, through the research of Stevenson (1996,
2001), Durbin (2001), Roberts (2002), Gettys (2003), Crenshaw (2003), McCathern
(2004), White (2005), Carpenter (2006), Kaczor (2006), and Maxey (2008), the influence
of poverty was found to be so great that it was critical to control for poverty index in
this study to ascertain whether school size was a predictor of student achievement. The
use of grouping similar poverty index schools into poverty index strata sought to control
for poverty differently than the previous researchers.
In addition, the study sought to determine if other variables related to school
outcomes, whether in concert with school size, individually, or in combination with
other SC DOE Annual School Report Card variables entered. Again, in South Carolina,
through the research of Stevenson (1996, 2001), Durbin (2001), Roberts (2002), Gettys
(2003), Crenshaw (2003), McCathern (2004), White (2005), Carpenter (2006), Kaczor
(2006), and Maxey (2008), few variables other than poverty index have been identified
as being predictors of student achievement. While ascertaining whether any one or
combination of variables from the SC DOE Annual School Report Card predicted student
achievement, it was critical to control for poverty.
The data for this study were taken from the SC DOE Annual School Report Card
provided in the 2008 Elementary School Fact File and the 2008 Elementary School
107
Performance Data File. The data were analyzed using the PASW Statistics Base 18
software program.
Chapter III has presented a description of the study design, procedures for
collecting data, and the format for the analysis of the data. Chapter IV contains an
analysis of the data collected by the researcher, followed by conclusions and
recommendations for further study in Chapter V.
108
CHAPTER IV
Results of the Study
The purpose of this study was to investigate the relationship between the size of
South Carolina public elementary schools with either PreKindergarten – 5 or
Kindergarten – 5 configurations and the student achievement of the schools. In
addition, it sought to determine if other variables related to school outcomes, whether
with school size, individually, or in combination with other SC DOE Annual School Report
Card variables predicted student achievement.
The investigation of the relationship between public elementary schools in South
Carolina and student achievement was conducted utilizing a systematic approach. First,
the relationship between public elementary school size and student achievement of
grades third, fourth, and fifth on PACT English/language arts and mathematics
(percentage of students scoring Proficient and Advanced) was examined by running a
Pearson correlation analysis for each individual item. Next, the research conducted the
same examination, but controlled for the variable poverty index.
The next statistical analysis the researcher conducted was to examine whether a
relationship existed between school size and third, fourth, and fifth grade Palmetto
Achievement Challenge Test (PACT) English/language arts and mathematics percentage
109
of students scoring Proficient and Advanced for the 2007-2008 school year. For this
analysis, the researcher attempted to control for SES by first determining whether
natural poverty index bands or strata occurred. No natural breaks were present. The
researcher then created poverty index strata for the public elementary schools using the
following groups: 0% - 49%, 50% - 59%, 60% - 69%, 70% - 79%, 80% - 89%, 90% - 94%,
and 95% - 100%. The groups created poverty index bands or strata with similar
numbers of schools. Pearson correlation analysis was conducted on school size and
student achievement within each strata.
The final examination of student achievement data was a stepwise multiple
regression of each of the variables measured on the South Carolina Department of
Education Annual Report Card. This was conducted for each grade (third, fourth, and
fifth) and PACT English/language arts and mathematics students scoring Proficient and
Advanced. Then a stepwise multiple regression was conducted for the same variables
within the poverty index strata.
This chapter is divided into four sections. Section one presents a general
description of the populations studied. The second section is an analysis of the
quantitative findings associated with research question one. Section three contains an
analysis of the quantitative findings that address research question two. The final
section provides an analysis of the quantitative findings addressing research question
three.
110
Descriptive Statistics
The sample in the investigation of the three research questions consisted of 441
of the 634 elementary schools which the South Carolina Department of Education
identified as public elementary schools for the 2007-2007 school year. The schools
chosen from the 634 were those with Prekindergarten or Kindergarten – 5 grade spans.
The elementary schools chosen for inclusion in the study ranged in size (i.e., student
enrollment or ADM) from a low of 100 students to a high of 1,253 students, with a
median of 573.0, a mean of 550.3 and a standard deviation of 208.9. Poverty index
percentages in the selected schools ranged from a low of 9.5% to a high of 99.2%, a
median of 76.2%, with a mean of 72.3% and a standard deviation of 20.5 (see Table 4.1).
Table 4.1
Descriptive Statistics for PreKindergarten - 5 and Kindergarten - 5 Elementary Schools
of 2007-2008 Poverty Index and 135-Day Average Daily Membership Variables
N
Range
Minimum
Maximum
Mean
Std. Deviation
Poverty Index
441.0
89.7
9.5
99.2
72.3
20.5
135-Day Average
Daily Membership
(ADM)
441.0
1153.0
100.0
1253.0
550.3
208.9
Valid N (listwise)
419.0
The percentage of students in third grade scoring Proficient and Advanced on
2007-2008 PACT English/language arts at the schools studied ranged from a low of
50.0% to a high of 100.0%. The mean was 86.3% with a standard deviation of 8.5. The
percentage of students in third grade scoring Proficient and Advanced on 2007-2008
PACT mathematics were a low of 28.3%, a high of 99.0%, and a mean of 76.0%. The
standard deviation for this category was 13.8 (see Table 4.2).
111
Table 4.2
Descriptive Statistics for Third Grade PreKindergarten - 5 and Kindergarten - 5 Elementary
Schools of 2007-2008 PACT English/Language Arts & Mathematics Data
N
Range
Minimum
Maximum
Mean
Std. Deviation
English/Language
Arts % Met
Standard
441.0
50.0
50.0
100.0
86.3
8.5
Mathematics %
Met Standard
441.0
70.7
28.3
99.0
76.0
13.8
The percentage of students in fourth grade scoring Proficient and Advanced on
2007-2008 PACT English/language arts at the schools studied was reported with a low of
41.4%, a high of 100.0%, a mean of 80.2% and with a standard deviation of 11.5. For the
percentage of students in fourth grade scoring Proficient and Advanced on 2007-2008
PACT mathematics, schools had as few as 35.0% of students scoring Proficient and
Advanced, with some schools with a high of 100.0%. The mean was 77.9% and the
standard deviation was 13.0 (see Table 4.3).
Table 4.3
Descriptive Statistics for Fourth Grade PreKindergarten - 5 and Kindergarten - 5 Elementary
Schools of 2007-2008 PACT English/Language Arts & Mathematics Data
N
Range
Minimum
Maximum
Mean
Std. Deviation
English/Language
Arts % Met
Standard
441.0
58.6
41.4
100.0
80.2
11.5
Mathematics %
Met Standard
441.0
65.0
35.0
100.0
77.9
13.0
The percentage of students in fifth grade scoring Proficient and Advanced on
2007-2008 PACT English/language arts and mathematics were also obtained. For
English/language arts, the percentage of students scoring Proficient and Advanced on
PACT for the 2007-2008 school year was a low of 41.9% and a high of 100.0%. The mean
was 76.8%. The standard deviation was 12.2. For mathematics, the low was 34.0%, the
112
high was 100.0%, the mean was 77.2%, and the standard deviation was 12.3 (see Table
4.4).
Table 4.4
Descriptive Statistics for Fifth Grade PreKindergarten - 5 and Kindergarten - 5 Elementary
Schools of 2007-2008 PACT English/Language Arts & Mathematics Data
N
Range
Minimum
Maximum
Mean
Std. Deviation
English/Language
Arts % Met
Standard
440.0
58.1
41.9
100.0
76.8
12.2
Mathematics %
Met Standard
440.0
66.0
34.0
100.0
77.2
12.3
Findings for Research Question One
The first research question was:
Does a relationship exist between the enrollment of South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and
student achievement in English/language arts and mathematics?
Achievement is defined by the percentage of the third, fourth and fifth
grade students scoring Proficient and Advanced on the 2007-2008
Palmetto Achievement Challenge Test. Do results vary when controlling
for poverty?
To answer this question, the researcher imported the data from the Excel
spreadsheet 2008 Elementary School Fact File into PASW Statistics Base 18 software
program. A simple Pearson correlation was run to determine if any relationship existed
that supported the use of the control variable of poverty and/or identified interactions
between the variables of school size and student achievement that might affect
generalization from the outcome of the study. The following section details the results
113
of the Pearson correlation on third, fourth, and fifth grade PACT English/language arts
and mathematics student achievement and school size.
Pearson Correlations
For third grade English/language arts, the data analysis indicated a positive
significant correlation with 135-day average daily membership (ADM) of 0.275 at p<0.01
level. For third grade PACT mathematics, a positive, significant correlation of 0.324 at
p<0.01 level was indicated with the variable 135-day average daily membership (ADM)
(see Tables 4.5 and 4.6).
Table 4.5
Correlation of Third Grade 2007-2008 PACT English/Language Arts
versus 135-Day Average Daily Membership
135-Day
English/Language
Average
Arts % Met
Daily
Standard
Membership
(ADM)
Pearson
1
.275
English/Language Correlation
Sig. (2Arts % Met
.000
tailed)
Standard
N
441
441
Pearson
.275
1
135-Day Average Correlation
Daily
Sig. (2.000
Membership
tailed)
(ADM)
N
441
441
114
Table 4.6
Correlation of Third Grade 2007-2008 PACT Mathematics
versus 135-Day Average Daily Membership
135-Day
Mathematics
Average Daily
% Met
Membership
Standard
(ADM)
Pearson
1
.324
Correlation
Mathematics %
Sig. (2-tailed)
.000
Met Standard
135-Day Average
Daily
Membership
(ADM)
N
Pearson
Correlation
441
441
.324
1
Sig. (2-tailed)
.000
N
441
441
The results of the Pearson correlation analysis between fourth grade students
scoring Proficient and Advanced in PACT English/language arts and ADM revealed a
positive, significant correlation at the p<0.01 level of 0.266. For the same grade, the
analysis of mathematics and ADM indicated a positive, significant result of 0.299 at the
p<0.01 level (see Tables 4.7 and 4.8).
Table 4.7
Correlation of Fourth Grade 2007-2008 PACT English/Language
Arts versus 135-Day Average Daily Membership
135-Day
English/Language
Average
Arts % Met
Daily
Standard
Membership
(ADM)
Pearson
1
.266
English/Language Correlation
Sig. (2Arts % Met
.000
tailed)
Standard
N
441
441
Pearson
.266
1
135-Day Average Correlation
Daily
Sig. (2.000
Membership
tailed)
(ADM)
N
441
441
115
Table 4.8
Correlation of Fourth Grade 2007-2008 PACT Mathematics
versus 135-Day Average Daily Membership
135-Day
Mathematics
Average Daily
% Met
Membership
Standard
(ADM)
Pearson
1
.299
Correlation
Mathematics %
Sig. (2-tailed)
.000
Met Standard
135-Day Average
Daily
Membership
(ADM)
N
Pearson
Correlation
441
441
.299
1
Sig. (2-tailed)
.000
N
441
441
The portion of fifth grade students scoring Proficient and Advanced on PACT
English/language arts data were run versus ADM. The relationship was positively
significant with a value of 0.325 at the p<0.01 level. Fifth grade mathematics student
achievement data were run versus ADM and the analysis indicated a positive
significance of 0.273 at the p<0.01 level (see Tables 4.9 and 4.10).
Table 4.9
Correlation of Fifth Grade 2007-2008 PACT English/Language Arts
versus 135-Day Average Daily Membership
135-Day
Average
English/Language
Daily
Arts % Met
Membership
Standard
(ADM)
Pearson
1
.325
135-Day Average Correlation
Daily
Sig. (2.000
Membership
tailed)
(ADM)
N
441
440
English/Language
Arts % Met
Standard
Pearson
Correlation
Sig. (2tailed)
.325
1
.000
N
440
116
440
Table 4.10
Correlation of Fifth Grade 2007-2008 PACT Mathematics
versus 135-Day Average Daily Membership
135-Day
Mathematics
Average Daily
% Met
Membership
Standard
(ADM)
Pearson
135-Day
1
.273
Correlation
Average Daily
Sig. (2-tailed)
.000
Membership
(ADM)
Mathematics %
Met Standard
N
441
440
Pearson
Correlation
.273
1
Sig. (2-tailed)
.000
N
440
440
In each of the subgroups of student achievement versus ADM of the schools
studied, a positive, significant correlation was indicated at p<0.01 level. That is, the
larger the ADM, the greater percentages of students scoring Proficient and Advanced on
PACT English/language arts and mathematics.
Partial Correlation Analysis Controlling for Poverty Index
Then, a partial correlation was run on the same data sets to control for the
possible effects of poverty. Partial correlation is a statistical procedure used to examine
a relationship between two variables while controlling the effect of a third variable
which may affect the relationship of the other two (Harris, 1995). In each of the
previous studies conducted in South Carolina, poverty was identified as the variable that
affected the relationship between school enrollment and student achievement
(Stevenson, 1996, 2001; Durbin, 2001; Crenshaw, 2003; McCathern, 2004; Carpenter,
2006; Kaczor, 2006; Maxey, 2008). Therefore, the researcher considered it critical to
run the data again, but “partialing” out the effects of poverty.
117
In all six recalculations, when controlling for poverty, no significant correlations
between student achievement and ADM were found. Tables 4.11 through 4.16 present
the outcomes of the partial correlation analysis for each data set while controlling for
poverty. The data tended to indicate a negative correlation between student
achievement and ADM; however, no statistical significance was found.
Table 4.11
Partial Correlation of Third Grade 2007-2008 PACT English/Language Arts versus
135-Day Average Daily Membership While Controlling for Poverty Index
English/Language
Arts % Met
Standard
135-Day
Average Daily
Membership
(ADM)
Correlation
1.000
-.017
Significance
(2-tailed)
.
.723
df
0
438
Correlation
-.017
1.000
Significance
(2-tailed)
.723
.
df
438
0
Control Variables
English/Language
Arts % Met
Standard
Poverty
Index
135-Day Average
Daily
Membership
(ADM)
Table 4.12
Partial Correlation of Third Grade 2007-2008 PACT Mathematics versus
135-Day Average Daily Membership While Controlling for Poverty Index
Mathematics
% Met
Standard
135-Day
Average Daily
Membership
(ADM)
Correlation
1.000
-.025
Significance
(2-tailed)
.
.598
df
0
438
Correlation
-.025
1.000
Significance
(2-tailed)
.598
.
df
438
0
Control Variables
Mathematics
% Met
Standard
Poverty Index
135-Day
Average Daily
Membership
(ADM)
118
Table 4.13
Partial Correlation of Fourth Grade 2007-2008 PACT English/Language Arts versus
135-Day Average Daily Membership While Controlling for Poverty Index
135-Day
English/Language
Average Daily
Control Variables
Arts % Met
Membership
Standard
(ADM)
English/Language
Arts % Met
Standard
Poverty
Index
135-Day Average
Daily
Membership
(ADM)
Correlation
1.000
-.089
Significance
(2-tailed)
.
.062
df
0
438
Correlation
-.089
1.000
Significance
(2-tailed)
.062
.
df
438
0
Table 4.14
Partial Correlation of Fourth Grade 2007-2008 PACT Mathematics versus
135-Day Average Daily Membership While Controlling for Poverty Index
135-Day
Mathematics
Average Daily
Control Variables
% Met
Membership
Standard
(ADM)
Mathematics
% Met
Standard
Correlation
1.000
-.059
Significance
(2-tailed)
.
.219
df
0
438
135-Day
Average Daily
Membership
(ADM)
Correlation
-.059
1.000
Significance
(2-tailed)
.219
.
df
438
0
Poverty Index
119
Table 4.15
Partial Correlation of Fifth Grade 2007-2008 PACT English/Language Arts versus
135-Day Average Daily Membership While Controlling for Poverty Index
135-Day
English/Language
Average Daily
Control Variables
Arts % Met
Membership
Standard
(ADM)
English/Language
Arts % Met
Standard
Poverty
Index
135-Day Average
Daily
Membership
(ADM)
Correlation
1.000
-.035
Significance
(2-tailed)
.
.468
df
0
437
Correlation
-.035
1.000
Significance
(2-tailed)
.468
.
df
437
0
Table 4.16
Partial Correlation of Fifth Grade 2007-2008 PACT Mathematics versus
135-Day Average Daily Membership While Controlling for Poverty Index
135-Day
Mathematics
Average Daily
Control Variables
% Met
Membership
Standard
(ADM)
Mathematics
% Met
Standard
Correlation
1.000
-.069
Significance
(2-tailed)
.
.149
df
0
437
135-Day
Average Daily
Membership
(ADM)
Correlation
-.069
1.000
Significance
(2-tailed)
.149
.
df
437
0
Poverty Index
Stepwise Multiple Regression Analysis
The researcher then analyzed the data by running a stepwise multiple regression
for the data set, again comparing student achievement in PACT English/language arts
and mathematics and ADM at each grade level. The stepwise regression was conducted
to ascertain whether one, both, or neither independent variable was predictive of
student achievement. As was the case with the earlier partial correlation analyses, ADM
120
was not significantly correlated to student achievement – positively or negatively at any
grade level for either subject.
The data did reveal significant correlations between student achievement and
poverty. For third grade English/language arts, the correlation between student
achievement and poverty index was 0.549, significant at the p<0.01 level (see Table
4.17). In the same grade, but with mathematics student achievement data, the
correlation with SES was 0.651, significant at the p<0.01 level (see Table 4.18).
Table 4.17
Stepwise Multiple Regression of Third Grade 2007-2008 PACT English/Language
Arts versus Poverty Index and 135-Day Average Daily Membership Variables
Model
R
1
.549a
a. Predictors: (Constant), Poverty Index
R Square
Adjusted R
Square
Sig. F
Change
.301
.300
.000
Table 4.18
Stepwise Multiple Regression of Third Grade 2007-2008 PACT Mathematics
versus Poverty Index and 135-Day Average Daily Membership Variables
Model
1
R
R Square
Adjusted R
Square
Sig. F
Change
.651a
.424
.423
.000
a. Predictors: (Constant), Poverty Index
The stepwise multiple regression analysis run for fourth grade English/language
arts performance data, produced a correlation with poverty index of 0.623, significant
at the p<0.01 level (see Table 4.19). For mathematics in the same grade, the outcome
of the stepwise multiple regression revealed a correlation with poverty of 0.645, again
significant at the p<0.01 level (see Table 4.20).
121
Table 4.19
Stepwise Multiple Regression of Fourth Grade 2007-2008 PACT
English/Language Arts versus Poverty Index and 135-Day Average Daily
Membership Variables
Model
1
R
R Square
Adjusted R
Square
Sig. F
Change
.623a
.388
.386
.000
a. Predictors: (Constant), Poverty Index
Table 4.20
Stepwise Multiple Regression of Fourth Grade 2007-2008 PACT Mathematics
versus Poverty Index and 135-Day Average Daily Membership Variables
Model
1
R
R Square
Adjusted R
Square
Sig. F
Change
.645a
.417
.415
.000
a. Predictors: (Constant), Poverty Index
Finally, the stepwise multiple regression analysis of fifth grade student
achievement performance data on PACT English/language arts, ADM and poverty index,
showed a significant correlation between student achievement and poverty index of
0.666 at the p<0.01 level (see Table 4.21). Analysis of mathematics performance data
for fifth grade revealed a significant correlation of 0.614 at the p<0.01 level with SES
(see Table 4.22).
Table 4.21
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT
English/Language Arts versus Poverty Index and 135-Day Average Daily
Membership Variables
Model
1
R
R Square
Adjusted R
Square
Sig. F
Change
.666a
.443
.442
.000
a. Predictors: (Constant), Poverty Index
122
Table 4.22
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT Mathematics
versus Poverty Index and 135-Day Average Daily Membership Variables
Model
1
R
R Square
Adjusted R
Square
Sig. F
Change
.614a
.377
.376
.000
a. Predictors: (Constant), Poverty Index
In sum, the analysis of the stepwise multiple regression data across grades and
subjects studied revealed a significant correlation between poverty index and student
achievement. The relationship is a negative one in each case. The negative correlation
indicates that as the poverty index of the school increased, the percentage of students
scoring Proficient and Advanced decreased in English/language arts and in mathematics
in third grade, fourth grade, and fifth grade.
Findings for Research Question Two
The second research question was as follows:
Does a relationship exist between the school size in South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and
student achievement in English/language arts and mathematics as
defined by the results of the third, fourth, and fifth grade 2007-2008
Palmetto Achievement Challenge Test scores when schools are grouped
by poverty level of schools? Achievement is defined as the percentage of
students scoring Proficient and Advanced.
Description of Schools within Poverty Index Strata
For the second research question, the researcher plotted the 441 public
elementary schools versus school size and also poverty index to ascertain whether
123
natural groups or strata existed. No obvious groupings or strata were identified. As a
result, the researcher grouped the schools with approximately the same number of
schools per strata. The poverty index strata with number of schools are as follows: 0% 49% (63 schools); 50% - 59% (48 schools); 60% - 69% (73 schools); 70% - 79% (71
school); 80% - 89% (75 schools); 90% - 94% (54 schools); 95% - 100% (57 schools). The
purpose of the poverty index strata was to control for the effects of poverty when
analyzing whether a relationship exists between student achievement and ADM.
In Strata 1 (0% - 49%), the lowest enrollment was 108.0 students and the highest
was 1,253.0 students with a mean size of 722.9. The standard deviation for the ADM
was 240.5. The poverty index range for the schools in this strata were from a low of
9.5% to a high of 49.9%. The mean poverty index was 35.3% with the standard
deviation 10.2 (see Table 4.23).
Table 4.23
Descriptive Statistics for Strata 1 (0% - 49%) PreKindergarten – 5 and Kindergarten – 5
Elementary Schools of 2007-2008 Poverty Index and 135-Day Average Daily Membership
Variables
Std.
N
Range
Minimum Maximum
Mean
Deviation
Poverty
63.0
40.4
9.5
49.9
35.3
10.2
Index
135-Day
Average
Daily
63.0
1145.0
108.0
1253.0
722.9
240.5
Membership
(ADM)
Student achievement was defined as the percentage of students scoring
Proficient and Advanced in English/language arts (ELA) and mathematics on the 20072008 Palmetto Achievement Challenge Test (PACT). For third grade students scoring
Proficient and Advanced on PACT English/language arts, the lowest percentage was
124
81.8%, the highest percentage was 100.0%, and the mean was 93.6%. The standard
deviation was 4.4. For mathematics, the lowest percentage was 75.6%, the highest
percentage was 99.0%, and the mean was 89.4%. The standard deviation was 4.7 (see
Table 4.24).
Table 4.24
Descriptive Statistics of Strata 1 (0% - 49%) Third Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
63.0
18.2
81.8
100.0
93.6
4.4
Arts % Met
Standard
Mathematics %
63.0
23.4
75.6
99.0
89.4
4.7
Met Standard
For fourth grade within this strata, analysis of the percentage of students scoring
Proficient and Advanced on English/language arts revealed a low percentage of 76.6%,
the high percentage of 98.9%, and the mean was 91.6%. The standard deviation was
5.1. For mathematics, the lowest percentage was 77.4%, the highest percentage was
100.0%, the median was 92.1% and the mean was 91.2%. The standard deviation was
4.7 (see Table 4.25).
Table 4.25
Descriptive Statistics of Strata 1 (0% - 49%) Fourth Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
63.0
22.3
76.6
98.9
91.6
5.1
Arts % Met
Standard
Mathematics %
63.0
22.6
77.4
100.0
91.2
4.7
Met Standard
Student achievement data for fifth grade in this Strata 1 (0% - 49%) for
English/language arts indicated the lowest percentage of students scoring Proficient and
Advanced was 77.8%, the highest percentage was 100.0%, and the mean was 89.4%.
125
The standard deviation was 5.2. For mathematics, the lowest percentage was 75.0%,
the highest percentage was 99.1%, the median was 88.5% and the mean was 88.9%.
The standard deviation was 5.3 (see Table 4.26).
Table 4.26
Descriptive Statistics of Strata 1 (0% - 49%) Fifth Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
63.0
22.2
77.8
100.0
89.4
5.2
Standard
Mathematics %
Met Standard
63.0
24.1
75.0
99.1
88.9
5.3
In Strata 2 (50% - 59%), the number of schools was 48. The lowest enrollment
was 283.0 students and the highest was 1,101.0 students, with the mean ADM of 688.4.
The standard deviation for the ADM for schools was 181.1. The poverty index range for
the schools was a low of 50.1% and high of 59.9%. The median poverty index was 55.9%
with the standard deviation 3.0 (see Table 4.27).
Table 4.27
Descriptive Statistics for Strata 2 (50% - 59%) PreKindergarten – 5 and Kindergarten – 5
Elementary Schools of 2007-2008 Poverty Index and 135-Day Average Daily Membership
Variables
Std.
N
Range
Minimum Maximum
Mean
Deviation
Poverty
48.0
9.8
50.1
59.9
55.4
3.0
Index
135-Day
Average
Daily
48.0
818.0
283.0
1101.0
688.4
181.1
Membership
(ADM)
Student achievement was defined as the percentage of students scoring
Proficient and Advanced in English/language arts (ELA) and mathematics on the 2007-
126
2008 Palmetto Achievement Challenge Test (PACT). For third grade students scoring
Proficient and Advanced on PACT English/language arts, the lowest percentage was
79.4%, the highest percentage was 99.2%, and the mean was 90.6%. The standard
deviation was 4.5. For mathematics, the lowest percentage was 65.1%, the highest
percentage was 95.3%, and the mean was 83.6%. The standard deviation was 7.3 (see
Table 4.28).
Table 4.28
Descriptive Statistics of Strata 2 (50% - 59%) Third Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
48.0
19.8
79.4
99.2
90.6
4.5
Standard
Mathematics %
48.0
30.2
65.1
95.3
83.6
7.3
Met Standard
For fourth grade, the researcher found the descriptive data for the percentage of
students scoring Proficient and Advanced in English/language arts. Analysis of the data
revealed a low percentage of 71.6%%, a high percentage of 97.1%, and the mean was
86.3%. The standard deviation was 5.6. For mathematics, the lowest percentage was
70.3%, the highest percentage was 93.9%, and the mean was 84.1%. The standard
deviation was 6.1 (see Table 4.29).
Table 4.29
Descriptive Statistics of Strata 2 (50% - 59%) Fourth Grade 2007-2008 PACT
English/Language Arts and Mathematics Data
English/Language
Arts % Met
Standard
Mathematics %
Met Standard
N
Range
Minimum
Maximum
Mean
Std.
Deviation
48.0
25.5
71.6
97.1
86.3
5.6
48.0
23.6
70.3
93.9
84.1
6.0
127
Student achievement data for fifth grade in Strata 2 (50% - 59%) for
English/language arts indicated the lowest percentage scoring Proficient and Advanced
was 66.7%, the highest percentage was 98.3%, and the mean was 84.0%. The standard
deviation was 6.3. For mathematics, the lowest percentage was 53.1%, the highest
percentage was 97.5%, the median was 82.1% and the mean was 81.7%. The standard
deviation was 8.4 (see Table 4.30).
Table 4.30
Descriptive Statistics of Strata 2 (50% - 59%) Fifth Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
N
Range
Minimum Maximum
Mean
Std. Deviation
English/Language
Arts % Met
48.0
31.6
66.7
98.3
84.0
6.3
Standard
Mathematics %
48.0
44.4
53.1
97.5
81.7
8.4
Met Standard
In Strata 3 (60% - 69%), the number of schools was 73. The lowest enrollment
was 100.0 students and the highest was 939.0 students with a mean enrollment of
590.0. The standard deviation for the ADM in this strata was 181.5. The poverty index
range for the schools was a low of 60.1% and high of 69.8%. The mean poverty index
was 64.4% with the standard deviation 2.9 (see Table 4.31).
Table 4.31
Descriptive Statistics for Strata 3 (60% - 69%) PreKindergarten – 5 and Kindergarten – 5
Elementary Schools of 2007-2008 Poverty Index and 135-Day Average Daily Membership
Variables
Std.
N
Range
Minimum Maximum
Mean
Deviation
Poverty
73.0
9.7
60.1
69.8
64.4
2.9
Index
135-Day
Average
Daily
73.0
839.0
100.0
939.0
590.0
181.5
Membership
(ADM)
128
In Strata 3 (60% - 69%), students scoring Proficient and Advanced in
English/language arts indicated a low percentage of 75.0%, a high percentage of 100.0%,
and a mean percentage of 89.3%. The standard deviation was 5.8. For mathematics,
the lowest percentage was 62.6%, the highest percentage was 99.0%, the median was
82.3% and the mean was 82.5%. The standard deviation was 7.1 (see Table 4.32).
Table 4.32
Descriptive Statistics of Strata 3 (60% - 69%) Third Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
73.0
25.0
75.0
100.0
89.3
5.8
Standard
Mathematics %
73.0
36.4
62.6
99.0
82.5
7.1
Met Standard
For fourth grade within this strata, the researcher found the descriptive data for
the percentage of students scoring Proficient and Advanced in English/language arts at
included schools on the 2007-2008 Palmetto Achievement Challenge Test. Analysis of
the data revealed the lowest percentage was 63.6%, the highest percentage was
100.0%, and the mean was 83.9%. The standard deviation was 7.4. For mathematics,
the lowest percentage was 54.5%, the highest percentage was 100.0%, the median was
82.5% and the mean was 82.7%. The standard deviation was 8.3 (see Table 4.33).
Table 4.33
Descriptive Statistics of Strata 3 (60% - 69%) Fourth Grade 2007-2008 PACT
English/Language Arts and Mathematics Data
English/Language
Arts % Met
Standard
Mathematics %
Met Standard
N
Range
Minimum
Maximum
Mean
Std.
Deviation
73.0
36.4
63.6
100.0
83.9
7.4
73.0
45.5
54.5
100.0
82.7
8.3
129
Student achievement data for fifth grade in Strata 3 (60% - 69%) for
English/language arts indicated the lowest percentage scoring Proficient and Advanced
was 50.0%, the highest percentage was 100.0%, and the mean was 81.6%. The standard
deviation was 8.8. For mathematics, the lowest percentage was 58.3%, the highest
percentage was 96.9%, the median was 83.3% and the mean was 82.3%. The standard
deviation was 8.1 (see Table 4.34).
Table 4.34
Descriptive Statistics of Strata 3 (60% - 69%) Fifth Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
73.0
50.0
50.0
100.0
81.6
8.8
Standard
Mathematics %
73.0
38.6
58.3
96.9
82.3
8.1
Met Standard
In Strata 4 (70% - 79%), the number of schools was 71. The lowest ADM was
132.0 students and the highest was 1,123.0 students with the mean enrollment 537.0.
The standard deviation for the ADM was 176.0. The poverty index range for the schools
was a low of 70.2% and high of 79.9%. The mean Poverty Index was 75.4% with the
standard deviation 3.0 (see Table 4.35).
Table 4.35
Descriptive Statistics for Strata 4 (70% - 79%) PreKindergarten – 5 and Kindergarten – 5
Elementary Schools of 2007-2008 Poverty Index and 135-Day Average Daily Membership
Variables
Std.
N
Range
Minimum Maximum
Mean
Deviation
Poverty
71.0
9.7
70.2
79.9
75.4
3.0
Index
135-Day
Average
Daily
71.0
991.0
132.0
1123.0
537.0
176.0
Membership
(ADM)
130
Student achievement was defined as the percentage of students scoring
Proficient and Advanced in English/language arts (ELA) and mathematics on the 20072008 Palmetto Achievement Challenge Test (PACT). For third grade students scoring
Proficient and Advanced on PACT English/language arts, the lowest percentage was
68.6%, the highest percentage was 98.3%, and the mean was 86.5%. The standard
deviation was 6.1. For mathematics, the lowest percentage was 34.8%, the highest
percentage was 96.7%, the median was 77.1% and the mean was 77.2%. The standard
deviation was 9.7 (see Table 4.36).
Table 4.36
Descriptive Statistics of Strata 4 (70% - 79%) Third Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
71.0
29.7
68.6
98.3
86.5
6.1
Standard
Mathematics %
71.0
61.9
34.8
96.7
77.2
9.7
Met Standard
For fourth grade, the researcher found the descriptive data for the percentage of
students scoring Proficient and Advanced in English/language arts at included schools on
the 2007-2008 PACT. Analysis of the percentage of students scoring Proficient and
Advanced on English/language arts revealed a low percentage of 66.0%, a high
percentage of 95.2%, and the mean was 81.6%. The standard deviation was 6.9. For
mathematics, the lowest percentage was 61.8%, the highest percentage was 94.4%, the
median was 79.7% and the mean was 79.3%. The standard deviation was 7.4 (see Table
4.37).
131
Table 4.37
Descriptive Statistics of Strata 4 (70% - 79%) Fourth Grade 2007-2008 PACT
English/Language Arts and Mathematics Data
English/Language
Arts % Met
Standard
Mathematics %
Met Standard
N
Range
Minimum
Maximum
Mean
Std.
Deviation
71.0
29.2
66.0
95.2
81.6
6.9
71.0
32.6
61.8
94.4
79.3
7.4
Student achievement data for fifth grade in Strata 4 (70% - 79%) for
English/language arts indicated the lowest percentage of students scoring Proficient and
Advanced was 52.5%, the highest percentage was 93.7%, and the mean was 77.3%. The
standard deviation was 8.8. For mathematics, the lowest percentage was 63.3%, the
highest percentage was 94.9%, the median was 77.6% and the mean was 78.1%. The
standard deviation was 7.4 (see Table 4.38).
Table 4.38
Descriptive Statistics of Strata 4 (70% - 79%) Fifth Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
71.0
41.2
52.5
93.7
77.3
8.8
Standard
Mathematics %
71.0
31.6
63.3
94.9
78.1
7.4
Met Standard
In Strata 5 (80% - 89%), the number of schools was 75. The lowest ADM was
135.0 students and the highest was 964.0 students with the mean enrollment of 512.3.
The standard deviation for the school size was 168.7. The poverty index range for the
schools in this strata was a low of 80.0% and high of 89.8%. The median poverty index
was 85.7% with a standard deviation 2.8 (see Table 4.39).
132
Table 4.39
Descriptive Statistics for Strata 5 (80% - 89%) PreKindergarten – 5 and Kindergarten – 5
Elementary Schools of 2007-2008 Poverty Index and 135-Day Average Daily Membership
Variables
Std.
N
Range
Minimum Maximum
Mean
Deviation
Poverty
75.0
9.8
80.0
89.8
85.3
2.8
Index
135-Day
Average
Daily
75.0
829.0
135.0
964.0
512.3
168.7
Membership
(ADM)
Student achievement was defined as the percentage of students scoring
Proficient and Advanced in English/language arts (ELA) and mathematics on the 20072008 Palmetto Achievement Challenge Test (PACT). For third grade students scoring
Proficient and Advanced on PACT English/language arts, the lowest percentage was
66.7%, the highest percentage was 100.0%, and the mean was 83.9%. The standard
deviation was 7.0. For mathematics, the lowest percentage was 48.4%, the highest
percentage was 92.8%, the median was 71.6% and the mean was 71.6%. The standard
deviation was 10.3 (see Table 4.40).
Table 4.40
Descriptive Statistics of Strata 5 (80% - 89%) Third Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
75.0
33.3
66.7
100.0
83.9
7.0
Standard
Mathematics %
75.0
44.4
48.4
92.8
71.6
10.3
Met Standard
For fourth grade, the researcher found the descriptive data for the percentage of
students scoring Proficient and Advanced in English/language arts at included schools on
the 2007-2008 PACT. Analysis of the percentage of students scoring Proficient and
133
Advanced on English/language arts revealed a low percentage of 54.7%, a high
percentage of 100.0%, and a mean of 77.2%. The standard deviation was 9.4. For
mathematics, the lowest percentage was 48.4%, the highest percentage was 94.8%, the
median was 77.6% and the mean was 75.8%. The standard deviation was 11.1 (see
Table 4.41).
Table 4.41
Descriptive Statistics of Strata 5 (80% - 89%) Fourth Grade 2007-2008 PACT
English/Language Arts and Mathematics Data
English/Language
Arts % Met
Standard
Mathematics %
Met Standard
N
Range
Minimum
Maximum
Mean
Std.
Deviation
75.0
45.3
54.7
100.0
77.2
9.4
75.0
46.4
48.4
94.8
75.8
11.1
Student achievement data for fifth grade in Strata 5 (0% - 49%) for
English/language arts indicated the lowest percentage of students scoring Proficient and
Advanced was 52.5%, the highest percentage was 100.0%, and the mean was 73.7%.
The standard deviation was 9.9. For mathematics, the lowest percentage was 45.2%,
the highest percentage was 94.3%, the median was 76.2% and the mean was 75.5%.
The standard deviation was 11.1 (see Table 4.42).
Table 4.42
Descriptive Statistics of Strata 5 (80% - 89%) Fifth Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
75.0
47.5
52.5
100.0
73.7
9.9
Standard
Mathematics %
75.0
49.1
45.2
94.3
75.5
11.1
Met Standard
134
In Strata 6 (90% - 94%), the number of schools was 54. The lowest ADM was
135.0 students and the highest was 661.0 students with the mean ADM of 415.1. The
standard deviation for the school size was 127.4. The poverty index range for the
schools was a low of 90.2% and high of 94.8%. The mean poverty index was 92.7% with
a standard deviation of 1.5 (see Table 4.43).
Table 4.43
Descriptive Statistics for Strata 6 (90% - 94%) PreKindergarten – 5 and Kindergarten – 5
Elementary Schools of 2007-2008 Poverty Index and 135-Day Average Daily Membership
Variables
Std.
N
Range
Minimum Maximum
Mean
Deviation
Poverty
54.0
4.6
90.2
94.8
92.7
1.5
Index
135-Day
Average
Daily
54.0
526.0
135.0
661.0
415.1
127.4
Membership
(ADM)
Student achievement was defined as the percentage of students scoring
Proficient and Advanced in English/language arts (ELA) and mathematics on the 20072008 Palmetto Achievement Challenge Test (PACT). For third grade students scoring
Proficient and Advanced on PACT English/language arts, the lowest percentage was
58.7%, the highest percentage was 98.1%, and the mean was 80.8%. The standard
deviation was 8.0. For mathematics, the lowest percentage was 38.7%, the highest
percentage was 94.0%, the median was 65.9% and the mean was 66.2%. The standard
deviation was 12.8 (see Table 4.44).
135
Table 4.44
Descriptive Statistics of Strata 6 (90% - 94%) Third Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
54.0
39.4
58.7
98.1
80.8
8.0
Arts % Met
Standard
Mathematics %
54.0
55.3
38.7
94.0
66.2
12.8
Met Standard
For fourth grade, the researcher found the descriptive data for the percentage of
students scoring Proficient and Advanced in English/language arts at included schools on
the 2007-2008 PACT. Analysis of the percentage of students scoring Proficient and
Advanced on English/language arts revealed a low percentage of 53.0%, a high
percentage of 100.0%, and a mean of 72.8%. The standard deviation was 10.5. For
mathematics, the lowest percentage was 45.6%, the highest percentage was 92.0%, the
median was 67.5% and the mean was 67.9%. The standard deviation was 11.5 (see
Table 4.45).
Table 4.45
Descriptive Statistics of Strata 6 (90% - 94%) Fourth Grade 2007-2008 PACT
English/Language Arts and Mathematics Data
English/Language
Arts % Met
Standard
Mathematics %
Met Standard
N
Range
Minimum
Maximum
Mean
Std.
Deviation
54.0
47.0
53.0
100.0
72.8
10.5
54.0
46.4
45.6
92.0
67.9
11.5
Student achievement data for fifth grade in Strata 6 (90% - 94%) for
English/language arts indicated the lowest percentage of students scoring Proficient and
Advanced was 90.9%, the highest percentage was 90.9% and the mean was 68.2%. The
standard deviation was 10.9. For mathematics, the lowest percentage was 47.2%, the
136
highest percentage was 90.5%, the median was 69.3% and the mean was 69.0%. The
standard deviation was 10.4 (see Table 4.46).
Table 4.46
Descriptive Statistics of Strata 6 (90% - 94%) Fifth Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
54.0
47.7
43.2
90.9
68.2
10.9
Standard
Mathematics %
54.0
43.3
47.2
90.5
69.0
10.4
Met Standard
In Strata 7 (95% - 100%), the number of schools was 57. The lowest ADM was
103.0 students and the highest was 693.0 students with the mean school size 387.3.
The standard deviation for the school size was 136.5. The poverty index range for the
schools was a low of 95.1% and high of 99.2%. The mean Poverty Index was 97.4% a
standard deviation of 1.1 (see Table 4.47).
Table 4.47
Descriptive Statistics for Strata 7 (95% - 100%) PreKindergarten – 5 and Kindergarten – 5
Elementary Schools of 2007-2008 Poverty Index and 135-Day Average Daily Membership
Variables
Std.
N
Range
Minimum Maximum
Mean
Deviation
Poverty
57.0
4.1
95.1
99.2
97.4
1.1
Index
135-Day
Average
Daily
57.0
590.0
103.0
693.0
387.3
136.5
Membership
(ADM)
Student achievement was defined as the percentage of students scoring
Proficient and Advanced in English/language arts (ELA) and mathematics on the 20072008 Palmetto Achievement Challenge Test (PACT). For third grade students scoring
Proficient and Advanced on PACT English/language arts, the lowest percentage was
137
50.0%, the highest percentage was 100.0%, and the mean was 78.9%. The standard
deviation was 11.5. For mathematics, the lowest percentage was 28.3%, the highest
percentage was 95.0%, the median was 60.6% and the mean was 59.9%. The standard
deviation was 16.0 (see Table 4.48).
Table 4.48
Descriptive Statistics of Strata 7 (94% - 100%) Third Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
57.0
50.0
50.0
100.0
78.9
11.5
Arts % Met
Standard
Mathematics %
57.0
66.7
28.3
95.0
59.9
16.0
Met Standard
For fourth grade, the researcher found the descriptive data for the percentage of
students scoring Proficient and Advanced in English/language arts at included schools on
the 2007-2008 PACT. Analysis of the percentage of students scoring Proficient and
Advanced on English/language arts revealed a low percentage of 41.4%, a high
percentage of 96.2%, and a mean of 66.9%. The standard deviation was 14.0. For
mathematics, the lowest percentage was 35.0%, the highest percentage was 93.5%, the
median was 60.3% and the mean was 62.2%. The standard deviation was 14.6 (see
Table 4.49).
Table 4.49
Descriptive Statistics of Strata 7 (94% - 100%) Fourth Grade 2007-2008 PACT
English/Language Arts and Mathematics Data
English/Language
Arts % Met
Standard
Mathematics %
Met Standard
N
Range
Minimum
Maximum
Mean
Std.
Deviation
57.0
54.8
41.4
96.2
66.9
14.0
57.0
58.5
35.0
93.5
62.2
14.6
138
Student achievement data for fifth grade in Strata 7 (95% - 100%) for
English/language arts indicated the lowest percentage of students scoring Proficient and
Advanced was 41.9%, the highest percentage was 88.0%, and the mean was 62.2%. The
standard deviation was 10.9. For mathematics, the lowest percentage was 34.0%, the
highest percentage was 100.0%, the median was 60.8% and the mean was 62.3%. The
standard deviation was 13.4 (see Table 4.50).
Table 4.50
Descriptive Statistics of Strata 7 (94% - 100%) Fifth Grade 2007-2008 PACT English/Language
Arts and Mathematics Data
Std.
N
Range
Minimum Maximum
Mean
Deviation
English/Language
Arts % Met
56.0
46.1
41.9
88.0
62.2
10.9
Standard
Mathematics %
56.0
66.0
34.0
100.0
62.3
13.4
Met Standard
Pearson Correlation Analysis Within Poverty Index Strata
The researcher then conducted a Pearson correlation analysis of the data in each
poverty index strata, comparing student achievement (percentage of students scoring
Proficient and Advanced on PACT English/language arts and mathematics) to ADM.
Analysis was performed for the third, fourth, and fifth grades individually. The
percentages of students scoring Proficient and Advanced were the outcome measures
used. The significance level as was set at p<0.05. The tables were created within the
PASW Statistics Base 18 software program used to conduct the analysis for this study.
The Pearson correlation analysis of student achievement to ADM yielded six
subsets of significant correlations out of forty-two subsets. By poverty index strata,
139
student achievement subject areas for which significant correlations were found with
school size are as follows:
•
Strata 4 (70% - 79%): Fourth Grade 2007-2008 PACT English/Language Arts –
-0.287 (see Table 4.51).
Table 4.51
Correlation of Strata 4 (70% - 79%) Fourth Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership
135-Day
English/Language
Average
Arts % Met
Daily
Standard
Membership
(ADM)
Pearson
1
-.287*
English/Language Correlation
Sig. (2Arts % Met
.015
tailed)
Standard
N
71
71
Pearson
*
1
-.287
135-Day Average Correlation
Daily
Sig. (2.015
Membership
tailed)
(ADM)
N
71
71
*. Correlation is significant at the 0.05 level (2-tailed).
•
Strata 6 (90% - 94%): Fourth Grade 2007-2008 PACT English/Language Arts –
-0.301 (see Table 4.52).
140
Table 4.52
Correlation of Strata 6 (90% - 95%) Fourth Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership
135-Day
English/Language
Average
Arts % Met
Daily
Standard
Membership
(ADM)
Pearson
1
-.301*
Correlation
English/Language
Sig. (2Arts % Met
.027
tailed)
Standard
N
54
54
Pearson
1
-.301*
135-Day Average Correlation
Daily
Sig. (2.027
Membership
tailed)
(ADM)
N
54
54
*. Correlation is significant at the 0.05 level (2-tailed).
•
Strata 6 (90% - 94%): Fifth Grade 2007-2008 PACT Mathematics – -0.332 (see
Table 4.53).
Table 4.53
Correlation of Strata 6 (90% - 95%) Fifth Grade 2007-2008 PACT
Mathematics versus 135-Day Average Daily Membership
135-Day
Mathematics
Average Daily
% Met
Membership
Standard
(ADM)
Pearson
1
-.332*
Correlation
Mathematics %
Sig. (2-tailed)
.014
Met Standard
135-Day Average
Daily
Membership
(ADM)
N
Pearson
Correlation
54
54
*
-.332
Sig. (2-tailed)
.014
N
54
1
54
*. Correlation is significant at the 0.05 level (2-tailed).
•
Strata 7 (95% - 100%): Third Grade 2007-2008 PACT English/Language Arts –
-0.389 (see Table 4.54).
141
Table 4.54
Correlation of Strata 7 (95% - 100%) Third Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership
135-Day
English/Language
Average
Arts % Met
Daily
Standard
Membership
(ADM)
Pearson
1
-.389**
Correlation
English/Language
Sig. (2Arts % Met
.003
tailed)
Standard
N
57
57
Pearson
1
-.389**
135-Day Average Correlation
Daily
Sig. (2.003
Membership
tailed)
(ADM)
N
57
57
**. Correlation is significant at the 0.01 level (2-tailed).
•
Strata 7 (95% - 100%): Fourth Grade 2007-2008 PACT English/Language Arts –
-0.322 (see Table 4.55).
Table 4.55
Correlation of Strata 7 (95% - 100%) Fourth Grade 2007-2008
PACT English/Language Arts versus 135-Day Average Daily
Membership
135-Day
English/Language
Average
Arts % Met
Daily
Standard
Membership
(ADM)
Pearson
1
-.322*
English/Language Correlation
Sig. (2Arts % Met
.015
tailed)
Standard
N
57
57
Pearson
1
-.322*
135-Day Average Correlation
Daily
Sig. (2.015
Membership
tailed)
(ADM)
N
57
57
*. Correlation is significant at the 0.05 level (2-tailed).
•
Strata 7 (95% - 100%): Fifth Grade 2007-2008 PACT English/Language Arts –
142
-0.265 (see Table 4.56).
Table 4.56
Correlation of Strata 7 (95% - 100%) Fifth Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership
135-Day
English/Language
Average
Arts % Met
Daily
Standard
Membership
(ADM)
Pearson
1
-.265*
English/Language Correlation
Sig. (2Arts % Met
.049
tailed)
Standard
N
56
56
Pearson
-.265*
1
135-Day Average Correlation
Daily
Sig. (2.049
Membership
tailed)
(ADM)
N
56
57
Each of the six significant correlations indicated a negative relationship. In a
correlation, a negative correlation is indicative of an inverse relationship. For schools
within each of the noted poverty index strata, as the ADM of the school increased, the
likelihood that students would score Proficient or Advanced on PACT in
English/language arts or in mathematics decreased. The remaining subgroup analyses
demonstrated no significant correlation. All six significant correlations were in the
strata with schools with greater student poverty. Four of the significant correlations
were in strata of schools with the highest poverty in the state.
Partial Correlation Analysis Within Poverty Index Strata
Following the Pearson correlation analysis, the researcher conducted a partial
correlation analysis to control for poverty within each poverty index strata. Previous
research in South Carolina has demonstrated the effect of poverty to be as high as sixtythree percent for English/language arts and sixty percent for mathematics (Carpenter,
143
2006). As a result, the researcher analyzed the data using a partial correlation analysis.
The researcher ran the partial correlation in each poverty index strata for third grade,
fourth grade, and fifth grade results for PACT English/language arts and mathematics
and public elementary school size, while controlling for the poverty index. The purpose
of partialing out the poverty index within each poverty index strata is to ascertain its
effect on student achievement. The outcomes of the partial correlation analysis within
the seven poverty index strata (forty-two total subsets) revealed no significant
correlations except for six subsets. The six subsets which indicated a significant
correlation between school size and student achievement are listed in Tables 4.57
through 4.62. No pattern was observed among the six subsets; however, all six subsets
indicated negative relationships. The results of the partial correlation between student
achievement and ADM while controlling for poverty index within poverty index strata
confirmed previous studies in South Carolina: ADM has no significant relationship to
student achievement.
Table 4.57
Partial Correlation of Strata 7 (95% - 100%) Third Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership while
controlling for Poverty Index
135-Day
English/Language
Average Daily
Control Variables
Arts % Met
Membership
Standard
(ADM)
Poverty
Index
English/Language
Arts % Met
Standard
Correlation
1.000
-.376
Significance
(2-tailed)
.
.004
df
0
54
135-Day Average
Daily
Membership
(ADM)
Correlation
-.376
1.000
Significance
(2-tailed)
.004
.
df
54
0
144
Table 4.58
Partial Correlation of Strata 1 (0% - 49%) Fourth Grade 2007-2008 PACT
Mathematics versus 135-Day Average Daily Membership while
controlling for Poverty Index
Mathematics
% Met
Standard
135-Day
Average Daily
Membership
(ADM)
Correlation
1.000
-.262
Significance
(2-tailed)
.
.040
df
0
60
Correlation
-.262
1.000
Significance
(2-tailed)
.040
.
df
60
0
Control Variables
Mathematics
% Met
Standard
Poverty Index
135-Day
Average Daily
Membership
(ADM)
Table 4.59
Partial Correlation of Strata 4 (70% - 79%) Fourth Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership while
controlling for Poverty Index
135-Day
English/Language
Average Daily
Control Variables
Arts % Met
Membership
Standard
(ADM)
English/Language
Arts % Met
Standard
Poverty
Index
135-Day Average
Daily
Membership
(ADM)
Correlation
1.000
-.275
Significance
(2-tailed)
.
.021
df
0
68
Correlation
-.275
1.000
Significance
(2-tailed)
.021
.
df
68
0
145
Table 4.60
Partial Correlation of Strata 6 (90% - 94%) Fourth Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership while
controlling for Poverty Index
135-Day
English/Language
Average Daily
Control Variables
Arts % Met
Membership
Standard
(ADM)
English/Language
Arts % Met
Standard
Poverty
Index
135-Day Average
Daily
Membership
(ADM)
Correlation
1.000
-.302
Significance
(2-tailed)
.
.028
df
0
51
Correlation
-.302
1.000
Significance
(2-tailed)
.028
.
df
51
0
Table 4.61
Partial Correlation of Strata 7 (95% - 100%) Fourth Grade 2007-2008 PACT
English/Language Arts versus 135-Day Average Daily Membership while
controlling for Poverty Index
135-Day
English/Language
Average Daily
Control Variables
Arts % Met
Membership
Standard
(ADM)
English/Language
Arts % Met
Standard
Poverty
Index
135-Day Average
Daily
Membership
(ADM)
Correlation
1.000
-.294
Significance
(2-tailed)
.
.028
df
0
54
Correlation
-.294
1.000
Significance
(2-tailed)
.028
.
df
54
0
146
Table 4.62
Partial Correlation of Strata 6 (90% - 94%) Fifth Grade 2007-2008 PACT
Mathematics versus 135-Day Average Daily Membership while
controlling for Poverty Index
Mathematics
% Met
Standard
135-Day
Average Daily
Membership
(ADM)
Correlation
1.000
-.346
Significance
(2-tailed)
.
.011
df
0
51
Correlation
Significance
(2-tailed)
-.346
1.000
.011
.
df
51
0
Control Variables
Mathematics
% Met
Standard
Poverty Index
135-Day
Average Daily
Membership
(ADM)
Stepwise Multiple Regression Analysis within Poverty Index Strata
For the final statistical analysis, the researcher conducted a stepwise multiple
regression analysis within each poverty index strata. As previously stated, Carpenter’s
(2006) research on the effects of school size on student achievement in South Carolina
indicated the effect of poverty to be as high as 63% for English/language arts and 60%
for mathematics. Roberts’ (2002) research indicated the effect of poverty to be as high
as 70% for English/language arts. Therefore, the researcher analyzed the data using a
stepwise multiple regression analysis to further examine whether poverty was a factor.
The researcher ran the stepwise multiple regression for third grade, fourth grade, and
fifth grade for PACT English/language arts and mathematics and 135-day average daily
membership of students.
The researcher ran a stepwise multiple regression analysis for all
PreKindergarten – 5 and Kindergarten – 5 public elementary schools in South Carolina in
third grade, fourth grade, and fifth grade using the dependent variables PACT
147
English/language arts and mathematics and independent variables of poverty index and
ADM. The outcomes of these six stepwise multiple regression analyses yielded poverty
index as a significant predictive variable for student achievement (see Table 4.63
through Table 4.68):
•
Third Grade 2007-2008 PACT English/Language Arts – poverty index was a
significant predictive variable (see Table 4.63).
Table 4.63
Stepwise Multiple Regression of Third Grade 2007-2008 PACT English/Language
Arts versus Poverty Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
.300
.000
1
.549a
.301
a. Predictors: (Constant), Poverty Index
•
Third Grade 2007-2008 PACT Mathematics – poverty index was a significant
predictive variable (see Table 4.64).
Table 4.64
Stepwise Multiple Regression of Third Grade 2007-2008 PACT Mathematics
versus Poverty Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.651a
.424
.423
.000
a. Predictors: (Constant), Poverty Index
•
Fourth Grade 2007-2008 PACT English/Language Arts – poverty index was the
most significant predictor (see Table 4.65).
Table 4.65
Stepwise Regression of Fourth Grade 2007-2008 PACT English/Language Arts
versus Poverty Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.623a
.388
.386
.000
a. Predictors: (Constant), Poverty Index
148
•
Fourth Grade 2007-2008 PACT Mathematics – poverty index was a significant
predictive variable (see Table 4.66).
Table 4.66
Stepwise Regression of Fourth Grade 2007-2008 PACT Mathematics versus
Poverty Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.645a
.417
.415
.000
a. Predictors: (Constant), Poverty Index
•
Fifth Grade 2007-2008 PACT English/Language Arts – poverty index was a
significant predictive variable (see Table 4.67).
Table 4.67
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT English/Language
Arts versus Poverty Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.666a
.443
.442
.000
a. Predictors: (Constant), Poverty Index
•
Fifth Grade 2007-2008 PACT Mathematics – poverty index was a significant
predictive variable (see Table 4.68).
Table 4.68
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT Mathematics versus
Poverty Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.614a
.377
.376
.000
a. Predictors: (Constant), Poverty Index
A stepwise multiple regression was then conducted for third grade, fourth grade,
and fifth grade within the seven poverty index strata for PACT English/language arts and
mathematics as the dependent variables. The independent variables were poverty
149
index and ADM. The results of the stepwise multiple regression that indicated
significant predictive variables were presented. These are presented in Table 4.69
through Table 4.85. The excluded subsets did not indicate a significant predictive
variable or combination of variables.
•
Strata 1 (0% - 49%): Third Grade 2007-2008 PACT Mathematics – poverty index
was a significant predictive variable (see Table 4.69).
Table 4.69
Stepwise Multiple Regression of Strata 1 (0% - 49%) Third Grade 2007-2008
PACT English/Language Arts versus Poverty Index and Average Daily
Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.280a
.078
.063
.026
a. Predictors: (Constant), Poverty Index
•
Strata 1 (0% - 49%): Third Grade 2007-2008 PACT Mathematics – poverty index
was a significant predictive variable (see Table 4.70).
Table 4.70
Stepwise Multiple Regression of Strata 1 (0% - 49%) Third Grade 2007-2008
PACT Mathematics versus Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.425a
.181
.167
.001
a. Predictors: (Constant), Poverty Index
•
Strata 1 (0% - 49%): Fourth Grade 2007-2008 PACT Mathematics – poverty index
was a significant predictor; however, poverty index and 135-day average daily
membership indicated a combination of predictive variables (see Table 4.71).
150
Table 4.71
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fourth Grade 2007-2008
PACT Mathematics versus Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.329a
.108
.094
.008
b
2
.169
.141
.040
.411
a. Predictors: (Constant), Poverty Index
b. Predictors: (Constant), Poverty Index, 135-Day Average Daily Membership (ADM)
•
Strata 1 (0% - 49%): Fifth Grade 2007-2008 PACT English/Language Arts –
poverty index was a significant predictive variable (see Table 4.72).
Table 4.72
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fifth Grade 2007-2008 PACT
English/Language Arts versus Poverty Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.335a
.112
.098
.007
a. Predictors: (Constant), Poverty Index
•
Strata 1 (0% - 49%): Fifth Grade 2007-2008 PACT Mathematics – poverty index
was a significant predictive variable (see Table 4.73).
Table 4.73
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fifth Grade 2007-2008 PACT
Mathematics versus Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.318a
.101
.086
.011
a. Predictors: (Constant), Poverty Index
•
Strata 3 (60% - 69%): Fourth Grade 2007-2008 PACT English/Language Arts –
poverty index was a significant predictive variable (see Table 4.74).
151
Table 4.74
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fourth Grade 2007-2008
PACT English/Language Arts versus Poverty Index and Average Daily
Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.239a
.057
.044
.041
a. Predictors: (Constant), Poverty Index
•
Strata 3 (60% - 69%): Fifth Grade 2007-2008 PACT English/Language Arts –
poverty index was a significant predictive variable (see Table 4.75).
Table 4.75
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fifth Grade 2007-2008
PACT English/Language Arts versus Poverty Index and Average Daily
Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.249a
.062
.049
.034
a. Predictors: (Constant), Poverty Index
•
Strata 3 (60% - 69%): Fifth Grade 2007-2008 PACT Mathematics – poverty index
was a significant predictive variable (see Table 4.76).
Table 4.76
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fifth Grade 2007-2008
PACT Mathematics versus Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.278a
.077
.064
.017
a. Predictors: (Constant), Poverty Index
•
Strata 4 (70% - 79%): Fourth Grade 2007-2008 PACT English/Language Arts –
poverty index was a significant predictive variable (see Table 4.77).
152
Table 4.77
Stepwise Multiple Regression of Strata 4 (70% - 79%) Fourth Grade 2007-2008
PACT English/Language Arts versus Poverty Index and Average Daily
Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.287a
.083
.069
.015
a. Predictors: (Constant), 135-Day Average Daily Membership (ADM)
•
Strata 6 (90% - 94%): Fourth Grade 2007-2008 PACT English/Language Arts –
135-day average daily membership was a significant predictive variable (see
Table 4.78).
Table 4.78
Stepwise Multiple Regression of Strata 6 (90% - 94%) Fourth Grade 2007-2008
PACT English/Language Arts versus Poverty Index and Average Daily
Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.301a
.090
.073
.027
a. Predictors: (Constant), 135-Day Average Daily Membership (ADM)
•
Strata 6 (90% - 94%): Fifth Grade 2007-2008 PACT Mathematics – 135-day
average daily membership was a significant predictive variable (see Table 4.79).
Table 4.79
Stepwise Multiple Regression of Strata 6 (90% - 94%) Fifth Grade 2007-2008
PACT Mathematics versus Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.332a
.110
.093
.014
a. Predictors: (Constant), 135-Day Average Daily Membership (ADM)
•
Strata 7 (95% - 100%): Third Grade 2007-2008 PACT English/Language Arts – 135day average daily membership was a significant predictive variable (see Table
4.80).
153
Table 4.80
Stepwise Multiple Regression of Strata 7 (95% - 100%) Third Grade 2007-2008
PACT English/Language Arts versus Poverty Index and Average Daily
Membership
Model
R
R Square
Adjusted R
Square
Sig. F
Change
1
.389a
.152
.136
.003
a. Predictors: (Constant), 135-Day Average Daily Membership (ADM)
•
Strata 7 (95% - 100%): Third Grade 2007-2008 PACT Mathematics – 135-day
average daily membership was a significant predictive variable (see Table 4.81).
Table 4.81
Stepwise Multiple Regression of Strata 7 (95% - 100%) Third Grade 2007-2008
PACT Mathematics versus Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.317a
.100
.084
.016
a. Predictors: (Constant), Poverty Index
•
Strata 7 (95% - 100%): Fourth Grade 2007-2008 PACT English/Language Arts –
poverty index was a significant predictive variable; however, poverty index and
135-day average daily membership indicate a combination of predictive variables
(see Table 4.82).
Table 4.82
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fourth Grade 2007-2008
PACT English/Language Arts versus Poverty Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.354a
.125
.109
.007
b
2
.201
.172
.028
.448
a. Predictors: (Constant), Poverty Index
b. Predictors: (Constant), Poverty Index, 135-Day Average Daily Membership (ADM)
154
•
Strata 7 (95% - 100%): Fourth Grade 2007-2008 PACT Mathematics – poverty
index was a significant predictive variable (see Table 4.83).
Table 4.83
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fourth Grade 2007-2008
PACT Mathematics versus Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.360a
.130
.114
.006
a. Predictors: (Constant), Poverty Index
•
Strata 7 (95% - 100%): Fifth Grade 2007-2008 PACT English/Language Arts –
poverty index was a significant predictive variable (see Table 4.84).
Table 4.84
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fifth Grade 2007-2008
PACT English/Language Arts versus Poverty Index and Average Daily
Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.363a
.131
.115
.006
a. Predictors: (Constant), Poverty Index
•
Strata 7 (95% - 100%): Fifth Grade 2007-2008 PACT Mathematics – poverty index
was a significant predictive variable (see Table 4.85).
Table 4.85
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fifth Grade 2007-2008
PACT Mathematics versus Index and Average Daily Membership
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.306a
.094
.077
.022
a. Predictors: (Constant), Poverty Index
155
Summary of stepwise multiple regression for poverty index strata
The results of the stepwise multiple regression indicated significant predictive
variables in all grades for all subjects. These are summarized in Table 4.86. Poverty
index was identified as the most predictive variable in fourteen of the forty-two subsets.
The relationship indicated a negative correlation, which means that as poverty index
increased student achievement decreased. 135-day average daily membership was
identified individually in three subsets. The relationship indicated a positive correlation,
which means that as 135-day average daily membership increased student achievement
increased. Poverty index and 135-day average daily membership were revealed to be a
combination of predictive variables in two subsets: Strata 1 (0% - 49%) fourth grade
mathematics and Strata 7 (95% - 100%) fourth grade English/language arts. No grade
level or subject was indicated more frequently than another grade level or subject.
Strata 7 (95% - 100%) had the most subsets indicate predictive variables: six of six
possible outcomes. Poverty index was the predictive variable in all six subsets. 135-day
average daily membership was identified as a variable in combination with poverty
index for fourth grade English/language arts of Strata 7 (95% - 100%). Five of the six
subsets were indicated in Strata 1 (0% - 49%) and poverty index was the predictive
variable. Three times out of the six possible subsets were identified from Strata 3 (60%
- 69%): fourth grade English/language arts, fifth grade English/language arts and fifth
grade mathematics. Neither poverty index nor 135-day average daily membership was
indicated as a predictive variable individually or in combination in any subset within
Strata 2 (50% - 59%) nor Strata 5 (80% - 89%). Strata 4 (70% - 79%) had only one subset
156
identified as a having a predictive variable. That variable was 135-day average daily
membership for fourth grade PACT English/language arts.
The summary of the outcomes of the stepwise multiple regression reveals that
twenty-five subsets of forty-two subsets indicated no significant predictive variables.
This is more than half of the subsets analyzed. Of the seventeen subsets with a
significant predictive variable or combination of variables, poverty index was indicated
83.4% of the time despite the effort to negate the effects of poverty index by
categorizing the schools in poverty index strata. 135-day average daily membership was
indicated as a predictive variable in individually three times; however, the strata, grade
level, and subject area of these three subsets does not indicate a pattern or reveal a
significant finding. Based on the outcomes of the research conducted for research
question two, it can be summarized that ADM is not a predictive variable for student
achievement when poverty index is controlled.
157
Table 4.86
Stepwise Multiple Regression Summary of PACT English/Language Arts and Mathematics versus
Poverty Index and 135-Day Average Daily Membership (Poverty Index Strata with Significant
Relationships Listed Only)
135-Day Average
Strata
Grade
Subject
Poverty Index
Daily Membership
Strata 1 (0%-49%)
Third
ELA
.280
Strata 1 (0%-49%)
Third
Mathematics
.425
Strata 1 (0%-49%)
Fourth
Mathematics
.329
Strata 1 (0%-49%)
Fifth
ELA
.335
Strata 1 (0%-49%)
Fifth
Mathematics
.318
Strata 3 (60%-69%)
Fourth
ELA
.239
Strata 3 (60%-69%)
Fifth
ELA
.249
Strata 3 (60%-69%)
Fifth
Mathematics
.278
Strata 4 (70%-79%)
Fourth
ELA
.287
Strata 6 (90%-94%)
Fourth
ELA
.301
Strata 6 (90%-94%)
Fifth
Mathematics
.332
Strata 7 (95%-100%)
Third
ELA
.389
Strata 7 (95%-100%)
Third
Mathematics
.317
Strata 7 (95%-100%)
Fourth
ELA
.354
Strata 7 (95%-100%)
Fourth
Mathematics
.360
Strata 7 (95%-100%)
Fifth
ELA
.363
Strata 7 (95%-100%)
Fifth
Mathematics
.306
.411
.448
Findings for Research Question Three
The third research question was as follows:
Can student achievement in South Carolina’s PreKindergarten – 5 or
Kindergarten – 5 public elementary schools in English/language arts and
mathematics as measured by the third, fourth and fifth grade 2007-2008
Palmetto Achievement Challenge Test be predicted by at least one, and possibly
a combination, of the following variables:
1.
2.
3.
4.
5.
Poverty index
School size or average daily membership
First graders that attended full-day kindergarten
Retention rate
Student attendance rate
158
6. Eligible for gifted and talented
7. Percent objectives met
8. Students with disabilities other than speech
9. Students older than usual for grade
10. Suspended or expelled
11. Number of teachers with advanced degrees
12. Continuing contract teachers
13. Classes not taught by highly qualified teachers
14. Teachers with emergency or provisional certificates
15. Teachers returning from the previous school year
16. Teacher attendance rate
17. Average teacher salary
18. Professional development days per teacher
19. Principal’s or director’s years at the schools
20. Student-teacher ratio
21. Prime instructional time
22. Dollars spent per student
23. Spent on teacher salaries
24. Opportunities in the arts
25. Parents attending conferences
26. SACS accreditation
27. Portable Classrooms
28. Percent of teachers satisfied with the learning environment
29. Percent of students satisfied with the learning environment
30. Percent of parents satisfied with the learning environment
31. Percent of teachers satisfied with social and physical environment
32. Percent of students satisfied with social and physical environment
33. Percent of parents satisfied with social and physical environment
34. Percent of teachers satisfied with home-school relations
35. Percent of students satisfied with home-school relations
36. Percent of parents satisfied with home-school relations
37. Vacancies for more than nine weeks
38. Character development program
39. Percent of expenditures for instruction
Stepwise Multiple Regression of All Schools by Grade Level and Subject
For the last research question, the researcher did the following: A stepwise
multiple regression was conducted using student achievement data in third grade,
fourth grade, and fifth grade and data variables provided by the South Carolina
Department of Education 2008 Annual School Report Card. The student achievement
159
data are the 2007-2008 Palmetto Achievement Challenge Test percentage of students
scoring Proficient and Advanced in English/language arts and mathematics. The data
are the dependent variable. The independent variables were obtained from the 2008
Elementary School Fact File provided by the SC DOE Annual School Report Card. Using
the 441 public elementary schools with grades PreKindergarten – 5 and Kindergarten 5, a stepwise multiple regression analysis was run for each grade level and subject to
ascertain whether a variable or combination of variables demonstrated a correlation to
student achievement in English/language arts and then mathematics. The tables were
created from the PASW Statistics Base 18 software program which was used to conduct
the analysis for this study.
For third grade PACT English/language arts, the variable percent objectives met
yielded R = 0.655, which represented a significant correlation between this predictor
variable and students scoring Proficient and Advanced in third grade (see Table 4.87).
The R2 outcome was 0.429, which means that percent objectives met accounted for
42.9% of the variation of student achievement. The final model outcome of the
stepwise multiple regression was that a combination of five variables was predictive of
variance for student achievement: percent objectives met, poverty index, teachers
returning from the previous school year, prime instructional time, and SACS
accreditation. The correlation R for this final model was 0.733. The R2 value was 0.538,
which reveals that the combination of five variables predicted 53.8% of the outcome of
students scoring Proficient and Advanced. The Adjusted R2 was 0.531. Since the
160
Adjusted R2 value is very similar to the R2 value in the final model, this combination of
variables is generalizable.
Table 4.87
Stepwise Multiple Regression of Third Grade 2007-2008 PACT English/Language Arts versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
6
R Square
Adjusted R Square
Sig. F Change
.655a
.429
.428
.000
b
.509
.507
.000
c
.518
.514
.007
d
.527
.522
.005
e
.532
.527
.027
f
.538
.531
.030
.714
.720
.726
.730
.733
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Poverty Index
c. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year
d. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Prime instructional time
e. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Prime instructional time, SACS accreditation
f. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Prime instructional time, SACS accreditation, % Eligible for gifted and talented
g. Dependent Variable: English/Language Arts % Met Standard
The researcher also conducted a stepwise multiple regression for third grade
PACT mathematics (see results in Table 4.88). The first model outcome revealed that
the variable percent objectives met yielded R = 0.697, which represented a significant
correlation between this predictor variable and students scoring Proficient and
Advanced in mathematics in third grade. The R2 outcome was 0.486, which means that
percent objectives met accounted for 48.6% of the variation of student achievement.
The final model outcome of the stepwise multiple regression was that a
combination of eight variables was predictive of variance for student achievement:
percent objectives met, poverty index, teachers returning from the previous school
161
year, prime instructional time, percent of expenditures for instruction, percent eligible
for gifted and talented, percent teachers satisfied with school/home relations, and
school size (or average daily membership). The correlation R for this final model was
0.827. The R2 value was 0.683, which reveals that the variables were predictive of
68.3% of the variance in the percentage of students scoring Proficient and Advanced at
a school. The Adjusted R2 was 0.677. Since the Adjusted R2 value is very similar to the
R2 value in the final model, this combination of variables is generalizable.
Table 4.88
Stepwise Multiple Regression of Third Grade 2007-2008 PACT Mathematics versus SC DOE Annual
School Report Card Variables
Model
R
1
2
3
4
5
6
7
8
R Square
Adjusted R Square
Sig. F Change
.697a
.486
.485
.000
b
.632
.630
.000
c
.649
.646
.000
d
.660
.657
.000
e
.668
.664
.002
f
.674
.670
.005
g
.679
.674
.015
h
.683
.677
.019
.795
.806
.813
.817
.821
.824
.827
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Poverty Index
c. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year
d. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Prime instructional time
e. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Prime instructional time, % Percent of expenditures for instruction
f. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Prime instructional time, % Percent of expenditures for instruction, % Eligible for
gifted and talented
g. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Prime instructional time, % Percent of expenditures for instruction, % Eligible for
gifted and talented, % Teachers satisfied with school/home relations
h. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Prime instructional time, % Percent of expenditures for instruction, % Eligible for
gifted and talented, % Teachers satisfied with school/home relations, 135-Day Average Daily
Membership (ADM)
162
i. Dependent Variable: Mathematics % Met Standard
The researcher conducted a stepwise multiple regression for fourth grade PACT
English/language arts (see results in Table 4.89). The first model outcome revealed that
the variable percent objectives met yielded R = 0.686, which represented a significant
correlation between this predictor variable and students scoring Proficient and
Advanced in English/language arts in fourth grade. The final model outcome of the
stepwise multiple regression (model 4) was that a combination of four variables were
predictive of the variance for student achievement: percent objectives met, poverty
index, teachers returning from the previous school year, and percent teachers satisfied
with school/home relations. The correlation R for this final model was 0.785, which is
positive and significant. The R2 value was 0.616, which reveals that the variables
predicted 61.6% of the variance in the percentage of students scoring Proficient and
Advanced at a school. The Adjusted R2 value is very similar to the R2 value in the final
model, so this combination of variables is generalizable.
Table 4.89
Stepwise Multiple Regression of Fourth Grade 2007-2008 PACT English/Language Arts versus SC DOE
Annual School Report Card Variables
Model
R
1
2
3
4
R Square
Adjusted R Square
Sig. F Change
.686a
.470
.469
.000
b
.594
.592
.000
c
.610
.608
.000
d
.616
.613
.013
.771
.781
.785
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Poverty Index
c. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year
d. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers returning from the
previous school year, % Teachers satisfied with school/home relations
e. Dependent Variable: English/Language Arts % Met Standard
163
The researcher conducted a stepwise multiple regression for fourth grade PACT
mathematics (see results in Table 4.90). The first model outcome revealed that the
variable percent objectives met yielded R = 0.704, which represented a significant
correlation between this predictor variable and students scoring Proficient and
Advanced in mathematics in fourth grade. The R2 outcome was 0.496, which means
that percent objectives met accounted for 49.6% of the variation of student
achievement. The final model outcome (Model 8) of the stepwise multiple regression
indicated that a combination of eight variables was predictive of the variance for
student achievement: percent objectives met, poverty index, percent teachers satisfied
with social and physical environment, teachers returning from the previous school year,
percent eligible for gifted and talented, first graders who attended full-day kindergarten,
student attendance rate, and percent of expenditures for instruction. The correlation R
for this final model was 0.823, which is positive and significant. The R2 value was 0.677,
which reveals that the combination of eight variables accounted for 67.7% of the
variance in the percentage of students scoring Proficient and Advanced at a school. The
Adjusted R2 was 0.670. The Adjusted R2 value is very similar to the R2 value in the final
model, so this combination of variables is generalizable.
164
Table 4.90
Stepwise Multiple Regression of Fourth Grade 2007-2008 PACT Mathematics versus SC DOE Annual
School Report Card Variables
Model
1
2
3
4
5
6
7
R
R Square
Adjusted R Square
Sig. F Change
a
.496
.495
.000
b
.633
.632
.000
c
.649
.646
.000
d
.659
.656
.001
e
.665
.661
.005
f
.669
.665
.024
g
.673
.668
.031
.704
.796
.806
.812
.816
.818
.820
h
8
.823
.677
.670
.034
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Poverty Index
c. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers satisfied with social and
physical environment
d. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers satisfied with social and
physical environment, % Teachers returning from the previous school year
e. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers satisfied with social and
physical environment, % Teachers returning from the previous school year, % Eligible for gifted and
talented
f. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers satisfied with social and
physical environment, % Teachers returning from the previous school year, % Eligible for gifted and
talented, % First graders who attended full-day kindergarten
g. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers satisfied with social and
physical environment, % Teachers returning from the previous school year, % Eligible for gifted and
talented, % First graders who attended full-day kindergarten, % Student Attendance Rate
h. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Teachers satisfied with social and
physical environment, % Teachers returning from the previous school year, % Eligible for gifted and
talented, % First graders who attended full-day kindergarten, % Student Attendance Rate, % Percent of
expenditures for instruction
i. Dependent Variable: Mathematics % Met Standard
The researcher conducted a stepwise multiple regression for fifth grade PACT
English/language arts (see results in Table 4.91). The first model outcome revealed that
the variable poverty index yielded R = 0.674, which represented a significant correlation
between this predictor variable and students scoring Proficient and Advanced in
English/language arts in fifth grade. The R2 outcome was 0.454, which means that the
poverty index variable accounted for 45.4% of the variation of student achievement.
165
The final model outcome (Model 6) of the stepwise multiple regression indicate that a
combination of six variables was predictive of variance for student achievement:
poverty index, percent objectives met, percent parents satisfied with learning
environment, teachers returning from the previous school year, opportunities in the
arts, and percent of expenditures for instruction. The correlation R for this final model
was 0.795, which is positive and significant. The R2 value was 0.633, which reveals that
the combination of six variables accounted for 63.3% of the variance in the percentage
of students scoring Proficient and Advanced at a school. The Adjusted R2 was 0.627.
Since the Adjusted R2 value is very similar to the R2 value in the final model, the
combination of variables is generalizable.
Table 4.91
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT English/Language Arts versus SC DOE
Annual School Report Card Variables
Model
R
1
2
3
4
5
6
R Square
Adjusted R Square
Sig. F Change
.674a
.454
.453
.000
b
.602
.600
.000
c
.619
.616
.000
d
.625
.621
.011
e
.628
.624
.045
f
.633
.627
.024
.776
.787
.790
.793
.795
a. Predictors: (Constant), Poverty Index
b. Predictors: (Constant), Poverty Index, % Percent Objectives Met
c. Predictors: (Constant), Poverty Index, % Percent Objectives Met, % Parents satisfied with learning
environment
d. Predictors: (Constant), Poverty Index, % Percent Objectives Met, % Parents satisfied with learning
environment, % Teachers returning from the previous school year
e. Predictors: (Constant), Poverty Index, % Percent Objectives Met, % Parents satisfied with learning
environment, % Teachers returning from the previous school year, Opportunities in the arts
f. Predictors: (Constant), Poverty Index, % Percent Objectives Met, % Parents satisfied with learning
environment, % Teachers returning from the previous school year, Opportunities in the arts, % Percent
of expenditures for instruction
g. Dependent Variable: English/Language Arts % Met Standard
166
Finally, the researcher conducted a stepwise multiple regression for fifth grade
PACT mathematics (see results in Table 4.92). The first model outcome revealed that
the variable percent objectives met yielded R = 0.669, which represented a significant
correlation between this predictor variable and students scoring Proficient and
Advanced in mathematics in fifth grade. The R2 outcome was 0.447, which means that
percent objectives met accounted for 44.7% of the variation of student achievement.
The final model outcome (Model 10) of the stepwise multiple regression indicated that a
combination of ten variables were predictors of variance for student achievement:
percent objectives met, poverty index, percent parents satisfied with learning
environment, percent students satisfied with social and physical environment, teachers
returning from the previous school year, percent teachers satisfied with school/home
relations, opportunities in the arts, percent of expenditures for instruction, percent
eligible for gifted and talented, and teachers with emergency or provisional certificates.
The correlation R for this final model was 0.821, which is positive and significant. The R2
value was 0.674, which reveals that the combination of the ten variables accounted for
67.4% of the variance in the percentage of students scoring Proficient and Advanced at
a school in fifth grade on PACT mathematics. The Adjusted R2 was 0.666. The Adjusted
R2 value is very similar to the R2 value in the final model, the combination of these
predictive variables is generalizable.
167
Table 4.92
Stepwise Multiple Regression of Fifth Grade 2007-2008 PACT Mathematics versus SC DOE Annual
School Report Card Variables
Model
R
1
2
3
4
5
6
R Square
Adjusted R Square
Sig. F Change
.669a
.447
.446
.000
b
.584
.582
.000
c
.618
.615
.000
d
.633
.629
.000
e
.644
.639
.000
f
.650
.645
.005
.764
.786
.795
.802
.806
7
.810
g
.656
.651
.008
8
.815h
.664
.657
.003
9
.819i
.670
.663
.007
j
.674
.666
.028
10
.821
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Poverty Index
c. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Parents satisfied with learning
environment
d. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Parents satisfied with learning
environment, % Students satisfied with social and physical environment
e. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Parents satisfied with learning
environment, % Students satisfied with social and physical environment, % Teachers returning from the
previous school year
f. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Parents satisfied with learning
environment, % Students satisfied with social and physical environment, % Teachers returning from the
previous school year, % Teachers satisfied with school/home relations
g. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Parents satisfied with learning
environment, % Students satisfied with social and physical environment, % Teachers returning from the
previous school year, % Teachers satisfied with school/home relations, Opportunities in the arts
h. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Parents satisfied with learning
environment, % Students satisfied with social and physical environment, % Teachers returning from the
previous school year, % Teachers satisfied with school/home relations, Opportunities in the arts, %
Percent of expenditures for instruction
i. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Parents satisfied with learning
environment, % Students satisfied with social and physical environment, % Teachers returning from the
previous school year, % Teachers satisfied with school/home relations, Opportunities in the arts, %
Percent of expenditures for instruction, % Eligible for gifted and talented
j. Predictors: (Constant), % Percent Objectives Met, Poverty Index, % Parents satisfied with learning
environment, % Students satisfied with social and physical environment, % Teachers returning from the
previous school year, % Teachers satisfied with school/home relations, Opportunities in the arts, %
Percent of expenditures for instruction, % Eligible for gifted and talented, % Teachers with emergency or
provisional certificates
k. Dependent Variable: Mathematics % Met
Standard
168
Summary of Stepwise Multiple Regression Analysis for All Schools and All Subjects
In five of the six subgroups tested, the first predictor variable of student
achievement was percent objectives met (see results in Table 4.93). The lone exception
was fifth grade PACT English/language arts, for which the poverty index variable was the
first predictor correlated to student achievement. The variable teachers returning from
the previous school year was identified as predictor variable in five subgroups: third
grade PACT English/language arts, third grade PACT mathematics, fourth grade PACT
English/language arts, fourth grade PACT mathematics, fifth grade PACT
English/language arts, and fifth grade PACT mathematics.
One variable, percent of expenditures for instruction, was identified as a
predictor variable in four subgroups: third grade PACT mathematics, fourth grade PACT
mathematics, fifth grade PACT English/language arts, and fifth grade PACT mathematics.
In all six subgroups tested, the value of the correlation coefficient (R) was not less than
0.655 revealing that the predictor value was significant and had a positive relationship
with student achievement.
In all six subgroups, the poverty index occurred either in the first model or
second model as a predictive variable or combination predictive variable for student
achievement. This observation supported the powerful effects of poverty on student
achievement found in previous studies on student achievement and school size in South
Carolina (Stevenson, 1996, 2001; Durbin, 2001; Crenshaw, 2003; McCathern, 2004;
Carpenter, 2006; Kaczor, 2006; Maxey, 2008). Based on this observation, the researcher
conducted a second stepwise multiple regression analysis.
169
Table 4.93
Summary of Stepwise Multiple Regression Analysis for All Schools and All Subjects
Third Grade
Fourth Grade
Fifth Grade
SC DOE Annual School Report Card Variables
ELA
Math
ELA
Math
ELA Math
Poverty index
2
2
2
2
1
2
Average daily membership
8
First graders that attended full-day kindergarten
6
Student attendance rate
7
Eligible for gifted and talented
6
6
5
9
Percent objectives met
1
1
1
1
2
1
Teachers with emergency or provisional
certificates
10
Teachers returning from the previous school year
3
3
3
4
4
5
Prime instructional time
4
5
Opportunities in the arts
5
7
SACS accreditation
5
Percent of parents satisfied with the learning
environment
3
3
Percent of teachers satisfied with social and
physical environment
3
Percent of students satisfied with social and
physical environment
4
Percent of teachers satisfied with home-school
relations
7
4
6
Percent of expenditures for instruction
5
8
6
8
Numbers represent the model when the variable occurs; for example, 1 = the most predictive variable.
Stepwise Multiple Regression Analysis Within Poverty Index Strata
The stepwise multiple regression analysis was conducted a second time utilizing
the same student achievement data and independent variables. The dependent
variable was 2007-2008 Palmetto Achievement Challenge Test percentage of students
scoring Proficient and Advanced in English/language arts and mathematics in third,
fourth, and fifth grade. The independent variables were the reported items on the 2008
SC DOE Annual School Report Card. The difference in this analysis was the data were
run within the poverty index strata (0% - 49%, 50% - 59%, 60% - 69%, 70% - 79%, 80% 89%, 90% - 94%, and 95% - 100%) to determine whether a variable or set of variables
correlated to student achievement. The data were run by poverty index strata, by grade
170
level, and for English/language arts, then mathematics. The tables were created from
the PASW Statistics Base 18 software program were used to conduct the analysis for this
study.
Stepwise multiple regression for Strata 1 (0% - 49%)
The outcome of the stepwise multiple regression for third grade PACT
English/language arts for schools in the poverty index strata 0% - 49% revealed the
single most predictive variable of older than usual for grade, with a R = 0.431 (see
results in Table 4.94). This variable is considered significant correlation and a predictive
variable for students scoring Proficient and Advanced in English/language arts in third
grade. The Adjusted R2 outcome was 0.172. The interpretation of this value is that the
variable older than usual for grade accounts for 17.2% of the variation of student
achievement in schools in Strata 1 (0% - 49%) for students in third grade scoring
Proficient and Advanced on PACT English/language arts in the 2007-2008 school year.
The final stepwise multiple regression analysis indicated that a combination of
four variables were significant predictive variables for student achievement: older than
usual for grade, parents attending conferences, poverty index, students with disabilities
other than speech. The correlation R for this final model was 0.720, which is a positive
correlation and significant. The Adjusted R2 value was 0.484, which means the four
variables in combination accounted for 48.4% of the variance in the percentage of
students scoring Proficient and Advanced at a school on third grade PACT
English/language arts.
171
Table 4.94
Stepwise Multiple Regression of Strata 1 (0% - 49%) Third Grade 2007-2008 PACT
English/Language Arts versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.431a
.186
.172
.001
2
b
.353
.330
.000
c
.474
.446
.001
d
.519
.484
.028
3
4
.594
.689
.720
a. Predictors: (Constant), % Older than usual for grade
b. Predictors: (Constant), % Older than usual for grade, % Parents attending conferences
c. Predictors: (Constant), % Older than usual for grade, % Parents attending conferences, Poverty
Index
d. Predictors: (Constant), % Older than usual for grade, % Parents attending conferences, Poverty
Index, % Students with disabilities other than speech
e. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for third grade PACT
mathematics for schools in Strata 1 (0% - 49%) produced the single most predictive
variable of percent eligible for gifted and talented, with a R = 0.547 (see results in Table
4.95). This variable is significant and a predictor variable for students scoring Proficient
and Advanced in mathematic in third grade. The Adjusted R2 outcome was 0.287. The
interpretation of this value means that the variable percent eligible for gifted and
talented accounted for 28.7% of the variation of student achievement in schools in
Strata 1 (0% - 49%) for students in third grade scoring Proficient and Advanced on PACT
mathematics in the 2007-2008 school year.
The final outcome of the stepwise multiple regression revealed that a
combination of six variables was predictive of variance for student achievement:
percent eligible for gifted and talented, percent objectives met, older than usual for
grade, poverty index, parents attending conferences, and teachers with emergency or
provisional certificates. The correlation R for this final model was 0.879, which is a
172
positive correlation and significant. The Adjusted R2 was 0.746, which means the six
variables accounted for 74.6% of the variance for students scoring Proficient and
Advanced.
Table 4.95
Stepwise Multiple Regression of Strata 1 (0% - 49%) Third Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.547a
.299
.287
.000
b
2
.562
.547
.000
c
.614
.594
.008
4
.820
d
.672
.648
.003
5
.862e
.743
.719
.000
6
f
.772
.746
.013
3
.750
.784
.879
a. Predictors: (Constant), % Eligible for gifted and talented
b. Predictors: (Constant), % Eligible for gifted and talented, % Percent Objectives Met
c. Predictors: (Constant), % Eligible for gifted and talented, % Percent Objectives Met, % Older
than usual for grade
d. Predictors: (Constant), % Eligible for gifted and talented, % Percent Objectives Met, % Older
than usual for grade, Poverty Index
e. Predictors: (Constant), % Eligible for gifted and talented, % Percent Objectives Met, % Older
than usual for grade, Poverty Index, % Parents attending conferences
f. Predictors: (Constant), % Eligible for gifted and talented, % Percent Objectives Met, % Older
than usual for grade, Poverty Index, % Parents attending conferences, % Teachers with
emergency or provisional certificates
g. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
English/language arts for schools in Strata 1 (0% - 49%) indicated the single most
predictive variable of percent parents satisfied with school/home relations, with a R =
0.487 (see results in Table 4.96). This predictive coefficient value indicated a significant
relationship. The Adjusted R2 outcome was 0.224, which means that the variable
percent parents satisfied with school/home relations accounted for 22.4% of the
variation in student achievement. The final outcome of the stepwise multiple
173
regression indicated a combination of six variables were predictors of variance for
student achievement: percent parents satisfied with school/home relations, students
with disabilities other than speech, parents attending conferences, older than usual for
grade, percent teachers satisfied with learning environment, poverty index. The
correlation R for this final model was 0.752, which is positive and significant. The
Adjusted R2 value was 0.516, which means the six variables in combination accounted
for 51.6% of the variance in the percentage of students scoring Proficient and Advanced
at a school on fourth grade PACT English/language arts.
Table 4.96
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fourth Grade 2007-2008 PACT
English/Language Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
6
R Square
Adjusted R Square
Sig. F Change
.487a
.237
.224
.000
b
.368
.345
.001
c
.419
.387
.031
d
.473
.435
.020
e
.526
.482
.017
f
.566
.516
.033
.606
.647
.688
.725
.752
a. Predictors: (Constant), % Parents satisfied with school/home relations
b. Predictors: (Constant), % Parents satisfied with school/home relations, % Students with
disabilities other than speech
c. Predictors: (Constant), % Parents satisfied with school/home relations, % Students with
disabilities other than speech, % Parents attending conferences
d. Predictors: (Constant), % Parents satisfied with school/home relations, % Students with
disabilities other than speech, % Parents attending conferences, % Older than usual for grade
e. Predictors: (Constant), % Parents satisfied with school/home relations, % Students with
disabilities other than speech, % Parents attending conferences, % Older than usual for grade, %
Teachers satisfied with learning environment
f. Predictors: (Constant), % Parents satisfied with school/home relations, % Students with
disabilities other than speech, % Parents attending conferences, % Older than usual for grade, %
Teachers satisfied with learning environment, Poverty Index
g. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
mathematics for schools in Strata 1 (0% - 49%) indicated the single most predictive
174
variable of percent parents satisfied with school/home relations, with a R = 0.555 (see
Table 4.97). This predictive coefficient value is significant. The Adjusted R2 outcome
was 0.296, which means that the variable percent parents satisfied with school/home
relations accounted for 29.6% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated a combination of
six variables were predictors of variance for student achievement: percent parents
satisfied with school/home relations, poverty index, parents attending conferences,
students with disabilities other than speech, percent teachers satisfied with learning
environment, and older than usual for grade. The correlation R for this final model was
0.761, which is positive and significant. The Adjusted R2 value was 0.531, which means
the six variables in combination accounted for 53.1% of the variance in the percentage
of students scoring Proficient and Advanced at a school on fourth grade PACT
mathematics.
Table 4.97
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fourth Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
6
R Square
Adjusted R Square
Sig. F Change
.555a
.308
.296
.000
b
.412
.391
.002
c
.460
.431
.029
d
.503
.467
.034
e
.545
.503
.030
f
.579
.531
.044
.642
.678
.709
.738
.761
a. Predictors: (Constant), % Parents satisfied with school/home relations
b. Predictors: (Constant), % Parents satisfied with school/home relations, Poverty Index
c. Predictors: (Constant), % Parents satisfied with school/home relations, Poverty Index, % Parents
attending conferences
d. Predictors: (Constant), % Parents satisfied with school/home relations, Poverty Index, %
Parents attending conferences, % Students with disabilities other than speech
175
e. Predictors: (Constant), % Parents satisfied with school/home relations, Poverty Index, %
Parents attending conferences, % Students with disabilities other than speech, % Teachers
satisfied with learning environment
f. Predictors: (Constant), % Parents satisfied with school/home relations, Poverty Index, % Parents
attending conferences, % Students with disabilities other than speech, % Teachers satisfied with
learning environment, % Older than usual for grade
g. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
English/language arts for schools Strata 1 (0% - 49%) produced the single most
predictive variable to be percent objectives met, with a R = 0.409 (see Table 4.98). This
predictive coefficient value is significant. The Adjusted R2 outcome was 0.153, which
means that the predictor variable percent objectives met accounted for 15.3% of the
variation of student achievement.
The final outcome of the stepwise multiple regression indicated five variables in
combination were predictors of variance in student achievement: percent objectives
met, teachers returning from the previous school year, poverty index, older than usual
for grade, and percent students satisfied with school/home relations. The correlation R
for this final combination of predictor variables was 0.762, which is positive and
significant. The Adjusted R2 value was 0.542, which means the five predictor variables in
combination accounted for 54.2% of the variance in the percentage of students scoring
Proficient and Advanced at a school on fifth grade PACT English/language arts.
176
Table 4.98
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fifth Grade 2007-2008 PACT English/Language Arts
versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
R Square
Adjusted R Square
Sig. F Change
.409a
.167
.153
.001
b
.304
.279
.001
c
.456
.426
.000
d
.534
.501
.004
e
.580
.542
.018
.551
.675
.731
.762
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year
c. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year,
Poverty Index
d. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year,
Poverty Index, % Older than usual for grade
e. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year,
Poverty Index, % Older than usual for grade, % Students satisfied with school/home relations
f. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
mathematics for schools Strata 1 (0% - 49%) indicated the single most predictive
variable of percent objectives met, with a R = 0.532 (see Table 4.99). This coefficient
value reveals a significant relationship. The Adjusted R2 outcome was 0.271, which
means that the predictor variable percent objectives met accounted for 27.1% of the
variation of student achievement.
The final outcome of the stepwise multiple regression indicated six variables in
combination were predictors of variance in student achievement: percent objectives
met, older than usual for grade, poverty index, percent students satisfied with
school/home relations, percent teachers satisfied with school/home relations, and SACS
accreditation. The correlation R for this final combination of predictor variables was
0.825, which is positive and significant. The Adjusted R2 value was 0.645, which means
177
the six predictor variables in combination accounted for 64.5% of the variance in the
percentage of students scoring Proficient and Advanced at a school on fifth grade PACT
mathematics.
Table 4.99
Stepwise Multiple Regression of Strata 1 (0% - 49%) Fifth Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.532a
.283
.271
.000
b
2
.426
.406
.000
c
.555
.531
.000
4
.789
d
.623
.596
.003
5
.807e
.651
.619
.042
6
f
.681
.645
.031
3
.653
.745
.825
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade
c. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, Poverty Index
d. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, Poverty Index, %
Students satisfied with school/home relations
e. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, Poverty Index, %
Students satisfied with school/home relations, % Teachers satisfied with school/home relations
f. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, Poverty Index, %
Students satisfied with school/home relations, % Teachers satisfied with school/home relations, SACS
accreditation
g. Dependent Variable: Mathematics % Met Standard
Stepwise multiple regression for Strata 2 (50% - 59%)
The outcome of the stepwise multiple regression for third grade PACT
English/language arts for schools Strata 2 (50% - 59%) produced the single most
predictive variable of percent objectives met, with a R = 0.554 (see Table 4.100). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.290, which means that the predictor variable percent objectives met accounted for
29.0% of the variation of student achievement.
178
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
met, character development program, and SACS accreditation. The correlation R for this
final combination of predictor variables was 0.704, which is positive and significant. The
Adjusted R2 value was 0.454, which means the three predictor variables in combination
accounted for 45.4% of the variance in the percentage of students scoring Proficient and
Advanced at a school on third grade PACT English/language arts.
Table 4.100
Stepwise Multiple Regression of Strata 2 (50% - 59%) Third Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.554a
.307
.290
.000
b
.432
.402
.006
c
.495
.454
.038
.657
.704
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Character Development Program
c. Predictors: (Constant), % Percent Objectives Met, Character Development Program, SACS accreditation
d. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for third grade PACT
mathematics for schools in Strata 2 (50% - 59%) indicated the single most predictive
variable of percent parents satisfied with learning environment, with a R = 0.529 (see
Table 4.101). This predictive coefficient value is significant. The Adjusted R2 outcome
was 0.262, which means that the predictor variable percent parents satisfied with
learning environment accounted for 26.2% of the variation of student achievement.
The final outcome of the stepwise multiple regression indicated four variables in
combination were predictors of variance in student achievement: percent parents
179
satisfied with learning environment, SACS accreditation, students with disabilities other
than speech, and percent teachers satisfied with school/home relations. The correlation
R for this final combination of predictor variables was 0.764, which is positive and
significant. The Adjusted R2 value was 0.537, which means the four predictor variables
in combination accounted for 53.7% of the variance in the percentage of students
scoring Proficient and Advanced at a school on third grade PACT mathematics.
Table 4.101
Stepwise Multiple Regression of Strata 2 (50% - 59%) Third Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.529a
.280
.262
.000
2
.651
b
.424
.394
.004
3
.731c
.535
.497
.005
4
d
.584
.537
.047
.764
a. Predictors: (Constant), % Parents satisfied with learning environment
b. Predictors: (Constant), % Parents satisfied with learning environment, SACS accreditation
c. Predictors: (Constant), % Parents satisfied with learning environment, SACS accreditation, % Students
with disabilities other than speech
d. Predictors: (Constant), % Parents satisfied with learning environment, SACS accreditation, % Students
with disabilities other than speech, % Teachers satisfied with school/home relations
e. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
English/language arts for schools in Strata 2 (50% - 59%) produced the single most
predictive variable of percent objectives met, with a R = 0.538 (see Table 4.102). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.272, which means that the predictor variable percent objectives met accounted for
27.2% of the variation of student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
180
met, teachers returning from the previous school year, poverty index, older than usual
for grade, and first graders who attended full-day kindergarten. The correlation R for
this final combination of predictor variables was 0.683, which is positive and significant.
The Adjusted R2 value was 0.423, which means the three predictor variables in
combination accounted for 42.3% of the variance in the percentage of students scoring
Proficient and Advanced at a school on fourth grade PACT English/language arts.
Table 4.102
Stepwise Multiple Regression of Strata 2 (50% - 59%) Fourth Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.538a
2
.613
b
.290
.272
.000
.376
.343
.028
3
.683c
.467
.423
.016
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade
c. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, % First graders who
attended full-day kindergarten
d. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
mathematics for schools in Strata 2 (50% - 59%) indicated the single most predictive
variable of percent objectives met, with a R = 0.522 (see Table 4.103). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.254, which means that
the predictor variable percent objectives met accounted for 25.4% of the variation of
student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
met, percent eligible for gifted and talented, and dollars spent per student. The
181
correlation R for this final combination of predictor variables was 0.694, which is
positive and significant. The Adjusted R2 value was 0.439, which means the three
predictor variables in combination accounted for 43.9% of the variance in the
percentage of students scoring Proficient and Advanced at a school on fourth grade
PACT mathematics.
Table 4.103
Stepwise Multiple Regression of Strata 2 (50% - 59%) Fourth Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.522a
.273
.254
.000
b
.358
.324
.031
c
.481
.439
.005
.598
.694
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented
c. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented, Dollars spent per
student
d. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
English/language arts for schools in Strata 2 (50% - 59%) produced the single most
predictive variable of percent objectives met, with a R = 0.434 (see Table 4.104). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.167, which means that the predictor variable percent objectives met accounted for
16.7% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated two variables in
combination were predictors of variance for student achievement: percent objectives
met and percent teachers satisfied with school/home relations. The correlation R for
this final combination of predictor variables was 0.547, which is positive and significant.
182
The Adjusted R2 value was 0.262, which means the two predictor variables in
combination accounted for 26.2% of the variance in the percentage of students scoring
Proficient and Advanced at a school on fifth grade PACT English/language arts within
this poverty index strata.
Table 4.104
Stepwise Multiple Regression of Strata 2 (50% - 59%) Fifth Grade 2007-2008 PACT
English/Language Arts versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.434a
.188
.167
.005
b
2
.299
.262
.019
.547
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with school/home relations
c. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
mathematics for schools in Strata 2 (50% - 59%) indicated the single most predictive
variable of percent objectives met, with a R = 0.546 (see Table 4.105). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.280, which means that
the predictor variable percent objectives met accounted for 28.0% of the variation of
student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
met, percent eligible for gifted and talented, and percent students satisfied with social
and physical environment. The correlation R for this final combination of predictor
variables was 0.717, which is positive and significant. The Adjusted R2 value was 0.475,
which means the three predictor variables in combination accounted for 47.5% of the
183
variance in the percentage of students scoring Proficient and Advanced at a school on
fifth grade PACT mathematics within.
Table 4.105
Stepwise Multiple Regression of Strata 2 (50% - 59%) Fifth Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.546a
.298
.280
.000
b
.446
.417
.003
c
.514
.475
.029
.668
.717
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented
c. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented, % Students
satisfied with social and physical environment
d. Dependent Variable: Mathematics % Met Standard
Stepwise multiple regression for Strata 3 (60% - 69%)
The outcome of the stepwise multiple regression for third grade PACT
English/language arts for schools in Strata 3 (60% - 69%) produced the single most
predictive variable of percent objectives met, with a R = 0.531 (see Table 4.106). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.271 which means that the predictor variable percent objectives met accounted for
27.1% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
met, teachers with advanced degrees, and student-teacher ratio. The correlation R for
this final combination of predictor variables was 0.629, which is positive and significant.
The Adjusted R2 value was 0.368, which means the three predictor variables in
combination accounted for 36.8% of the variance in the percentage of students scoring
184
Proficient and Advanced at a school on third grade PACT English/language arts within
this poverty index strata.
Table 4.106
Stepwise Multiple Regression of Strata 3 (60% - 69%) Third Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.531a
.282
.271
.000
b
.349
.329
.011
c
.395
.368
.028
.591
.629
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers with advanced degrees
c. Predictors: (Constant), % Percent Objectives Met, % Teachers with advanced degrees, Student-teacher
ratio
d. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for third grade PACT
mathematics for schools in Strata 3 (60% - 69%) indicated the single most predictive
variable of percent objectives met, with a R = 0.487 (see Table 4.107). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.226, which means that
the predictor variable percent objectives met accounted for 22.6% of the variation of
student achievement.
The final outcome of the stepwise multiple regression indicated six variables in
combination were predictors of variance in student achievement: percent objectives
met, older than usual for grade, spent on teacher salaries, parents attending
conferences, SACS accreditation, and student-teacher ratio. The correlation R for this
final combination of predictor variables was 0.713, which is positive and significant. The
Adjusted R2 value was 0.462, which means the six predictor variables in combination
185
accounted for 46.2% of the variance in the percentage of students scoring Proficient and
Advanced at a school on third grade PACT mathematics.
Table 4.107
Stepwise Multiple Regression of Strata 3 (60% - 69%) Third Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
6
R Square
Adjusted R Square
Sig. F Change
.487a
.237
.226
.000
b
.333
.313
.003
c
.384
.356
.022
d
.430
.395
.026
e
.477
.436
.019
f
.509
.462
.049
.577
.620
.656
.691
.713
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade
c. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, % Spent on teacher
salaries
d. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, % Spent on teacher
salaries, % Parents attending conferences
e. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, % Spent on teacher
salaries, % Parents attending conferences, SACS accreditation
f. Predictors: (Constant), % Percent Objectives Met, % Older than usual for grade, % Spent on teacher
salaries, % Parents attending conferences, SACS accreditation, Student-teacher ratio
g. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
English/language arts for schools in Strata 3 (60% - 69%) produced the single most
predictive variable of percent objectives met, with a R = 0.483 (see Table 4.108). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.222 which means that the predictor variable percent objectives met accounted for
22.2% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
met, continuing contract teachers, and professional development per teacher. The
186
correlation R for this final combination of predictor variables was 0.597, which is
positive and significant. The Adjusted R2 value was 0.327, which means the three
predictor variables in combination accounted for 32.7% of the variance in the
percentage of students scoring Proficient and Advanced at a school on fourth grade
PACT English/language arts.
Table 4.108
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fourth Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.483a
.233
.222
.000
b
.317
.297
.005
c
.356
.327
.050
.563
.597
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Continuing contract teachers
c. Predictors: (Constant), % Percent Objectives Met, % Continuing contract teachers, Professional
development days per teacher
d. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
mathematics for schools in Strata 3 (60% - 69%) indicated the single most predictive
variable of percent objectives met, with a R = 0.592 (see Table 4.109). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.341, which means that
the predictor variable percent objectives met accounted for 34.1% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated four variables in
combination were predictors of variance for student achievement: percent objectives
met, continuing contract teachers, spent on teacher salaries, and students with
disabilities other than speech. The correlation R for this final combination of predictor
187
variables was 0.688, which is positive and significant. The Adjusted R2 value was 0.441,
which means the four predictor variables in combination accounted for 44.1% of the
variance in the percentage of students scoring Proficient and Advanced at a school on
fourth grade PACT mathematics within.
Table 4.109
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fourth Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
R Square
Adjusted R Square
Sig. F Change
.592a
.350
.341
.000
b
.395
.377
.030
c
.433
.407
.039
d
.473
.441
.030
.628
.658
.688
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Continuing contract teachers
c. Predictors: (Constant), % Percent Objectives Met, % Continuing contract teachers, % Spent on teacher
salaries
d. Predictors: (Constant), % Percent Objectives Met, % Continuing contract teachers, % Spent on teacher
salaries, % Students with disabilities other than speech
e. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
English/language arts for schools in Strata 3 (60% - 69%) produced only one predictive
variable. Percent objectives met is the variable indicated with a R value of 0.501 (see
Table 4.110). This coefficient value indicates a significant relationship. The Adjusted R2
outcome was 0.240, which means that the predictor variable percent objectives met
accounted for 24.0% of the variation in student achievement.
188
Table 4.110
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fifth Grade 2007-2008 PACT
English/Language Arts versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.501a
.251
.240
.000
a. Predictors: (Constant), % Percent Objectives Met
b. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
mathematics for schools in Strata 3 (60% - 69%) indicated the single most predictive
variable of percent objectives met, with a R = 0.536 (see Table 4.111). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.277, which means that
the predictor variable percent objectives met accounted for 27.7% of the variation of
student achievement.
The final outcome of the stepwise multiple regression indicated four variables in
combination were predictors of variance in student achievement: percent objectives
met, teachers returning from the previous school year, percent students satisfied with
learning environment, and percent parents satisfied with school/home environment.
The correlation R for this final combination of predictor variables was 0.686, which is
positive and significant. The Adjusted R2 value was 0.437, which means the four
predictor variables in combination accounted for 43.7% of the variance in the
percentage of students scoring Proficient and Advanced at a school on fifth grade PACT
mathematics.
189
Table 4.111
Stepwise Multiple Regression of Strata 3 (60% - 69%) Fifth Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
R Square
Adjusted R Square
Sig. F Change
.536a
.287
.277
.000
b
.387
.369
.002
c
.426
.400
.038
d
.470
.437
.024
.622
.653
.686
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year
c. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year,
% Students satisfied with learning environment
d. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year,
% Students satisfied with learning environment, % Parents satisfied with school/home relations
e. Dependent Variable: Mathematics % Met Standard
Stepwise multiple regression for Strata 4 (70% - 79%)
The outcome of the stepwise multiple regression for third grade PACT
English/language arts for schools in Strata 4 (70% - 79%) produced the single most
predictive variable of percent objectives met, with a R = 0.464 (see Table 4.112). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.204, which means that the predictor variable percent objectives met accounted for
20.4% of the variation of student achievement.
The final outcome of the stepwise multiple regression indicated eight variables in
combination were predictors of variance in student achievement: percent objectives
met, percent eligible for gifted and talented, percent students satisfied with social and
physical environment, school size or average daily membership, first graders who
attended full-day kindergarten, older than usual for grade, continuing contract teachers,
and percent retention rate. The correlation R for this final combination of predictor
variables was 0.758, which is positive and significant. The Adjusted R2 value was 0.517,
190
which means the eight predictor variables in combination accounted for 51.7% of the
variance in the percentage of students scoring Proficient and Advanced at a school on
third grade PACT English/language arts.
Table 4.112
Stepwise Multiple Regression of Strata 4 (70% - 79%) Third Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.464a
.215
.204
.000
b
2
.287
.265
.012
c
.352
.322
.013
4
.630
d
.397
.359
.031
5
.671e
.450
.407
.016
6
f
.487
.437
.040
g
.528
.474
.024
h
.574
.517
.013
3
7
8
.535
.593
.698
.727
.758
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented
c. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented, % Students
satisfied with social and physical environment
d. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented, % Students
satisfied with social and physical environment, 135-Day Average Daily Membership (ADM)
e. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented, % Students
satisfied with social and physical environment, 135-Day Average Daily Membership (ADM), % First
graders who attended full-day kindergarten
f. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented, % Students
satisfied with social and physical environment, 135-Day Average Daily Membership (ADM), % First
graders who attended full-day kindergarten, % Older than usual for grade
g. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented, % Students
satisfied with social and physical environment, 135-Day Average Daily Membership (ADM), % First
graders who attended full-day kindergarten, % Older than usual for grade, % Continuing contract
teachers
h. Predictors: (Constant), % Percent Objectives Met, % Eligible for gifted and talented, % Students
satisfied with social and physical environment, 135-Day Average Daily Membership (ADM), % First
graders who attended full-day kindergarten, % Older than usual for grade, % Continuing contract
teachers, % Retention rate
i. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for third grade PACT
mathematics for schools in Strata 4 (70% - 79%) indicated the single most predictive
variable of percent objectives met, with a R = 0.601 (see Table 4.113). This predictive
191
coefficient value is significant. The Adjusted R2 outcome was 0.351, which means that
the predictor variable percent objectives met accounted for 35.1% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated five variables in
combination were predictors of variance in student achievement: percent objectives
met, percent teachers satisfied with school/home relations, percent students satisfied
with learning environment, teachers with advanced degrees, and percent parents
satisfied with learning environment. The correlation R for this final combination of
predictor variables was 0.755, which is positive and significant. The Adjusted R2 value
was 0.536, which means the five predictor variables in combination accounted for 53.6%
of the variance in the percentage of students scoring Proficient and Advanced at a
school on third grade PACT mathematics.
Table 4.113
Stepwise Multiple Regression of Strata 4 (70% - 79%) Third Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
R Square
Adjusted R Square
Sig. F Change
.601a
.361
.351
.000
b
.446
.429
.002
c
.504
.481
.008
d
.535
.506
.042
e
.570
.536
.028
.668
.710
.731
.755
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with school/home relations
c. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with school/home relations, %
Students satisfied with learning environment
d. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with school/home relations, %
Students satisfied with learning environment, % Teachers with advanced degrees
e. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with school/home relations, %
Students satisfied with learning environment, % Teachers with advanced degrees, % Parents satisfied
with learning environment
f. Dependent Variable: Mathematics % Met Standard
192
The outcome of the stepwise multiple regression for fourth grade PACT
English/language arts for schools in Strata 4 (70% - 79%) produced the single most
predictive variable of percent objectives met, with a R = 0.454 (see Table 4.114). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.194, which means that the predictor variable percent objectives met accounted for
19.4% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated four variables in
combination were predictors of variance in student achievement: percent objectives
met, teachers returning from the previous school year, character development program,
and school size or average daily membership. The correlation R for this final
combination of predictor variables was 0.626, which is positive and significant. The
Adjusted R2 value was 0.354, which means the four predictor variables in combination
accounted for 35.4% of the variance in the percentage of students scoring Proficient and
Advanced at a school on fourth grade PACT English/language arts within this poverty
index strata.
Table 4.114
Stepwise Multiple Regression of Strata 4 (70% - 79%) Fourth Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
R Square
Adjusted R Square
Sig. F Change
.454a
.206
.194
.000
b
.277
.255
.013
c
.341
.311
.014
d
.392
.354
.024
.527
.584
.626
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year
c. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year,
Character Development Program
193
d. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year,
Character Development Program, 135-Day Average Daily Membership (ADM)
e. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
mathematics for schools in Strata 4 (70% - 79%) indicated the single most predictive
variable of percent objectives met, with a R = 0.512 (see Table 4.115). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.251, which means that
the predictor variable percent objectives met accounted for 25.1% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated two variables in
combination were predictors of variance in student achievement: percent objectives
met and teachers returning from the previous school year. The correlation R for this
final combination of predictor variables was 0.566, which is positive and significant. The
Adjusted R2 value was 0.300, which means the two predictor variables in combination
accounted for 30.0% of the variance in the percentage of students scoring Proficient and
Advanced at a school on fourth grade PACT mathematics within.
Table 4.115
Stepwise Multiple Regression of Strata 4 (70% - 79%) Fourth Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.512a
.262
.251
.000
b
2
.321
.300
.020
.566
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers returning from the previous school year
c. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
English/language arts for schools in Strata 4 (70% - 79%) produced the single most
194
predictive variable of percent parents satisfied with learning environment, with a R =
0.451 (see Table 4.116). This coefficient value indicates a significant relationship. The
Adjusted R2 outcome was 0.191, which means that the predictor variable percent
parents satisfied with learning environment accounted for 19.1% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated four variables in
combination were predictors of variance in student achievement: percent parents
satisfied with learning environment, percent portable classrooms, percent retention
rate, and percent teacher attendance rate. The correlation R for this final combination
of predictor variables was 0.629, which is positive and significant. The Adjusted R2 value
was 0.358, which means the four predictor variables in combination accounted for
35.8% of the variance in the percentage of students scoring Proficient and Advanced at
a school on fifth grade PACT English/language arts.
Table 4.116
Stepwise Multiple Regression of Strata 4 (70% - 79%) Fifth Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
R Square
Adjusted R Square
Sig. F Change
.451a
.203
.191
.000
b
.281
.260
.009
c
.347
.317
.013
d
.396
.358
.027
.530
.589
.629
a. Predictors: (Constant), % Parents satisfied with learning environment
b. Predictors: (Constant), % Parents satisfied with learning environment, % Portable classrooms
c. Predictors: (Constant), % Parents satisfied with learning environment, % Portable classrooms, %
Retention rate
d. Predictors: (Constant), % Parents satisfied with learning environment, % Portable classrooms, %
Retention rate, % Teacher Attendance Rate
e. Dependent Variable: English/Language Arts % Met Standard
195
The outcome of the stepwise multiple regression for fifth grade PACT
mathematics for schools in Strata 4 (70% - 79%) indicated the single most predictive
variable of percent parents satisfied with learning environment, with a R = 0.410 (see
Table 4.117). This predictive coefficient value is significant. The Adjusted R2 outcome
was 0.156, which means that the predictor variable percent parents satisfied with
learning environment accounted for 15.6% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent parents
satisfied with learning environment, percent portable classrooms, and character
development program. The correlation R for this final combination of predictor
variables was 0.559, which is positive and significant. The Adjusted R2 value was 0.280,
which means the three predictor variables in combination accounted for 28.0% of the
variance in the percentage of students scoring Proficient and Advanced at a school on
fifth grade PACT mathematics.
Table 4.117
Stepwise Multiple Regression of Strata 4 (70% - 79%) Fifth Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.410a
.168
.156
.000
b
.263
.241
.005
c
.312
.280
.036
.513
.559
a. Predictors: (Constant), % Parents satisfied with learning environment
b. Predictors: (Constant), % Parents satisfied with learning environment, % Portable classrooms
c. Predictors: (Constant), % Parents satisfied with learning environment, % Portable classrooms,
Character Development Program
d. Dependent Variable: Mathematics % Met Standard
196
Stepwise multiple regression for Strata 5 (80% - 89%)
The outcome of the stepwise multiple regression for third grade PACT
English/language arts for schools in Strata 5 (80% - 89%) produced the single most
predictive variable of percent objectives met, with a R = 0.478 (see Table 4.118). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.218, which means that the predictor variable percent objectives met accounted for
21.8% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance for student achievement: percent objectives
met, school size or average daily membership, and SACS accreditation. The correlation
R for this final combination of predictor variables was 0.592, which is positive and
significant. The Adjusted R2 value was 0.322, which means the three predictor variables
in combination accounted for 32.2% of the variance in the percentage of students
scoring Proficient and Advanced at a school on third grade PACT English/language arts
within this poverty index strata.
Table 4.118
Stepwise Multiple Regression of Strata 5 (80% - 89%) Third Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.478a
.229
.218
.000
b
.308
.288
.006
c
.350
.322
.039
.555
.592
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, 135-Day Average Daily Membership (ADM)
c. Predictors: (Constant), % Percent Objectives Met, 135-Day Average Daily Membership (ADM), SACS
accreditation
d. Dependent Variable: English/Language Arts % Met Standard
197
The outcome of the stepwise multiple regression for third grade PACT
mathematics for schools in Strata 5 (80% - 89%) indicated the single most predictive
variable of percent objectives met, with a R = 0.609 (see Table 4.119). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.362, which means that
the predictor variable percent objectives met accounted for 36.2% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated five variables in
combination were predictors of variance in student achievement: percent objectives
met, SACS accreditation, student-teacher ratio, first graders who attended full-day
kindergarten, and school size or average daily membership. The correlation R for this
final combination of predictor variables was 0.729, which is positive and significant. The
Adjusted R2 value was 0.496, which means the five predictor variables in combination
accounted for 49.6% of the variance in the percentage of students scoring Proficient and
Advanced at a school on third grade PACT mathematics.
Table 4.119
Stepwise Multiple Regression of Strata 5 (80% - 89%) Third Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
R Square
Adjusted R Square
Sig. F Change
.609a
.371
.362
.000
b
.417
.400
.023
c
.457
.433
.028
d
.502
.472
.016
e
.531
.496
.045
.646
.676
.708
.729
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, SACS accreditation
c. Predictors: (Constant), % Percent Objectives Met, SACS accreditation, Student-teacher ratio
d. Predictors: (Constant), % Percent Objectives Met, SACS accreditation, Student-teacher ratio, % First
graders who attended full-day kindergarten
198
e. Predictors: (Constant), % Percent Objectives Met, SACS accreditation, Student-teacher ratio, % First
graders who attended full-day kindergarten, 135-Day Average Daily Membership (ADM)
f. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
English/language arts for schools in Strata 5 (80% - 89%) produced the single most
predictive variable of percent objectives met, with a R = 0.584 (see Table 4.120). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.332, which means that the predictor variable percent objectives met accounted for
33.2% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated two variables in
combination were predictors of variance in student achievement: percent objectives
met and student-teacher ratio. The correlation R for this final combination of predictor
variables was 0.631, which is positive and significant. The Adjusted R2 value was 0.380,
which means the two predictor variables in combination accounted for 38.20% of the
variance in the percentage of students scoring Proficient and Advanced at a school on
fourth grade PACT English/language arts within this poverty index strata.
Table 4.120
Stepwise Multiple Regression of Strata 5 (80% - 89%) Fourth Grade 2007-2008 PACT
English/Language Arts versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.584a
.341
.332
.000
b
2
.398
.380
.013
.631
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Student-teacher ratio
c. Dependent Variable: English/Language Arts % Met Standard
199
The outcome of the stepwise multiple regression for fourth grade PACT
mathematics for schools in Strata 5 (80% - 89%) indicated the single most predictive
variable of percent objectives met, with a R = 0.591 (see Table 4.121). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.340, which means that
the predictor variable percent objectives met accounted for 34.0% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
met, first graders who attended full-day kindergarten, and percent expenditure for
instruction. The correlation R for this final combination of predictor variables was
0.650, which is positive and significant. The Adjusted R2 value was 0.397, which means
the three predictor variables in combination accounted for 39.7% of the variance in the
percentage of students scoring Proficient and Advanced at a school on fourth grade
PACT mathematics.
Table 4.121
Stepwise Multiple Regression of Strata 5 (80% - 89%) Fourth Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.591a
.349
.340
.000
b
.388
.371
.038
c
.423
.397
.048
.623
.650
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % First graders who attended full-day kindergarten
c. Predictors: (Constant), % Percent Objectives Met, % First graders who attended full-day kindergarten,
% Percent of expenditures for instruction
d. Dependent Variable: Mathematics % Met Standard
200
The outcome of the stepwise multiple regression for fifth grade PACT
English/language arts for schools in Strata 5 (80% - 89%) produced the single most
predictive variable of percent objectives met, with a R = 0.533 (see Table 4.122). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.274, which means that the predictor variable percent objectives met accounted for
27.4% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated two variables in
combination were predictors of variance in student achievement: percent objectives
met and SACS accreditation. The correlation R for this final combination of predictor
variables was 0.605, which is positive and significant. The Adjusted R2 value was 0.348,
which means the two predictor variables in combination accounted for 34.8% of the
variance in the percentage of students scoring Proficient and Advanced at a school on
fifth grade PACT English/language arts.
Table 4.122
Stepwise Multiple Regression of Strata 5 (80% - 89%) Fifth Grade 2007-2008 PACT
English/Language Arts versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.533a
.284
.274
.000
b
2
.366
.348
.004
.605
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, SACS accreditation
c. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
mathematics for schools in Strata 5 (80% - 89%) indicated the single most predictive
variable of percent objectives met, with a R = 0.614 (see Table 4.123). This predictive
201
coefficient value is significant. The Adjusted R2 outcome was 0.368, which means that
the predictor variable percent objectives met accounted for 36.8% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated five variables in
combination were predictors of variance in student achievement: percent objectives
met, percent students satisfied with social and physical environment, SACS
accreditation, teachers returning from the previous school year, and percent classes not
taught by highly qualified teachers. The correlation R for this final combination of
predictor variables was 0.755, which is positive and significant. The Adjusted R2 value
was 0.538, which means the five predictor variables in combination accounted for 53.8%
of the variance in the percentage of students scoring Proficient and Advanced at a
school on fifth grade PACT mathematics.
Table 4.123
Stepwise Multiple Regression of Strata 5 (80% - 89%) Fifth Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
R Square
Adjusted R Square
Sig. F Change
.614a
.377
.368
.000
b
.434
.417
.011
c
.471
.447
.033
d
.504
.475
.036
e
.571
.538
.002
.658
.686
.710
.755
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Students satisfied with social and physical
environment
c. Predictors: (Constant), % Percent Objectives Met, % Students satisfied with social and physical
environment, SACS accreditation
d. Predictors: (Constant), % Percent Objectives Met, % Students satisfied with social and physical
environment, SACS accreditation, % Teachers returning from the previous school year
e. Predictors: (Constant), % Percent Objectives Met, % Students satisfied with social and physical
environment, SACS accreditation, % Teachers returning from the previous school year, % Classes not
taught by highly qualified teachers
202
f. Dependent Variable: Mathematics % Met Standard
Stepwise multiple regression for Strata 6 (90% - 94%)
The outcome of the stepwise multiple regression for third grade PACT
English/language arts for schools in Strata 6 (90% - 94%) produced the single most
predictive variable of percent objectives met, with a R = 0.567 (see Table 4.124). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.308, which means that the predictor variable percent objectives met accounted for
30.8% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance for student achievement: percent objectives
met, continuing contract teachers, and percent teachers satisfied with social and
physical environment. The correlation R for this final combination of predictor variables
was 0.684, which is positive and significant. The Adjusted R2 value was 0.434, which
means the three predictor variables in combination accounted for 43.4% of the variance
in the percentage of students scoring Proficient and Advanced at a school on third grade
PACT English/language arts within this poverty index strata.
Table 4.124
Stepwise Multiple Regression of Strata 6 (90% - 94%) Third Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.567a
.322
.308
.000
b
.422
.398
.006
c
.468
.434
.049
.649
.684
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Continuing contract teachers
c. Predictors: (Constant), % Percent Objectives Met, % Continuing contract teachers, % Teachers satisfied
203
with social and physical environment
d. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for third grade PACT
mathematics for schools in Strata 6 (90% - 94%) indicated the only one predictive
variable. This predictive variable is percent objectives met, with a R = 0.551 (see Table
4.125). The Adjusted R2 outcome was 0.289, which means that the predictor variable
percent objectives met accounted for 28.9% of the variance in the percentage of
students scoring Proficient and Advanced at a school on third grade PACT mathematics.
Table 4.125
Stepwise Multiple Regression of Strata 6 (90% - 94%) Third Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.551a
.303
.289
.000
a. Predictors: (Constant), % Percent Objectives Met
b. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
English/language arts for schools in Strata 6 (90% - 94%) produced the single most
predictive variable of percent objectives met, with a R = 0.639 (see Table 4.126). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.396, which means that the predictor variable percent objectives met accounted for
39.6% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated four variables in
combination were predictors of variance in student achievement: percent objectives
met, percent vacancies for more than nine weeks, percent teacher attendance rate, and
student-teacher ratio. The correlation R for this final combination of predictor variables
204
was 0.767, which is positive and significant. The Adjusted R2 value was 0.552, which
means the four predictor variables in combination accounted for 55.2% of the variance
in the percentage of students scoring Proficient and Advanced at a school on fourth
grade PACT English/language arts.
Table 4.126
Stepwise Multiple Regression of Strata 6 (90% - 94%) Fourth Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
R Square
Adjusted R Square
Sig. F Change
.639a
.408
.396
.000
b
.507
.486
.003
c
.547
.518
.045
d
.588
.552
.039
.712
.740
.767
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Vacancies for more than nine weeks
c. Predictors: (Constant), % Percent Objectives Met, % Vacancies for more than nine weeks, % Teacher
Attendance Rate
d. Predictors: (Constant), % Percent Objectives Met, % Vacancies for more than nine weeks, % Teacher
Attendance Rate, Student-teacher ratio
e. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
mathematics for schools in Strata 6 (90% - 94%) indicated the single most predictive
variable of percent objectives met, with a R = 0.631 (see Table 4.127). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.386, which means that
the predictor variable percent objectives met accounted for 38.6% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated two variables in
combination were predictors of variance in student achievement: percent objectives
met and percent parents satisfied with learning environment. The correlation R for this
final combination of predictor variables was 0.673, which is positive and significant. The
205
Adjusted R2 value was 0.430, which means the two predictor variables in combination
accounted for 43.0% of the variance in the percentage of students scoring Proficient and
Advanced at a school on fourth grade PACT mathematics.
Table 4.127
Stepwise Multiple Regression of Strata 6 (90% - 94%) Fourth Grade 2007-2008 PACT
Mathematics versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.631a
.398
.386
.000
b
2
.453
.430
.034
.673
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Parents satisfied with learning environment
c. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
English/language arts for schools in Strata 6 (90% - 94%) produced only one predictive
variable. The predictive variable indicated percent objectives met with the value of R =
0.533 (see Table 4.128). This coefficient value indicated a significant relationship. The
Adjusted R2 outcome was 0.269, which means that the predictor variable percent
objectives met accounted for 26.9% of the variance in the percentage of students
scoring Proficient and Advanced at a school on fifth grade PACT English/language arts
within this poverty index strata.
Table 4.128
Stepwise Multiple Regression of Strata 6 (90% - 94%) Fifth Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.533a
.284
.269
.000
a. Predictors: (Constant), % Percent Objectives Met
b. Dependent Variable: English/Language Arts % Met Standard
206
The outcome of the stepwise multiple regression for fifth grade PACT
mathematics for schools in Strata 6 (90% - 94%) indicated the single most predictive
variable of percent students satisfied with school/home relations, with a R = 0.565 (see
Table 4.129). This predictive coefficient value is significant. The Adjusted R2 outcome
was 0.305, which means that the predictor variable percent students satisfied with
school/home relations accounted for 30.5% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated five variables in
combination were predictors of variance in student achievement: percent students
satisfied with school/home relations, percent teachers satisfied with social and physical
environment, percent objectives met, teachers with emergency or provisional
certificates, and SACS accreditation. The correlation R for this final combination of
predictor variables was 0.804, which is positive and significant. The Adjusted R2 value
was 0.607, which means the five predictor variables in combination accounted for 60.7%
of the variance in the percentage of students scoring Proficient and Advanced at a
school on fifth grade PACT mathematics.
Table 4.129
Stepwise Multiple Regression of Strata 6 (90% - 94%) Fifth Grade 2007-2008 PACT Mathematics versus
SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
R Square
Adjusted R Square
Sig. F Change
.565a
.319
.305
.000
b
.433
.409
.003
c
.517
.487
.006
d
.567
.530
.026
e
.646
.607
.003
.658
.719
.753
.804
a. Predictors: (Constant), % Students satisfied with school/home relations
b. Predictors: (Constant), % Students satisfied with school/home relations, % Teachers satisfied with
social and physical environment
207
c. Predictors: (Constant), % Students satisfied with school/home relations, % Teachers satisfied with
social and physical environment, % Percent Objectives Met
d. Predictors: (Constant), % Students satisfied with school/home relations, % Teachers satisfied with
social and physical environment, % Percent Objectives Met, % Teachers with emergency or provisional
certificates
e. Predictors: (Constant), % Students satisfied with school/home relations, % Teachers satisfied with
social and physical environment, % Percent Objectives Met, % Teachers with emergency or provisional
certificates, SACS accreditation
f. Dependent Variable: Mathematics % Met Standard
Stepwise multiple regression for Strata 7 (95% - 100%)
The outcome of the stepwise multiple regression for third grade PACT
English/language arts for schools in Strata 7 (95% - 100%) produced the single most
predictive variable of percent objectives met, with a R = 0.630 (see Table 4.130). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.386, which means that the predictor variable percent objectives met accounted for
38.6% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
met, first graders who attended full-day kindergarten, and student-teacher ratio. The
correlation R for this final combination of predictor variables was 0.730, which is
positive and significant. The Adjusted R2 value was 0.506, which means the three
predictor variables in combination accounted for 50.6% of the variance in the
percentage of students scoring Proficient and Advanced at a school on third grade PACT
English/language arts.
208
Table 4.130
Stepwise Multiple Regression of Strata 7 (95% - 100%) Third Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.630a
.397
.386
.000
b
.475
.455
.007
c
.533
.506
.013
.689
.730
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % First graders who attended full-day kindergarten
c. Predictors: (Constant), % Percent Objectives Met, % First graders who attended full-day kindergarten,
Student-teacher ratio
d. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for third grade PACT
mathematics for schools in Strata 7 (95% - 100%) indicated the single most predictive
variable of percent objectives met, with a R = 0.626 (see Table 4.131). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.380, which means that
the predictor variable percent objectives met accounted for 38.0% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated three variables
in combination were predictors of variance in student achievement: percent objectives
met, prime instructional time, and teachers returning from the previous school year.
The correlation R for this final combination of predictor variables was 0.716, which is
positive and significant. The Adjusted R2 value was 0.485, which means the six predictor
variables in combination accounted for 48.5% of the variance in the percentage of
students scoring Proficient and Advanced at a school on third grade PACT mathematics.
209
Table 4.131
Stepwise Multiple Regression of Strata 7 (95% - 100%) Third Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
R Square
Adjusted R Square
Sig. F Change
.626a
.391
.380
.000
b
.444
.423
.028
c
.513
.485
.008
.666
.716
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Prime instructional time
c. Predictors: (Constant), % Percent Objectives Met, % Prime instructional time, % Teachers returning
from the previous school year
d. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
English/language arts for schools in Strata 7 (95% - 100%) produced the single most
predictive variable of percent objectives met, with a R = 0.618 (see Table 4.132). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.371, which means that the predictor variable percent objectives met accounted for
37.1% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated four variables in
combination were predictors of variance in student achievement: percent objectives
met, percent teachers satisfied with learning environment, poverty index, and teachers
with advanced degrees. The correlation R for this final combination of predictor
variables was 0.738, which is positive and significant. The Adjusted R2 value was 0.509,
which means the four predictor variables in combination accounted for 50.9% of the
variance in the percentage of students scoring Proficient and Advanced at a school on
fourth grade PACT English/language arts within this poverty index strata.
210
Table 4.132
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fourth Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
R Square
Adjusted R Square
Sig. F Change
.618a
.382
.371
.000
b
.453
.433
.010
c
.493
.464
.047
d
.544
.509
.019
.673
.702
.738
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with learning environment
c. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with learning environment,
Poverty Index
d. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with learning environment,
Poverty Index, % Teachers with advanced degrees
e. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fourth grade PACT
mathematics for schools in Strata 7 (95% - 100%) indicated the single most predictive
variable of percent objectives met, with a R = 0.632 (see Table 4.133). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.388, which means that
the predictor variable percent objectives met accounted for 38.8% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated six variables in
combination were predictors of variance in student achievement: percent objectives
met, percent teachers satisfied with learning environment, percent eligible for gifted
and talented, first graders who attended full-day kindergarten, student attendance rate,
and percent teachers satisfied with school/home relations. The correlation R for this
final combination of predictor variables was 0.833, which is positive and significant. The
Adjusted R2 value was 0.658, which means the six predictor variables in combination
211
accounted for 65.8% of the variance in the percentage of students scoring Proficient and
Advanced at a school on fourth grade PACT mathematics.
Table 4.133
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fourth Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
1
2
3
4
5
6
R Square
Adjusted R Square
Sig. F Change
.632a
.399
.388
.000
b
.509
.491
.001
c
.584
.561
.003
d
.635
.607
.009
e
.664
.631
.043
f
.694
.658
.030
.714
.764
.797
.815
.833
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with learning environment
c. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with learning environment, %
Eligible for gifted and talented
d. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with learning environment, %
Eligible for gifted and talented, % First graders who attended full-day kindergarten
e. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with learning environment, %
Eligible for gifted and talented, % First graders who attended full-day kindergarten, % Student
Attendance Rate
f. Predictors: (Constant), % Percent Objectives Met, % Teachers satisfied with learning environment, %
Eligible for gifted and talented, % First graders who attended full-day kindergarten, % Student
Attendance Rate, % Teachers satisfied with school/home relations
g. Dependent Variable: Mathematics % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
English/language arts for schools in Strata 7 (95% - 100%) produced the single most
predictive variable of percent objectives met, with a R = 0.602 (see Table 4.134). This
coefficient value indicates a significant relationship. The Adjusted R2 outcome was
0.350, which means that the predictor variable percent objectives met accounted for
35.0% of the variation in student achievement.
The final outcome of the stepwise multiple regression indicated four variables in
combination were predictors of variance in student achievement: percent objectives
212
met, poverty index, opportunities in the arts, and teachers with advanced degrees. The
correlation R for this final combination of predictor variables was 0.722, which is
positive and significant. The Adjusted R2 value was 0.484, which means the four
predictor variables in combination accounted for 48.4% of the variance in the
percentage of students scoring Proficient and Advanced at a school on fifth grade PACT
English/language arts.
Table 4.134
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fifth Grade 2007-2008 PACT English/Language
Arts versus SC DOE Annual School Report Card Variables
Model
R
1
.602a
2
.652
b
3
.687c
4
d
.521
.722
R Square
Adjusted R Square
Sig. F Change
.362
.350
.000
.425
.403
.020
.472
.441
.036
.484
.026
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Poverty Index
c. Predictors: (Constant), % Percent Objectives Met, Poverty Index, Opportunities in the arts
d. Predictors: (Constant), % Percent Objectives Met, Poverty Index, Opportunities in the arts, % Teachers
with advanced degrees
e. Dependent Variable: English/Language Arts % Met Standard
The outcome of the stepwise multiple regression for fifth grade PACT
mathematics for schools in Strata 7 (95% - 100%) indicated the single most predictive
variable of percent objectives met, with a R = 0.584 (see Table 4.134). This predictive
coefficient value is significant. The Adjusted R2 outcome was 0.329, which means that
the predictor variable percent objectives met accounted for 32.9% of the variation in
student achievement.
The final outcome of the stepwise multiple regression indicated five variables in
combination were predictors of variance in student achievement: percent objectives
213
met, professional development days per teacher, student attendance rate, poverty
index, and percent parents satisfied with learning environment. The correlation R for
this final combination of predictor variables was 0.765, which is positive and significant.
The Adjusted R2 value was 0.544, which means the five predictor variables in
combination accounted for 54.4% of the variance in the percentage of students scoring
Proficient and Advanced at a school on fifth grade PACT mathematics.
Table 4.135
Stepwise Multiple Regression of Strata 7 (95% - 100%) Fifth Grade 2007-2008 PACT Mathematics
versus SC DOE Annual School Report Card Variables
Model
R
R Square
Adjusted R Square
Sig. F Change
1
.584a
.341
.329
.000
2
.659
b
.434
.413
.005
3
.710c
.504
.476
.009
4
d
.548
.513
.030
e
.586
.544
.039
5
.741
.765
a. Predictors: (Constant), % Percent Objectives Met
b. Predictors: (Constant), % Percent Objectives Met, Professional development days per teacher
c. Predictors: (Constant), % Percent Objectives Met, Professional development days per teacher, %
Student Attendance Rate
d. Predictors: (Constant), % Percent Objectives Met, Professional development days per teacher, %
Student Attendance Rate, Poverty Index
e. Predictors: (Constant), % Percent Objectives Met, Professional development days per teacher, %
Student Attendance Rate, Poverty Index, % Parents satisfied with learning environment
f. Dependent Variable: Mathematics % Met Standard
Summary of stepwise multiple regression for each poverty index strata
The sixty-one PreKindergarten – 5 and Kindergarten – 5 public elementary
schools categorized in Strata 1 (0% - 49%) represent the most affluent schools in South
Carolina. Twelve predictor variables, whether individually or in combination with other
variables, were produced in poverty index Strata 1 (0% - 49%). The predictor variables
that were produced the most from the stepwise multiple regression were poverty index
214
and older than usual for grade (see Table 4.136). These variables were produced in all
six subsets: third grade PACT English/language arts and mathematics, fourth grade PACT
English/language arts and mathematics, and fifth grade PACT English/language arts and
mathematics. Parents attending conferences was the variable that was produced four
times - the second most times in combination with other variables. The predictor
variables percent objectives met and students with disabilities other than speech were
indicated three times each. Three survey items were produced two times each. The
survey items were percent teachers satisfied with learning environment, percent
students satisfied with school/home relations, and percent parents satisfied with
school/home relations.
The highest single predictive variable which produced the greatest adjusted R2
was percent parents satisfied with school/home (0.296) and the lowest adjusted R2 was
percent objectives met (0.153) (see Table 4.137). The combination of variables that
produced the highest adjusted R2 was found in third grade PACT mathematics with a
variance of 0.746, which indicated that 74.6% of the variability within this strata was
produced by the variables eligible for gifted and talented, percent objectives met, older
than usual for grade, poverty index, parents attending conferences, and teachers on
emergency or provisional.
215
Table 4.136
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 1 (0% - 49%)
Strata 1 (0% - 49%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math* Totals**
Poverty Index
3
4
6
2
3
3
6
Eligible for gifted and talented
1
1
Percent Objectives Met
2
1
1
3
Students with disabilities other than
2
4
3
speech
4
Older than usual for grade
1
3
4
6
4
2
6
Teachers with emergency or provisional
6
1
certificates
Teachers returning from the previous
2
1
school year
Parents attending conferences
2
5
3
3
4
SACS accreditation
6
1
Percent Teachers satisfied with learning
5
5
2
environment
Percent Teachers satisfied with
5
1
school/home relations
Percent Students satisfied with
5
4
2
school/home relations
Percent Parents satisfied with
1
1
2
school/home relations
*Numbers represent the order of the variables produced in the stepwise multiple regression.
**Represents the total instances the variable appears among the 6 subsets within the poverty index
strata
216
Table 4.137
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty Index
Strata 1 (0% - 49%) by Adjusted R2
Strata 1 (0% - 49%)
Third Grade
Fourth Grade
Fifth Grade
ELA*
Math*
ELA*
Math*
ELA*
Math*
.446
.648
.516
.391
.426
.531
Poverty Index
.287
Eligible for gifted and talented
.547
.153
.271
Percent Objectives Met
Students with disabilities other than
.484
.345
.467
speech
.172
.594
.435
.531
.501
.406
Older than usual for grade
Teachers with emergency or
.746
provisional certificates
Teachers returning from the
.279
previous school year
.330
.719
.387
.431
Parents attending conferences
.645
SACS accreditation
Percent Teachers satisfied with
.482
.503
learning environment
Percent Teachers satisfied with
.619
school/home relations
Percent Students satisfied with
.542
.596
school/home relations
Percent Parents satisfied with
.224
.296
school/home relations
*Numbers represent the strength of the correlation from the first variable produced to the final
combination of variables that demonstrated significance.
In Strata 2 (50% - 59%), forty-eight PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina were represented. Eleven predictor
variables, whether individually or in combination with other variables, were produced in
Strata 2 (50% - 59%). The predictor variable that was produced the most from the
stepwise multiple regression was percent objectives met (see Table 4.138). This variable
was produced in five out of six subsets: third grade PACT English/language arts, fourth
grade PACT English/language arts and mathematics, and fifth grade PACT
English/language arts and mathematics. A significant disparity existed between the
most produced predictor variable (percent objectives met) and the variables that were
217
produced the second most (eligible for gifted and talented, SACS accreditation, and
percent teachers satisfied with school/home relations). These three predictor variables
were produced only two times in combination with other variables. Interestingly, the
variables produced within each subset ranged from two variables to four variables.
The highest single predictive variable which produced the greatest adjusted R2
was percent objectives met (0.290) and the lowest adjusted R2 was percent objectives
met (0.167) (see Table 4.139). The combination of variables that produced the highest
adjusted R2 was found in third grade PACT mathematics with a variance of 0.537, which
indicated that 53.7% of the variability within this strata was produced by the variables
students with disabilities, SACS accreditation, percent parents satisfied with learning,
and percent teachers satisfied with school/home.
Table 4.138
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 2 (50% - 59%)
Strata 2 (50% - 59%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math* Totals**
First graders who attended full-day
3
1
kindergarten
Eligible for gifted and talented
2
2
2
Percent Objectives Met
1
1
1
1
1
5
Students with disabilities other than
3
1
speech
Older than usual for grade
2
1
Dollars spent per student
3
1
SACS accreditation
3
2
2
Percent Parents satisfied with learning
1
1
environment
Percent Students satisfied with social and
3
1
physical environment
Percent Teachers satisfied with
4
2
2
school/home relations
Character Development Program
2
1
*Numbers represent the order of the variables produced in the stepwise multiple regression.
**Represents the total instances the variable appears among the 6 subsets within the poverty index
strata
218
Table 4.139
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 2 (50% - 59%) by Adjusted R2
Strata 2 (50% - 59%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math*
.423
First graders who attended full-day kindergarten
.324
.417
Eligible for gifted and talented
.290
.272
.254
.167
.280
Percent Objectives Met
.497
Students with disabilities other than speech
.343
Older than usual for grade
.439
Dollars spent per student
.454
.394
SACS accreditation
.262
Percent Parents satisfied with learning environment
Percent Students satisfied with social and physical
.475
environment
.537
.262
Percent Teachers satisfied with school/home relations
.402
Character Development Program
*Numbers represent the strength of the correlation from the first variable produced to the final
combination of variables that demonstrated significance.
In Strata 3 (60% - 69%), seventy-one PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina were represented. Thirteen predictor
variables, whether individually or in combination with other variables, were produced in
Strata 3 (60% - 69%). The predictor variable that was produced the most from the
stepwise multiple regression was percent objectives met (see Table 4.140). This variable
was produced in six out of six subsets: third grade PACT English/language arts and
mathematics, fourth grade PACT English/language arts and mathematics, and fifth grade
PACT English/language arts and mathematics. A significant disparity existed between
the most produced predictor variable (percent objectives met) and the variables that
were produced the second most (continuing contract teachers, student-teacher ratio,
and spent on teacher salaries). These three predictor variables were produced only two
219
times in combination with other variables. The variables produced within each subset
ranged from one variable to six variables.
The highest single predictive variable which produced the greatest adjusted R2
was percent objectives met (0.341) and the lowest adjusted R2 was percent objectives
met (0.222) (see Table 4.141). The combination of variables that produced the highest
adjusted R2 was found in third grade PACT mathematics with a variance of 0.462, which
indicated that 46.2% of the variability was produced by the variables percent objectives
met, older than usual for grade, student-teacher ratio, spent on teacher salaries,
parents attending conferences, and SACS accreditation.
Table 4.140
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 3 (60% - 69%)
Strata 3 (60% - 69%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math* Totals**
Percent Objectives Met
1
1
1
1
1
1
6
Students with disabilities other than
4
1
speech
Older than usual for grade
2
1
Teachers with advanced degrees
2
1
Continuing contract teachers
2
2
2
Teachers returning from the previous
2
1
school year
Professional development days per teacher
3
1
Student-teacher ratio
3
6
2
Spent on teacher salaries
3
3
2
Parents attending conferences
4
1
SACS accreditation
5
1
Percent Students satisfied with learning
3
1
environment
Percent Parents satisfied with
4
1
school/home relations
*Numbers represent the order of the variables produced in the stepwise multiple regression.
**Represents the total instances the variable appears among the 6 subsets within the poverty index
strata
220
Table 4.141
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 3 (60% -69%) by Adjusted R2
Strata 3 (60% - 69%)
Third Grade
ELA*
.271
Percent Objectives Met
Math*
.226
Fourth Grade
ELA*
.222
Math*
.341
Fifth Grade
ELA*
.240
Math*
.277
.441
Students with disabilities other than speech
.313
Older than usual for grade
.329
Teachers with advanced degrees
.297
Continuing contract teachers
.377
.369
Teachers returning from the previous school year
.327
Professional development days per teacher
.368
Student-teacher ratio
.462
Spent on teacher salaries
.356
Parents attending conferences
.395
SACS accreditation
.436
.407
Percent Students satisfied with learning environment
Percent Parents satisfied with school/home relations
*Numbers represent the strength of the correlation from the first variable produced to the final
combination of variables that demonstrated significance.
.400
.437
In Strata 4 (70% - 79%), seventy-one PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina were represented. Sixteen predictor
variables, whether individually or in combination with other variables, were produced in
Strata 4 (70% - 79%). The predictor variable that was produced the most from the
stepwise multiple regression was percent objectives met (see Table 4.142). This variable
was produced in four out of six subsets: third grade PACT English/language arts and
mathematics and fourth grade PACT English/language arts and mathematics. The
difference between the most produced predictor variable (percent objectives met) and
the variable that was produced the second most (percent parents satisfied with learning
environment) was one. This predictor variable was produced three times in
combination with other variables. The variables 135-day average daily membership,
221
retention rate, teachers returning from the previous school year, portable classrooms,
and character development program were produced two times. The variables produced
within each subset ranged from two variables to eight variables.
The highest single predictive variable which produced the greatest adjusted R2
was percent parents satisfied with school/home (0.351) and the lowest adjusted R2 was
percent parents satisfied with learning (0.156) (see Table 4.143). The combination of
variables that produced the highest adjusted R2 was found in third grade PACT
mathematics with a variance of 0.536, which indicated that 53.6% of the variability
within this strata was produced by the variables percent objectives met, teachers with
advanced degrees, percent students satisfied with learning, percent parents satisfied
with learning, and percent teachers satisfied with school/home.
222
Table 4.142
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 4 (70% - 79%)
Strata 4 (70% - 79%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math* Totals**
135-Day Average Daily Membership (ADM)
4
4
2
First graders who attended full-day
1
kindergarten
5
Retention rate
8
3
2
Eligible for gifted and talented
2
1
Percent Objectives Met
1
1
1
1
4
Older than usual for grade
6
1
Teachers with advanced degrees
4
1
Continuing contract teachers
7
1
Teachers returning from the previous
2
2
2
school year
Teacher Attendance Rate
4
1
Portable classrooms
2
2
2
Percent Students satisfied with learning
3
1
environment
Percent Parents satisfied with learning
5
1
1
3
environment
Percent Students satisfied with social and
1
physical environment
3
Percent Teachers satisfied with
2
1
school/home relations
Character Development Program
3
3
2
*Numbers represent the order of the variables produced in the stepwise multiple regression.
**Represents the total instances the variable appears among the 6 subsets within the poverty index
strata
223
Table 4.143
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 4 (70% - 79%) by Adjusted R2
Strata 4 (70% - 79%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math*
.359
.354
135-Day Average Daily Membership (ADM)
.407
First graders who attended full-day kindergarten
.517
.317
Retention rate
.265
Eligible for gifted and talented
.204
.351
.194
.251
Percent Objectives Met
.437
Older than usual for grade
.506
Teachers with advanced degrees
.474
Continuing contract teachers
.255
.300
Teachers returning from the previous school year
.358
Teacher Attendance Rate
.260
.241
Portable classrooms
.481
Percent Students satisfied with learning environment
.536
.191
.156
Percent Parents satisfied with learning environment
Percent Students satisfied with social and physical
.322
environment
.429
Percent Teachers satisfied with school/home relations
.311
.280
Character Development Program
*Numbers represent the strength of the correlation from the first variable produced to the final
combination of variables that demonstrated significance.
In Strata 5 (80% - 89%), seventy-five PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina were represented. Nine predictor variables,
whether individually or in combination with other variables, were produced in Strata 5
(80% - 89%). This poverty index strata had the fewest number of predictor variables
produced. The predictor variable that was produced the most from the stepwise
multiple regression was percent objectives met (see Table 4.144). This variable was
produced in six out of six subsets: third grade PACT English/language arts and
mathematics, fourth grade PACT English/language arts and mathematics, and fifth grade
English/language arts and mathematics. The difference between the most produced
predictor variable (percent objectives met) and the variable that was produced the
224
second most (SACS accreditation) was two. This predictor variable was produced four
times in combination with other variables. The variables 135-day average daily
membership, first graders who attended full-day kindergarten, and student-teacher
ratio were produced two times. The variables produced within each subset ranged from
two variables to five variables.
The highest single predictive variable which produced the greatest adjusted R2
was percent objectives met (0.368) and the lowest adjusted R2 was percent objectives
met (0.218) (see Table 4.145). The combination of variables that produced the highest
adjusted R2 was found in fifth grade PACT mathematics with a variance of 0.538, which
indicated that 53.8% of the variability was produced by the variables percent objectives
met, classes not taught by highly qualified teachers, teachers returning from the
previous school year, SACS accreditation, and percent students satisfied with social and
physical.
Table 4.144
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 5 (80% - 89%)
Strata 5 (80% - 89%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math* Totals**
135-Day Average Daily Membership (ADM)
2
5
2
First graders who attended full-day
4
2
2
kindergarten
Percent Objectives Met
1
1
1
1
1
1
6
Classes not taught by highly qualified
5
1
teachers
Teachers returning from the previous
4
1
school year
Student-teacher ratio
3
2
2
SACS accreditation
3
2
2
3
4
Percent Students satisfied with social and
2
1
physical environment
Percent of expenditures for instruction
3
1
*Numbers represent the order of the variables produced in the stepwise multiple regression.
225
**Represents the total instances the variable appears among the 6 subsets within the poverty index
strata
Table 4.145
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 5(80% -89%) by Adjusted R2
Strata 5 (80% - 89%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math*
.288
.496
135-Day Average Daily Membership (ADM)
.472
.371
First graders who attended full-day kindergarten
.218
.362
.332
.340
.274
.368
Percent Objectives Met
.538
Classes not taught by highly qualified teachers
.475
Teachers returning from the previous school year
.433
.380
Student-teacher ratio
.322
.400
.348
.447
SACS accreditation
Percent Students satisfied with social and physical
.417
environment
.397
Percent of expenditures for instruction
*Numbers represent the strength of the correlation from the first variable produced to the final
combination of variables that demonstrated significance.
In Strata 6 (90% - 94%), fifty-six PreKindergarten – 5 and Kindergarten – 5 public
elementary schools in South Carolina were represented. Ten predictor variables,
whether individually or in combination with other variables, were produced in Strata 6
(90% - 94%). The predictor variable that was produced the most from the stepwise
multiple regression was percent objectives met (see Table 4.146). This variable was
produced in six out of six subsets: third grade PACT English/language arts and
mathematics, fourth grade PACT English/language arts and mathematics, and fifth grade
English/language arts and mathematics. The difference between the most produced
predictor variable (percent objectives met) and the variable that was produced the
second most (percent teachers satisfied with school/home relations) was four. This
predictor variable was produced two times in combination with other variables. The
remaining eight predictor variables produced from all of the subsets were indicated one
226
time each. The variables produced within each subset ranged from one variable to five
variables. Interestingly, two subsets only produced one predictive variable: third grade
PACT mathematics and fifth grade PACT English/language arts. Fourth grade PACT
mathematics produced only two variables from the stepwise multiple regression.
The highest single predictive variable which produced the greatest adjusted R2
was percent objectives met (0.434) and the lowest adjusted R2 was percent objectives
met (0.269) (see Table 4.147). The combination of variables that produced the highest
adjusted R2 was found in fifth grade PACT mathematics with a variance of 0.607, which
indicated that 60.7% of the variability was produced by the variables percent objectives
met, teachers with emergency or provisional, SACS accreditation, percent teachers
satisfied with social and physical, and percent students satisfied with school/home
relations.
Table 4.146
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 6 (90% - 94%)
Strata 6 (90% - 94%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math* Totals**
Percent Objectives Met
1
1
1
1
1
3
6
Continuing contract teachers
2
1
Teachers with emergency or provisional
4
1
certificates
Teacher Attendance Rate
3
1
Student-teacher ratio
4
1
SACS accreditation
5
1
Percent Parents satisfied with learning
2
1
environment
Percent Teachers satisfied with social and
2
2
physical environment
3
Percent Students satisfied with
1
1
school/home relations
Vacancies for more than nine weeks
2
1
*Numbers represent the order of the variables produced in the stepwise multiple regression.
**Represents the total instances the variable appears among the 6 subsets within the poverty index
strata
227
Table 4.147
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 6 (90% - 94%) by Adjusted R2
Strata 6 (90% - 94%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math*
.308
.434
.396
.386
.269
.487
Percent Objectives Met
.398
Continuing contract teachers
.530
Teachers with emergency or provisional certificates
.518
Teacher Attendance Rate
.552
Student-teacher ratio
.607
SACS accreditation
.430
Percent Parents satisfied with learning environment
Percent Teachers satisfied with social and physical
.434
.409
environment
.305
Percent Students satisfied with school/home relations
.486
Vacancies for more than nine weeks
*Numbers represent the strength of the correlation from the first variable produced to the final
combination of variables that demonstrated significance.
In Strata 7 (95% - 100%), fifty-seven PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina were represented. Fourteen predictor
variables, whether individually or in combination with other variables, were produced.
The predictor variable that was produced the most from the stepwise multiple
regression was percent objectives met (see Table 4.148). This variable was produced in
six out of six subsets: third grade PACT English/language arts and mathematics, fourth
grade PACT English/language arts and mathematics, and fifth grade English/language
arts and mathematics. The difference between the most produced predictor variable
(percent objectives met) and the variable that was produced the second most (poverty
index) was three. This predictor variable was produced three times in combination with
other variables. Four predictor variables were produced two times each: first graders
who attend full-day kindergarten, student attendance rate, teachers with advanced
degrees, and percent teachers satisfied with learning environment. The remaining nine
228
predictor variables produced from all of the subsets were indicated one time each. The
variables produced within each subset ranged from three variables to six variables.
The highest single predictive variable which produced the greatest adjusted R2
was percent objectives met (0.388) and the lowest adjusted R2 was percent objectives
met (0.329) (see Table 4.149). The combination of variables that produced the highest
adjusted R2 was found in fourth grade PACT mathematics with a variance of 0.658,
which indicated that 65.8% of the variability was produced by the variables first graders
who attended full-day kindergarten, student attendance rate, eligible for gifted and
talented, percent objectives met, percent teachers satisfied with learning, and percent
teachers satisfied with school/home relations.
Table 4.148
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 7 (95% - 100%)
Strata 7 (95% - 100%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math* Totals**
Poverty Index
3
2
4
3
First graders who attended full-day
4
2
kindergarten
2
Student Attendance Rate
5
3
2
Eligible for gifted and talented
3
1
Percent Objectives Met
1
1
1
1
1
1
6
Teachers with advanced degrees
4
4
2
Teachers returning from the previous
3
1
school year
Professional development days per teacher
2
1
Student-teacher ratio
3
1
Prime instructional time
2
1
Opportunities in the arts
3
1
Percent Teachers satisfied with learning
2
2
2
environment
Percent Parents satisfied with learning
5
1
environment
Percent Teachers satisfied with
6
1
school/home relations
*Numbers represent the order of the variables produced in the stepwise multiple regression.
**Represents the total instances the variable appears among the 6 subsets within the poverty index
229
strata
Table 4.149
Summary of the Order of Outcome Variables Produced by Stepwise Multiple Regression for Poverty
Index Strata 7 (95% - 100%) by Adjusted R2
Strata 7 (95% - 100%)
Third Grade
Fourth Grade
Fifth Grade
ELA* Math* ELA* Math* ELA* Math*
Poverty Index
.464
.403
.513
First graders who attended full-day kindergarten
.455
.607
Student Attendance Rate
.631
.476
Eligible for gifted and talented
.561
Percent Objectives Met
.386
.380
.371
.388
.350
.329
Teachers with advanced degrees
.509
.484
Teachers returning from the previous school year
.485
Professional development days per teacher
.413
Student-teacher ratio
.506
Prime instructional time
.423
Opportunities in the arts
.441
Percent Teachers satisfied with learning environment
.433
.491
Percent Parents satisfied with learning environment
.544
Percent Teachers satisfied with school/home relations
.658
*Numbers represent the strength of the correlation from the first variable produced to the final
combination of variables that demonstrated significance.
Summary of stepwise multiple regression for all poverty index strata
A stepwise multiple regression was conducted on student achievement data in
third grade, fourth grade, and fifth grade and variables from the South Carolina
Department of Education Annual School Report Card. Student achievement was the
percentage of students scoring Proficient and Advanced in English/language arts and
mathematics on the 2007-2008 Palmetto Achievement Challenge Test. The cumulative
results of the stepwise multiple regression between student achievement and the SC
OEC 2008 Annual School Report Card variables are as follows (see Table 4.150):
•
In five of the six poverty index strata for all grades and all subjects, percent
objectives met was the most predictive variable. One subgroup, fifth grade all
schools PACT English/language arts, poverty index was the predictive variable.
230
This subset was the only subset that did not have percent objectives met as the
highest predictive variable of student achievement.
•
The most predictive variable within each subset of the seven poverty index
strata, percent objectives met, was produced thirty-six times out of the fortytwo possible outcomes.
•
The predictive variables produced the second most often were poverty index,
older than usual for grade, and SACS accreditation. Each of these predictive
variables was produced nine times.
•
Four predictive variables were produced six times: first graders who attended
full-day kindergarten, teachers returning from the previous school year, studentteacher ratio, and percent parents satisfied with learning environment.
•
Three predictive variables were produced five times: eligible for gifted and
talented, students with disabilities other than speech, and parents attending
conferences.
•
The single highest predictive variable with the greatest adjusted R2 produced
among the six subsets within the seven poverty index strata was the variable
percent objectives met. This variable was indicated as the single highest
predictive variable of student achievement five times in the seven poverty index
strata with the following adjusted R2 values: 0.290, 0.341, 0.368, 0.434, and
0.388. The second most produced variable was percent parents satisfied with
school/home relations, which was indicated two times with adjusted R2 values of
0.296 and 0.351.
231
•
The combination of variables that produced the highest adjusted R2 was found in
third grade PACT mathematics with a variance of 0.746. Important to note, the
combination of variables with the highest adjusted R2 per poverty index strata
subset was found in third grade PACT mathematics four times, fifth grade PACT
mathematics two times, and one time in fourth grade PACT mathematics. No
poverty index subsets in PACT English/language arts were found that had a
combination of variables with the highest adjusted R2.
232
Table 4. 150
Summary of Stepwise Multiple Regression for Each Poverty Index Strata
Number of Occurrences / 42
Predictor Variables
Possible Occurrences
Poverty Index
9
135-Day Average Daily Membership (ADM)
4
First graders who attended full-day kindergarten
6
Retention rate
2
Student Attendance Rate
2
Eligible for gifted and talented
5
Percent Objectives Met
36
Students with disabilities other than speech
5
Older than usual for grade
9
Teachers with advanced degrees
4
Continuing contract teachers
4
Classes not taught by highly qualified teachers
1
Teachers with emergency or provisional certificates
2
Teachers returning from the previous school year
6
Teacher Attendance Rate
2
Professional development days per teacher
2
Student-teacher ratio
6
Prime instructional time
1
Dollars spent per student
1
Spent on teacher salaries
2
Opportunities in the arts
1
Parents attending conferences
5
SACS accreditation
9
Portable classrooms
2
Percent Teachers satisfied with learning environment
4
Percent Students satisfied with learning environment
2
Percent Parents satisfied with learning environment
6
Percent Teachers satisfied with social and physical environment
2
Percent Students satisfied with social and physical environment
3
Percent Teachers satisfied with school/home relations
5
Percent Students satisfied with school/home relations
3
Percent Parents satisfied with school/home relations
3
Vacancies for more than nine weeks
1
Character Development Program
3
Percent of expenditures for instruction
1
Summary
The relationship between elementary school size and student achievement as
measured by the 2007-2008 Palmetto Achievement Challenge Test data for third,
fourth, and fifth grade students in English/language arts and mathematics in South
233
Carolina was investigated. The investigation utilized descriptive and inferential
statistics, examining the variables’ relationships through simple and partial correlations,
and with schools grouped into poverty index strata. Also examined was the relationship
between student achievement and variables as reported on the South Carolina
Department of Education’s 2008 Annual School Report Card through the use of stepwise
multiple regression.
For the first research question, a Pearson correlation analysis was conducted on
student achievement and school size to ascertain whether a correlation existed.
A simple Pearson correlation was run to determine if any relationship existed that
supported the use of the control variable of poverty and/or identified interactions
between the variable of school size and student achievement that might affect
generalization from the outcome of the study. In all six subgroups, the results of the
Pearson correlation were positive and significant at p<0.01 level. When a partial
correlation was conducted on the same six subgroups, none of the subgroups revealed a
significant correlation between student achievement and school size (average daily
membership). When a stepwise multiple regression was conducted for each subgroup
using student achievement and school size (135-day average daily membership) as
variables, no significant correlations were note in the six subgroups. The data did reveal
negative correlations between student achievement and poverty in each subgroup;
however, the correlations were not significant.
For the second research question, a partial correlation analysis of student
achievement and school size was conducted on each poverty index strata, then each
234
subgroup within each strata to control for the effects of poverty. For each poverty index
strata 2007-2008 PACT English/language arts and PACT mathematics data of students
scoring Proficient and Advanced for third grade, fourth grade and fifth grade were
analyzed.
The forty-two separate partial correlations identified six subgroups with
significant negative correlations. The remaining thirty-six subgroups analyzed
demonstrated no significant correlations. The conclusion is that since only six in fortytwo analyses produced a significant correlation, school size is not a predictor of student
achievement for the schools within any of the seven poverty index strata, at least when
using the partial correlation approach. Following the partial correlation analysis, a
stepwise multiple regression analysis was conducted within each poverty index strata
for each subgroup. The outcome of the stepwise multiple regression analysis within the
seven poverty index strata revealed no significant correlations.
For the third research question, the results of the stepwise multiple regression
using student achievement data in third grade, fourth grade, and fifth grade and
variables from the 2007-2008 South Carolina Department of Education Annual School
Report Card were analyzed. The student achievement data were the 2007-2008
Palmetto Achievement Challenge Test percentage of students scoring Proficient and
Advanced in English/language arts and mathematics. The outcome of the stepwise
multiple regression was that for five of the six subgroups of third grade, fourth grade,
and fifth grade PACT English/language arts and mathematics, the variable percent
objectives met was most often identified first as having the highest correlation to
235
outcomes. The subgroup fifth grade all schools PACT English/language arts was the one
subgroup that did not have percent objectives met as the highest correlated variable to
student achievement. This subgroup produced the variable poverty index as the highest
correlated variable.
The stepwise multiple regression analysis was conducted a second time utilizing
the same student achievement data and dependent variables. The researcher
controlled for the effects of poverty by running the stepwise multiple regression on
schools within each poverty index strata (0% - 49%, 50% - 59%, 60% - 69%, 70% - 79%,
80% - 89%, 90% - 94%, and 95% - 100%). As in the previous stepwise multiple regression
analysis, the variable percent objectives met was identified as the variable with the
highest correlation to student achievement in the first model thirty-six times out of the
forty-two analyses. The variable percent parents satisfied with the learning
environment was the second highest predictive variable in the first model. The variable
parents satisfied with home-school relations was identified in two analyses as the
variable with the highest correlation. Other variables from the SC DOE Annual School
Report Card were identified as variables that were correlated to student achievement
within the stepwise multiple regression within a subgroup: poverty index, first graders
that attended full-day kindergarten, students with disabilities other than speech,
students older than usual for grade, teachers returning from the previous school year,
SACS accreditation, parents attending conferences, percent parents satisfied with the
learning environment, percent teachers satisfied with home-school relations, and
student-teacher ratio.
236
The first two research questions were constructed to determine whether school
size was correlated to student achievement when controlling for the effects of poverty
through the use of poverty index strata. The outcome of Pearson correlation, partial
correlation, and stepwise multiple regression analysis revealed that student school size
was not correlated to student achievement.
The third research question sought to ascertain whether a variable or set of
variables were correlated to student achievement. The variable percent objectives met
demonstrated a significant correlation to student achievement when the analysis was
conducted without controlling for the effects of poverty and when the researcher
controlled for the effects of poverty through the use of poverty index strata. Percent
objectives met was also the variable that was indicated as the single highest predictive
variable in four of the seven poverty index strata subsets with adjusted R2 values of
0.290, 0.341, 0.368, 0.434, and 0.388. A combination of variables that included SACS
accreditation, students older than usual for grade, poverty index, first graders that
attended full-day kindergarten, teachers returning from the previous school year,
student-teacher ratio, parents satisfied with the learning environment, students with
disabilities other than speech, teachers satisfied with home-school relations, and
parents attending conferences were found to most often be predictive of student
achievement. The combination of variables with the highest adjusted R2 per poverty
index strata subset was found in third grade PACT mathematics (four times), fifth grade
PACT mathematics (two times), and fourth grade PACT mathematics (one time). No
subsets with the combination of variables with the highest adjusted R2 per poverty
237
index strata subset were found in PACT English/language arts. Important to note is that
for this study, school size, or 135-day average daily membership, as a single variable, or,
in combination with multiple variables, did not indicate a significant predictive
relationship to student achievement.
Chapter IV provided the data analysis for the three research questions addressed
by this study. Chapter V contains a brief summary of the study’s purpose, a discussion
of the study’s findings, conclusions, and recommendations for future research.
238
CHAPTER V
Summary, Discussion, Conclusions, and Recommendations
The first four chapters presented the introduction to the study, the literature
pertaining to school size as well as other variables that may be predictive of student
achievement, the methodology utilized, and the findings for the research questions.
This final chapter contains a brief review of the purpose of the study, a synopsis of the
findings of the research questions, and a presentation of conclusions based upon an
analysis of the data. This chapter concludes with recommendations for educational
policy makers, educators, and researchers, as well as suggestions for future research.
Purpose of the Study and Its Design
One purpose of this study was to examine the relationship between the size of
South Carolina public elementary schools and student achievement while controlling for
the effect of socioeconomic status. A second purpose was to ascertain whether one
variable or combination of variables was predictive of student achievement utilizing the
South Carolina Department of Education (SC DOE) 2008 Annual School Report Card data.
The study was based on three research questions. The three research questions
investigated were:
1. Does a relationship exist between the enrollment of South Carolina’s
239
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and
student achievement in English/language arts and mathematics?
Achievement is defined by the percentage of the third, fourth and fifth grade
students scoring Proficient and Advanced on the 2007-2008 Palmetto
Achievement Challenge Test. Do results vary when controlling for poverty?
2. Does a relationship exist between the enrollment in South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and
student achievement in English/language arts and mathematics as defined by
the results of the third, fourth, and fifth grade 2007-2008 Palmetto
Achievement Challenge Test scores when schools are grouped by poverty
index of schools? Achievement is defined as the percentage of students
scoring Proficient and Advanced.
3. Can student achievement in South Carolina’s PreKindergarten – 5 or
Kindergarten – 5 public elementary schools in English/language arts and
mathematics as measured by the third, fourth and fifth grade 2007-2008
Palmetto Achievement Challenge Test be predicted by at least one, and
possibly a combination, of the following variables:
1. Poverty index
2. School size or average daily membership
3. First graders that attended full-day kindergarten
4. Retention rate
5. Student attendance rate
6. Eligible for gifted and talented
7. Percent objectives met
8. Students with disabilities other than speech
9. Students older than usual for grade
10. Suspended or expelled
240
11. Number of teachers with advanced degrees
12. Continuing contract teachers
13. Classes not taught by highly qualified teachers
14. Teachers with emergency or provisional certificates
15. Teachers returning from the previous school year
16. Teacher attendance rate
17. Average teacher salary
18. Professional development days per teacher
19. Principal’s or director’s years at the schools
20. Student-teacher ratio
21. Prime instructional time
22. Dollars spent per student
23. Spent on teacher salaries
24. Opportunities in the arts
25. Parents attending conferences
26. SACS accreditation
27. Portable classrooms
28. Percent of teachers satisfied with the learning environment
29. Percent of students satisfied with the learning environment
30. Percent of parents satisfied with the learning environment
31. Percent of teachers satisfied with social and physical environment
32. Percent of students satisfied with social and physical environment
33. Percent of parents satisfied with social and physical environment
34. Percent of teachers satisfied with home-school relations
35. Percent of students satisfied with home-school relations
36. Percent of parents satisfied with home-school relations
37. Vacancies for more than nine weeks
38. Character development program
39. Percent of expenditures for instruction
For research questions one and two, the independent variable was school size,
or 135-day average daily membership, and the control variable was the poverty index of
each PreKindergarten – 5 or Kindergarten – 5 public South Carolina elementary school.
The dependent variable was student achievement, which was measured as the
percentage of students scoring Proficient and Advanced on the 2008 Palmetto
Achievement Challenge Test (PACT) in the third, fourth, and fifth grades in
English/language arts and mathematics.
241
The elementary schools were placed into poverty index strata based on each
school’s poverty index. The seven percentile strata were: 0% - 49%, 50% - 59%, 60% 69%, 70% - 79%, 80% - 89%, 90% - 94%, and 95% - 100%. Each percentile strata
contained approximately the same number of schools. The number of schools in each
poverty index strata was: 0% - 49% (63 schools); 50% - 59% (48 schools); 60% - 69% (73
schools); 70% - 79% (71 school); 80% - 89% (75 schools); 90% - 94% (54 schools); 95% 100% (57 schools).
The dependent variable was student achievement, which was measured as the
percentage of students scoring Proficient and Advanced on the 2008 Palmetto
Achievement Challenge Test (PACT) in the third, fourth, and fifth grades in
English/language arts and mathematics. Building on Kaczor’s work (2006), the
researcher categorized the elementary schools into strata based on poverty index.
Seven poverty index strata were created. Then, student achievement data and SC DOE
2008 Annual School Report Card variables were analyzed within each strata to ascertain
whether one variable, or a combination of variables, was predictive of student
achievement. For this research question, the poverty index strata were utilized to
control for the effects of poverty.
Findings for the Study
Data collected and analyzed for this study provided answers for all three
research questions. PASW Statistics Base 18 software was used for all statistical
calculations and for the creation of the tables. Following a summary of the research
findings, the results are discussed in relation to the literature review.
242
Research Question One
The first research question for this study was:
Does a relationship exist between the enrollment of South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and
student achievement in English/language arts and mathematics?
Achievement is defined by the percentage of the third, fourth and fifth
grade students scoring Proficient and Advanced on the 2007-2008
Palmetto Achievement Challenge Test. Do results vary when controlling
for poverty?
To answer this question, descriptive statistics were calculated for the 441
schools based on student achievement data in third, fourth, and fifth grades for PACT
English/language arts and mathematics. Pearson correlations without statistical
controls were run to assess relationships among variables. Then, a partial correlation
technique was used to investigate the relationship between student achievement and
school size, or 135-day averaged daily membership, while controlling for poverty.
Finally, a stepwise multiple regression was conducted on the dependent variables PACT
English/language arts and mathematics and the independent variables of school size
and poverty index.
The Pearson correlation analyses indicated a positive and significant correlation
with 135-day average daily membership (ADM) for third, fourth, and fifth grade on PACT
English/language arts and mathematics. The interpretation of these analyses is that as
school size increases so does student achievement. This did not, however, continue to
243
hold true when the partial correlation analysis. In all six recalculations, when controlling
for poverty, no significant correlations between student achievement and ADM were
found. The data indicated a negative correlation between student achievement and
ADM, which the interpretation is school size is a negative predictor of student
achievement. Finally, the outcome of the stepwise multiple regression for the same
data sets produced the indications that ADM was not significantly correlated to student
achievement – positively nor negatively at each grade level for either subject.
However, the data did reveal significant correlations between student
achievement and poverty across all three grades and both subjects. The relationship
was a negative one in each case. A negative correlation indicates that as the poverty
index of the school increased, the percentage of students scoring Proficient and
Advanced decreased in English/language arts and in mathematics in third grade, fourth
grade, and fifth grade.
Research Question Two
The second research question for this study was:
Does a relationship exist between the enrollment in South Carolina’s
PreKindergarten – 5 or Kindergarten – 5 public elementary schools and
student achievement in English/language arts and mathematics as
defined by the results of the third, fourth, and fifth grade 2007-2008
Palmetto Achievement Challenge Test scores when schools are grouped
by poverty index of schools? Achievement is defined as the percentage
of students scoring Proficient and Advanced.
244
To answer this question, descriptive statistics were calculated within the seven
poverty index strata for third, fourth, and fifth grades for PACT English/language arts
and mathematics. Pearson correlations without statistical controls were run to assess
relationships among variables within each poverty index strata. Then, a partial
correlation technique was used to investigate the relationship between student
achievement and school size, or 135-day averaged daily membership, while controlling
for poverty within the poverty index strata. Finally, a stepwise multiple regression was
conducted on the dependent variables PACT English/language arts and mathematics
and the independent variables of school size and poverty index within the seven poverty
index strata.
The results of each Pearson correlation analysis of student achievement to ADM
yielded six subsets of significant correlations from a total of forty-two subsets. The
poverty index strata and student achievement subject areas indicated six significant
correlations. Each of the six significant correlations indicated a negative relationship.
The interpretation of these outcomes is that, for the schools within each of the six
poverty index strata, as the ADM of the school increased, it was highly likely the
percentage of students scoring Proficient and Advanced on PACT in English/language
arts or in mathematics decreased. The remaining thirty-six subgroups analyzed
demonstrated no significant correlation. All six significant correlations were in the
strata with schools with poverty indexes greater than 50%. Four of the significant
correlations were in strata of schools with the highest poverty in the state.
245
Then the researcher ran the partial correlation in each poverty index strata for
third grade, fourth grade, and fifth grade results for PACT English/language arts and
mathematics and public elementary school size, while controlling for the poverty index.
The outcomes of the partial correlation analysis within the seven poverty index strata
revealed no significant correlations. The results of the partial correlation between
student achievement and ADM while controlling for poverty index within poverty index
strata confirmed previous studies in South Carolina: ADM, or 135-day average daily
membership, demonstrated no relationship to student achievement.
For the final statistical analysis, the researcher conducted a stepwise multiple
regression analysis within each poverty index strata for all PreKindergarten – 5 and
Kindergarten – 5 public elementary schools in South Carolina in third grade, fourth
grade, and fifth grades. The dependent variables PACT English/language arts and
mathematics and independent variables of poverty index and ADM were utilized. The
results of the stepwise multiple regression indicated that variable poverty index was
identified as the most predictive variable in fourteen of the forty-two subsets despite
the effort to negate the effects of poverty index by categorizing the schools in poverty
index strata. 135-day average daily membership was indicated as a predictive variable
individually three times; however, the strata, grade level, and subject area of these
three subsets does not indicate a pattern or reveal a significant finding. Based on the
outcomes of the research conducted for research question two, it may be summarized
that ADM, or 135-day average daily membership, is not a predictive variable for student
achievement when poverty index is controlled.
246
Research Question Three
The third research question was:
Can student achievement in South Carolina’s PreKindergarten – 5 or
Kindergarten – 5 public elementary schools in English/language arts and
mathematics as measured by the third, fourth and fifth grade 2007-2008
Palmetto Achievement Challenge Test be predicted by at least one, and
possibly a combination, of the following variables:
1. Poverty index
2. School size or average daily membership
3. First graders that attended full-day kindergarten
4. Retention rate
5. Student attendance rate
6. Eligible for gifted and talented
7. Percent objectives met
8. Students with disabilities other than speech
9. Students older than usual for grade
10. Suspended or expelled
11. Number of teachers with advanced degrees
12. Continuing contract teachers
13. Classes not taught by highly qualified teachers
14. Teachers with emergency or provisional certificates
15. Teachers returning from the previous school year
16. Teacher attendance rate
17. Average teacher salary
18. Professional development days per teacher
19. Principal’s or director’s years at the schools
20. Student-teacher ratio
21. Prime instructional time
22. Dollars spent per student
23. Spent on teacher salaries
24. Opportunities in the arts
25. Parents attending conferences
26. SACS accreditation
27. Portable classrooms
28. Percent of teachers satisfied with the learning environment
29. Percent of students satisfied with the learning environment
30. Percent of parents satisfied with the learning environment
247
31. Percent of teachers satisfied with social and physical environment
32. Percent of students satisfied with social and physical environment
33. Percent of parents satisfied with social and physical environment
34. Percent of teachers satisfied with home-school relations
35. Percent of students satisfied with home-school relations
36. Percent of parents satisfied with home-school relations
37. Vacancies for more than nine weeks
38. Character development program
39. Percent of expenditures for instruction
To answer this question, a stepwise multiple regression was calculated within
the seven poverty index strata in third, fourth, and fifth grades for PACT
English/language arts and mathematics. The independent variables were the thirty-nine
South Carolina Department of Education 2008 Annual School Report Card items. The
dependent variables were the percentage of students scoring Proficient and Advanced
on PACT English/language arts and mathematics in third, fourth, and fifth grades. The
stepwise multiple regression analysis was utilized to indicate one variable, or
combination of variables that may predict student achievement.
Data for the sixty-one PreKindergarten – 5 and Kindergarten – 5 public
elementary schools categorized in Strata 1 (0% - 49%) indicated twelve predictor
variables, whether individually or in combination with other variables. The predictor
variables that were produced the most often were poverty index and older than usual
for grade (six subsets), parents attending conferences (four subsets), and percent
objectives met and students with disabilities other than speech (three subsets). The
final adjusted R2 for the three grades and both student achievement subjects were:
0.484, 0.746, 0.546, 0.531, 0.501, and 0.645. The majority of these variable
combinations accounted for 50% or more of the variance of student achievement
248
respectively. In summary, outcomes indicate that the combination of poverty index,
older than usual for grade, parents attending conferences, percent objectives met, and
students with disabilities other than speech are correlated to student achievement.
In Strata 2 (50% - 59%), forty-eight PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina produced eleven predictor variables,
whether individually or in combination with other variables. The predictor variables
that were produced the most often were percent objectives met (six subsets), eligible
for gifted and talented (two subsets), SACS accreditation (two subsets), and percent
teachers satisfied with school/home relations (two subsets). The final adjusted R2 for
the three grades and both student achievement subjects were: 0.454, 0.537, 0.423,
0.439, 0.262, and 0.475. Only one of these variable combinations accounted for 50% or
more of the variance of student achievement. In summary, analysis of these outcomes
indicates that the combination of percent objectives met, eligible for gifted and
talented, SACS accreditation, and percent teachers satisfied with school/home relations
is correlated to student achievement.
In Strata 3 (60% - 69%), seventy-one PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina produced thirteen predictor variables,
whether individually or in combination with other variables. The predictor variables
that were produced the most from the stepwise multiple regression were percent
objectives met (six subsets), continuing contract teachers (two subsets), student-teacher
ratio (two subsets), and spent on teacher salaries (two subsets). The final adjusted R2 for
the three grades and both student achievement subjects were: 0.368, 0.463, 0.327,
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0.441, 0.240, and 0.437. None of these variable combinations accounted for 50% or
more of the variance of student achievement. However, the adjusted R2 ranged from
24.0% to 46.3% of the variance. In summary, analysis of these outcomes indicates that
the combination of percent objectives met, continuing contract teachers, studentteacher ratio, and spent on teacher salaries is correlated to student achievement.
In Strata 4 (70% - 79%), seventy-one PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina sixteen predictor variables, whether
individually or in combination with other variables, were produced. The predictor
variables that were produced the most were percent objectives met (four subsets),
percent parents satisfied with learning environment (three subsets), 135-day average
daily membership (two subsets), retention rate (two subsets), teachers returning from
the previous school year (two subsets), portable classrooms (two subsets), and
character development program (two subsets). The final adjusted R2 for the three
grades and both student achievement subjects were: 0.517, 0.536, 0.354, 0.300, 0.358,
and 0.241. Two of these variable combinations accounted for 50% or more of the
variance of student achievement. In summary, analysis of these outcomes indicates
that the combination of percent objectives met, percent parents satisfied with learning
environment, 135-day average daily membership, retention rate, teacher returning from
the previous school year, portable classrooms, and character development program is
correlated to student achievement.
In Strata 5 (80% - 89%), seventy-five PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina produced nine predictor variables, whether
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individually or in combination with other variables. The predictor variables that were
produced the most were percent objectives met (six subsets), SACS accreditation (four
subsets), 135-day average daily membership (two subsets), first graders who attended
full-day kindergarten (two subsets), and student-teacher ratio (two subsets). The final
adjusted R2 for the three grades and both student achievement subjects were: 0.322,
0.496, 0.380, 0.397, 0.348, and 0.538. One of these variable combinations accounted
for 50% or more of the variance of student achievement; however, the adjusted R2
ranged from 32.2% to 53.8% of the variance. In summary, analysis of these outcomes
indicates that the combination of percent objectives met, SACS accreditation, 135-day
average daily membership, first graders who attended full-day kindergarten, and
student-teacher ratio is correlated to student achievement.
In Strata 6 (90% - 94%), fifty-six PreKindergarten – 5 and Kindergarten – 5 public
elementary schools in South Carolina produced ten predictor variables, whether
individually or in combination with other variables. The predictor variables that were
produced the most were percent objectives met (six subsets) and percent teachers
satisfied with school/home relations (two subsets). The final adjusted R2 for the three
grades and both student achievement subjects were: 0.434, 0.434, 0.552, 0.430, 0.269,
and 0.607. Two of these variable combinations accounted for 50% or more of the
variance of student achievement; however, three other combinations of variables’
adjusted R2 ranged from 43.0% to 43.4% of the variance. In summary, analysis of these
outcomes indicates that the combination of percent objectives met and percent
teachers satisfied with school/home relations is correlated to student achievement.
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In Strata 7 (95% - 100%), fifty-seven PreKindergarten – 5 and Kindergarten – 5
public elementary schools in South Carolina produced fourteen predictor variables,
whether individually or in combination with other variables. The predictor variables
that were produced the most percent objectives met (six subsets), poverty index (three
subsets), first graders who attend full-day kindergarten (two subsets), student
attendance rate (two subsets), teachers with advanced degrees (two subsets), and
percent teachers satisfied with learning environment (two subsets). The final adjusted
R2 for the three grades and both student achievement subjects were: 0.506, 0.485,
0.509, 0.658, 0.484, and 0.544. Four of these variable combinations accounted for 50%
or more of the variance of student achievement. However, the two combinations of
variables remaining had adjusted R2 outcomes that 48.4% and 48.5% of the variance. In
summary, analysis of these outcomes indicates that the combination of percent
objectives met, poverty index, first graders who attend full-day kindergarten, student
attendance rate, teachers with advanced degrees, and percent teachers satisfied with
learning environment is correlated to student achievement.
Summary of Results of Research Question Three
The results of the stepwise multiple regression using student achievement and
the SC OEC 2008 Annual School Report Card variables for the seven poverty index strata
indicated that the variable percent objectives met was significant thirty-six times out of
the forty-two possible times. Percent objectives met was also the variable that was
indicated as the single highest predictive variable in four of the seven poverty index
strata subsets with adjusted R2 values of 0.290, 0.341, 0.368, 0.434, and 0.388. The
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predictive variables that were significant the second most often were poverty index,
older than usual for grade, and SACS accreditation. Each of these predictive variables
was produced nine times. Four predictive variables were produced six times: first
graders who attended full-day kindergarten, teachers returning from the previous
school year, student-teacher ratio, and percent parents satisfied with learning
environment. Three predictive variables were produced five times: eligible for gifted
and talented, students with disabilities other than speech, and parents attending
conferences.
A pattern was observed regarding certain variables. Percent objectives met was
repeatedly significant throughout the forty-two subsets. In strata 1 (0% - 49%), which
consisted of the most affluent schools, percent objectives met was produced the fewest
(three times). In contrast, the predictor variable poverty index was the most notable
predictor in strata 1 (0% - 49%). This variable was significant in only one other poverty
index strata, which was the final one: strata 7 (95% - 100%). Poverty index was a factor
in the lowest poverty index strata and the highest poverty index strata.
Interestingly, in each poverty index strata, survey items were predictor variables
a minimum of two times and a maximum of four times. Percent parents satisfied with
learning and percent teachers satisfied with school/home are predictor variables that
were produced six times and five times respectively out of a possible forty-two subsets.
Another important observation is that in all seven poverty index strata, the
combination of variables with the highest predictors of student achievement was in
PACT mathematics – third grade four times, fifth grade two times, and one time in
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fourth grade. The following variables were not significant in any subset as predictor
variables: suspended or expelled, average teacher salary, principal’s or director’s years
at the school and percent parents satisfied with social and physical. In summary,
analysis of the seven poverty index strata outcomes indicates that the variable of
percent objectives met increases student achievement.
The next sub-sections of this chapter present a discussion of the findings for
each research question and how the results are related to the literature.
Discussion of Findings
In a review of the literature, poverty was demonstrated to be a predictor of
student achievement in a large number of studies nationally, (Friedkin & Necochea,
1998; O’Hare, 1988; Howley & Bickel, 2000; McMillen, 2004; Sirin, 2005; Weber, 2005;
Archibald, 2006). Following Friedkin and Necochea’s (1988) study of California schools,
which concluded that small schools appeared to positively affect student achievement
for high poverty populations, Howley built on this research focus. Beginning in 1988,
Howley and Bickel replicated the California study in a major series of studies entitled
The Matthew Project. The studies were conducted in Georgia, Ohio, Montana, Texas,
and West Virginia. Howley and Bickel (2000) found that smaller schools offset the
negative effects of high poverty for students in all grade levels. Larger school size
benefited achievement in affluent communities, but it was detrimental in impoverished
communities (Howley, Strange, and Bickel, 2000). Therefore, students in high poverty
may perform better in smaller schools, while affluent students may excel in larger
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environments. The Matthew Project’s outcomes influenced research studies conducted
in South Carolina.
In the ten South Carolina studies, which focused on school size and student
achievement, poverty was found to be a significant contributing variable as well
(Stevenson, 1996; Durbin, 2001; Roberts, 2002; Gettys, 2003; Crenshaw, 2003;
McCathern, 2004; White, 2005; Carpenter, 2006; Kaczor, 2006; and Maxey, 2008). The
relationship between the size of South Carolina public elementary schools and student
achievement has been examined previously in four studies: Stevenson (1996),
McCathern (2004), White (2005), and Carpenter (2006). Studies conducted of South
Carolina public middle schools (Roberts, 2002; Gettys, 2003; and Kaczor, 2006) and
public high schools (Durbin, 2001; Crenshaw, 2003; and Maxey, 2008), were analyzed to
ascertain the relationship between school size and student achievement. The summary
of the researchers’ studies concluded that in South Carolina school size has not
demonstrated a significant relationship to student achievement. The researchers
acknowledged that poverty index was a significant influence on student achievement
despite researchers’ efforts to neutralize the effects of this variable.
For research question one of this study, the outcome supported McCathern’s
(2004) and Carpenter’s (2006) assertion that poverty is a variable that significantly
influences student achievement in public elementary schools in South Carolina. The
initial results of the Pearson correlation indicated a positive and significant correlation
with 135-day average daily membership (ADM) for third, fourth, and fifth grade on PACT
English/language arts and mathematics. However, when a partial correlation analysis
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was conducted on the same data sets, controlling for poverty, no significant correlations
between student achievement and ADM were found. The data tended to indicate a
negative correlation between student achievement and ADM. The interpretation of
these data is that school size is a negative predictor of student achievement. When the
researcher conducted a stepwise multiple regression for the same data sets, the
outcomes indicated that ADM was not significantly correlated to student achievement –
positively or negatively, at any grade level studied for either subject. The conclusion
from the first research question analysis was that school size is not indicated as a
predictor of student achievement.
However, the data from research question one did reveal significant correlations
between student achievement and poverty across all three grades and both subjects.
The relationship indicated a negative one in each case. The negative correlation
indicates that as the poverty index of the school increased, the percentage of students
scoring Proficient and Advanced decreased in English/language arts and in mathematics
in third grade, fourth grade, and fifth grade. These outcomes supported the conclusions
of McCathern (2004) and Carpenter (2006) in their respective studies on school size and
public elementary schools in South Carolina.
For research question two, the researcher built upon the methodology utilized in
the studies conducted by Stevenson (1996) and Kaczor (2006). Both researchers utilized
grouping schools in South Carolina to neutralize the effects of poverty when conducting
correlation analyses to measure whether school size had an effect on student
achievement. Stevenson (1996) conducted his study within the five elementary school
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levels created by the South Carolina Department of Education. Kaczor (2006) created
“strata” based on poverty indexes of the middle schools she studied. The researcher
utilized this methodology to neutralize the powerful effects of poverty. The elementary
schools were placed into poverty index strata based on each school’s poverty index.
The 7 percentile strata were: 0% - 49%, 50% - 59%, 60% - 69%, 70% - 79%, 80% - 89%,
90% - 94%, and 95% - 100%. Each percentile strata contained approximately the same
number of schools. The number of schools in each poverty index strata was: 0% - 49%
(63 schools); 50% - 59% (48 schools); 60% - 69% (73 schools); 70% - 79% (71 school);
80% - 89% (75 schools); 90% - 94% (54 schools); 95% - 100% (57 schools).
As reference previously, a delimitation utilizing the poverty index strata is no
natural groupings emerged when the variables poverty index and school size were
applied to a scatterplot. Therefore, the researcher arbitrarily placed the schools into
strata with approximately the same number of schools within each strata. This created
seven poverty index bands: 0% - 49%, 50% - 59%, 60% - 69%, 70% - 79%, 80% - 89%,
90% - 94%, and 95% - 100%. The researcher cautions that the outcome of the research
may have produced varied results if the schools were sorted into a different number of
strata.
The arbitrary placement caused three unique poverty index strata: one poverty
index strata with schools ranging from 0% to 49%, one poverty index strata with schools
ranging from 90% - 94%, and finally, one poverty index strata with schools ranging from
95% - 100%. Due to the three unique poverty index strata, the researcher cautions that
a school with a poverty index of 0% may be significantly different from a school with a
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poverty index of 49%, while in contrast, a school with a poverty index of 90% is not
significantly different from a school with a poverty index of 100%. It is important to
note that a different method of sorting the schools in these three specific poverty index
strata may have produced different outcomes. Additionally, these three unique poverty
index strata prevented the researcher from comparing the schools with the lowest and
highest poverty indexes. As a result, the researcher could not ascertain whether any
patterns existed that may have produced different results of this study between the
schools with a poverty index range of 0% - 10% and 90% - 100%.
The researcher conducted two statistical analyses: a partial correlation
controlling for poverty index and a stepwise multiple regression. The researcher ran the
partial correlation in each poverty index strata for third grade, fourth grade, and fifth
grade results for PACT English/language arts and mathematics and public elementary
school size, while controlling for the poverty index. The outcomes of the partial
correlation analysis within the seven poverty index strata revealed no significant
correlations. The results of the partial correlation between student achievement and
ADM while controlling for poverty index within poverty index strata ascertained that
ADM, or 135-day average daily membership, had no relationship on student
achievement.
The results of the stepwise multiple regression indicated that the variable of
poverty index was identified as the most predictive variable in fourteen of the forty-two
subsets, despite the effort to negate the affects of poverty index by categorizing the
schools in poverty index strata. 135-day average daily membership was indicated as a
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predictive variable individually three times; however, the strata, grade level, and subject
area of these three subsets does not indicate a pattern or reveal a significant finding.
Based on the outcomes of the research conducted for research question two, it may be
summarized that ADM, or 135-day average daily membership, is not a predictive
variable for student achievement when poverty index is controlled.
The determination from both statistical analyses does not support the
conclusions of Howley’s (1988) The Matthew Project nor Kaczor’s (2006) study.
Howley’s landmark study concluded that schools with high poverty demonstrate
increased student achievement as school size decreases. Howley also concluded the
reverse for low poverty schools – the lower the poverty of the school, student
achievement increases as school size increases. In Kaczor’s study (2006) she concluded
that as the size of the middle school increased, the percentage of students scoring
proficient or advanced on 6th grade PACT mathematics decreased. This conclusion was
not supported in this study, but a possible reason is Kaczor’s study focused on the
middle grades and this study focused on the elementary grades. However, the
determination of research question two did support the conclusions of the studies
conducted by McCathern (2004) and Carpenter (2006): ADM, or 135-day average daily
membership, is not a predictive variable for student achievement when poverty index is
controlled.
Stevenson (2009) states why school size may not be a predictive variable to
student achievement:
•
factors outside schooling have such a large impact;
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•
even within the schooling process, other educational factors are much more
important;
•
high costs may well be unacceptable to the public, and/or the same funds
may be more productively used elsewhere (i.e., enhancing teaching); and
both learning and delivery of education are so complex that individual
variables may have no meaning in isolation (p. 9).
Stevenson further suggests that “these factors must be considered—and
controlled for in the research process—before any absolute conclusions can be reached
about the specific effects of school size alone” (p. 9). The outcomes of this study
indicate support for Stevenson’s statements.
Stevenson (2006) noted in a review of the South Carolina state-wide studies, that
the socioeconomic status of students was the greatest predictor of student
achievement. However, he also notes, and McCathern (2004) concurred, that other
variables may be predictors of student achievement as well:
The first relates to “masking.” With poverty level of the student body accounting
for as much as three-fourths of the variability in academic outcomes and school
climate among schools, can the real effects of school size and other variables be
adequately identified at this point in time? The 2001 findings by Stevenson
(student attendance) and McCathern in 2004 (teacher experience) indicate that
other factors periodically do emerge along with poverty as predictors school
success. With this in mind, would school size actually emerge as a predictive
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factor in student performance and school climate if the exceedingly harsh, huge
effects of poverty could be fully controlled? (p. 6)
Stevenson’s question summarizes what researchers nationally and state-wide
have attempted to determine in their studies: is there a variable or a set of variables
that may be predictors of student achievement, when poverty is controlled? Research
question three sought to ascertain whether a variable, or combination of variables,
were predictors of student achievement.
The results of the stepwise multiple regression between student achievement
and the SC OEC 2008 Annual School Report Card variables for the seven poverty index
strata area indicated the variable percent objectives was significant thirty-six times out
of the forty-two possible outcomes. Percent objectives met is the variable that
represents the indicator which “reports the percentage of the NCLB adequate yearly
progress objectives for the school that were met” (SC EOC, 2008, p. A-9).
This variable utilizes the percentage of students scoring Proficient and Advanced
on PACT English/language arts as well as mathematics on the SC DOE 2008 Annual
School Report Card. However, the percentage represents a compliance rating, which is
comprised of the following items at the elementary school level in South Carolina (SC
EOC, 2008): percent student attendance, percent of students tested in English/Language
Arts and Mathematics for all students, and percent of students meeting performance
objective for all students. These are the minimum items which represent the
compliance rating for the variable percent objectives met. The minimum number of
items that encompass the compliance rating is five: percent student attendance,
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percent students tested in English/language arts all students, percent students tested in
mathematics all students, percent of students meeting performance objective for all
students in English/language arts, and percent students meeting performance objective
for all students in mathematics. If the subgroups within the school population meet the
minimum number required by the state for reporting purposes for subgroups, these
items are factored into the compliance rating as well. The subgroups are as follows:
White, African-American, Asian-Pacific Islander, Hispanic, American Indian/Alaskan,
Disabled, Not Disabled, Migrant, Non-Migrant, Limited English Proficiency, Subsidized
Meals, and Full-Pay Meals. A total of twenty-nine items may factor into the compliance
indicator should the minimum number for each subgroup within a school be met.
Since the variable percent objectives met was demonstrated to be a significant
predictive variable for student achievement, it is recommend that educators use the SC
DOE Annual School Report Card as well as Annual Adequate Yearly Progress Report Card
to identify subgroup populations that indicate “not met.” Educators should create and
implement instructional practices and professional development that target the
subgroups. Currently, qualitative research by practitioners like Hord and Sommers
(2009) and Dufour, Eaker, and Dufour (2005) emphasize the creation of professional
learning communities which emphasize the use of data to identify deficit areas in
student achievement, identify goals for that subgroup of students, provide
differentiated instruction, and progress monitor frequently to determine whether the
subgroup of students is improving. The implementation of this type of systematic effort
with the items identified as “not met” on the Adequate Yearly Progress report would
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improve student achievement among the students in the subgroups as well as the
school population overall.
The variable percent objectives met was demonstrated to be a significant
predictive variable in this research; however, the researcher must caution the reader on
the generalizability of these outcomes for three reasons. In 2009, the South Carolina
Education Oversight Committee replaced the Palmetto Achievement Challenge Test
(PACT) with a revised state assessment entitled Palmetto Assessment of State
Standards. Had the researcher utilized the PASS data as the student achievement
variable the variable percent objectives met may not have demonstrated to be such a
significant predictive variable. A second reason is that stepwise multiple regression
analyses do not consider variables that are relatively similar. Predictive variable
combinations may have been “masked” by the use of the stepwise multiple regression
analysis. The researcher presents the outcome of research question three as an
exploratory in nature only. More in-depth analysis should be considered, however, a
more reliable statistical analysis which indicates relationships among predictive
variables is recommended. A third caution by the researcher is this research represents
a “snapshot” in time only. The recommendation is for future researchers to consider a
longitudinal study utilizing this researcher’s framework. The outcomes of a longitudinal
study may produce different outcomes or support the outcomes presented in this
research.
An interesting pattern was observed regarding certain variables. In strata 1 (0% 49%), which is contains the most affluent schools, percent objectives met was significant
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the fewest (three times). In contrast, the predictor variable poverty index was
significant the most in strata 1 (0% - 49%). This variable was produced in only one more
poverty index strata, which was the final one: strata 7 (95% - 100%). Poverty index was
produced in the lowest poverty index strata and the highest poverty index strata. Also
significant often in strata 1 (0% - 49%) was older than usual for grade. In each poverty
index strata, survey items were predictor variables a minimum of two times and a
maximum of four times.
Many of these variables were utilized by Crenshaw (2003) and Kaczor (2006) in
their respective studies on school size, school climate, and student achievement.
Crenshaw (2003) stated: “Within the low socioeconomic schools grouping, when
socioeconomic level was lower, achievement ratings were lower; teacher perception of
school climate was less positive; and teachers did not stay as long” (p. 89). In contrast,
Crenshaw (2003) observed that the higher socioeconomic levels had a positive impact
on school climate variables. Crenshaw stated:
…the higher socioeconomic schools had higher teacher attendance and student
attendance; teachers that stayed longer at the same school; fewer students that
drop out; and more positive perceptions of the learning environment, social and
physical environment, and home school relations by teachers and students. (p.
91)
Crenshaw’s conclusions are supported in the predictive variables produced in
strata 1 (0% - 49%) and strata 7 (95% - 100%) of this study. Many of the variables
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Crenshaw identified in her study demonstrated a positive correlation to student
achievement.
Based on the work of Crenshaw (2003) and Kaczor (2006), a recommendation is
to sort the SC DOE Annual School Report Card variables into the following groups:
•
Student Variables (first graders that attended full-day kindergarten, retention
rate, student attendance rate, eligible for gifted and talented, students with
disabilities other than speech, students older than usual for grade, and
suspended or expelled)
•
Teacher Variables (number of teachers with advanced degrees, continuing
contract teachers, classes not taught by highly qualified teachers, teachers
with emergency or provisional certificates, teachers returning from the
previous school year, teacher attendance rate, average teacher salary, and
professional development days per teacher, vacancies for more than nine
weeks)
•
Funding Variables (student-teacher ratio, prime instructional time, dollars
spent per student, spent on teacher salaries, and percent of expenditures for
instruction)
•
Programmatic Variables (opportunities in the arts, SACS accreditation,
character development program), and
•
Survey Variables (parents attending conferences, percent of teachers
satisfied with the learning environment, percent of students satisfied with
the learning environment, percent of parents satisfied with the learning
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environment, percent of teachers satisfied with social and physical
environment, percent of students satisfied with social and physical
environment, percent of parents satisfied with social and physical
environment, percent of teachers satisfied with home-school relations,
percent of students satisfied with home-school relations, and percent of
parents satisfied with home-school relations).
Research within these groupings may reduce the effect of “masking” when a stepwise
multiple regression and demonstrate one variable or a combination of variables that are
predictive of student achievement.
Ascertaining a variable or combination of variables that indicates a predictive
correlation to student achievement creates opportunities for educators to improve
student achievement. For example, Caldas (1993) conducted a study in which it was
concluded that student attendance rate was the single most significant variable which
schools could manipulate to affect student achievement in a positive manner. If a
variable like student attendance rate or SACS accreditation, or a combination of
variables like teacher variables (teachers returning from the previous school year,
teacher attendance rate, average teacher salary, and professional development days per
teacher, vacancies for more than nine weeks) mentioned previously indicate a
predictive correlation with student achievement, educators may apply prescriptive
interventions which results in increased student achievement.
Howley and Bickel’s (2000) research on school size and student achievement was
foundation to this study. Howley and Bickel (2000) found that the higher the poverty
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index of the community served by a school, the more student achievement was
benefited by smaller schools. Additionally, their research project entitled The Matthew
Project (1999) found that the influence of size varied by poverty index level, with size
exerting a negative influence on achievement in impoverished schools, but a positive
influence on achievement in affluent schools. That is, all else equal, larger school size
benefits achievement in affluent communities, but it is detrimental in impoverished
communities.
In this study, Howley and Bickel’s (2000) research could not be substantiated for
school size in South Carolina public elementary schools. School size was not a variable,
individually or in combination with additional variables, that was found to have a
predictive relationship with student achievement when controlling for poverty index.
In White’s (2005) study, she concluded that as elementary school size increased,
the percentage of students retained increased as well. Additionally, White (2005) found
that schools with larger student enrollments were associated with higher percentage of
students being suspended/expelled. This conclusion was not supported by the outcome
of research question three. In fact, the variable suspended or expelled, as well as,
average teacher salary, principal’s or director’s years at the school and percent parents
satisfied with social and physical were not produced in any of the forty-two subsets.
Conclusions
This study sought to expand the body of research that had previously examined
the relationship between school size and student achievement in elementary schools in
South Carolina and across the nation. Foundational to this study was Howley and
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Bickel’s (2000) postulation that school size influence varies by poverty index level. This
research outcome was not substantiated through this research; however, it is concluded
that the predictive variables that do affect student achievement vary by poverty index
of the schools.
Additionally, an investigation of the South Carolina Department of Education
Annual School Report Card variable, or combination of variables, that indicate a
predictive relationship with student achievement was conducted. From the outcome of
this study, policy makers, school boards, and educators may conclude that school size
does not indicate a substantial relationship with student achievement; however, the
effects of poverty on student achievement continue to be realized.
Educators and researchers may also conclude that a new body of research on
student achievement is increasingly becoming more needed – research on the variable,
or variables, that indicate a predictive relationship with student achievement. In South
Carolina, research into this area may produce strategies that educators can implement
in schools to increase student achievement for students regardless of the effects of
student achievement.
Recommendations
This study was conducted to contribute to the understanding of South Carolina
public elementary school size and its relationships to student achievement.
Additionally, this study was conducted to ascertain whether a variable, or combination
of variables, was predictive of student achievement when controlling for poverty. The
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next three sections present recommendations for policy makers, educators, and for
researchers.
Recommendations for Policy Makers
1. Since the variable percent objectives met was consistently the most
predictive variable in the poverty index strata, educational policy makers
should request or conduct investigations of the relationship between the
predictive variable and student achievement. Since the variable percent
objectives met is comprised of indicators for Adequate Yearly Progress,
policy makers should research strategies that positively influence the
relationship, which increases student achievement.
2. Policy makers should request or conduct further investigation into the
indicators that comprise poverty, which was a variable that indicated a
negative correlation with student achievement in this study. What are the
indicators that comprise poverty and what may be done to reduce its effect
on student achievement?
3. Policy makers should continue to seek or conduct studies that identify South
Carolina Department of Education Annual School Report Card variables – in
isolation or in combination with other variables - that impact student
achievement. The variables percent met objectives; poverty index; first
graders who attended full-day kindergarten; teachers returning from the
previous school year; student-teacher ratio; percent parents satisfied with
learning environment; eligible for gifted and talented; students with
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disabilities other than speech; and parents attending conferences were
indicated as being predictive variables in various combinations of student
achievement. These variables could be studied individually and collective to
determine whether the impact is realized at the middle school or high school
levels.
Recommendations for Educators
1. Educators must closely examine the impact that poverty has on student
achievement in order to develop strategies to diminish its effects while
increasing student achievement. Further studies should be conducted to
ascertain whether school size demonstrates a relationship with student
achievement once the effects of poverty are controlled because this study
was only a snapshot at one point in time using one measure.
2. Educators should investigate the variable percent objectives met and its
impact on student achievement. Since percent objectives met is comprised
of indicators for Adequate Yearly Progress, educators should research
strategies that positively influence the relationship, which increases student
achievement.
3. Educators should replicate this study in its entirety using the Palmetto
Assessment of State Standards (PASS), which is the replacement test for the
Palmetto Achievement Challenge Test (PACT), the student achievement
variable used in this research. A replication of this study using PASS would
be useful to ascertain whether school size continued to not indicate a
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relationship with student achievement. It would also be useful to determine
whether the variable percent objectives met was indicated as the most
predictive variable to student achievement.
4. Educators should utilize Adequate Yearly Progress Report Cards, which
indentify the indicators, and often the subgroups of students, that did not
meet adequate yearly progress benchmarks. Once identified, district and
school administrators should strategically implement professional
development for classroom teachers as well as instructional interventions for
students within subgroups to increase student achievement.
5. Educators should continue to seek to identify South Carolina Department of
Education Annual School Report Card variables that are similar in nature that
may be predictive of student achievement. As noted earlier, a sorting system
could address the major topics of Student Variables, Teacher Variables,
Funding Variables, Programmatic Variables, and Survey Variables. Identifying
combinations of SC DOE Annual School Report Card variables that are
predictive of student achievement, educators may apply prescriptive
interventions which results in increased student achievement.
Recommendations for Researchers
1. Poverty is such a strong variable that further research needs to be conducted
to determine more fully how poverty affects school performance. We know
it is a big factor, but not “why” poverty specifically influences school
performance. For example, a study could be conducted that analyzes the
271
effects of poverty on learning. It may be that students’ performance results
may vary by the type and range of poverty.
2. Researchers should replicate this study in its entirety using the Palmetto
Assessment of State Standards (PASS), which is the replacement test for the
Palmetto Achievement Challenge Test (PACT) used in this study, as the
student achievement variable. A replication of this study using PASS would
be useful to ascertain whether school size continued to not indicate a
relationship with student achievement. It would also be useful to determine
whether the variable percent objectives met was indicated as the most
predictive variable to student achievement.
3. Researchers should replicate this study longitudinally to ascertain whether a
predictive variable or a combination of predictive variables indicates a
significant relationship. The researcher could conduct a study on third grade
students with PASS English/language arts and mathematics data, then
conduct the same study for the same students in fourth grade with PASS
English/language arts and mathematics data. This could be conducted
through the students’ eighth grade.
4. Researchers should replicate this study at the middle school and high school
levels to ascertain whether sorting the public middle school and high schools
into poverty index bands produced indications that school size correlated to
student achievement. Additionally, it would be powerful to replicate the
research question three to determine whether the following variables were
272
indicated as predictor variables at these two levels: poverty index; first
graders who attended full-day kindergarten; teachers returning from the
previous school year; student-teacher ratio; percent parents satisfied with
learning environment; eligible for gifted and talented; students with
disabilities other than speech; and parents attending conferences.
5. As noted previously as a recommendation to educators, researchers should
continue to seek or conduct studies that identify South Carolina Department
of Education Annual School Report Card variables that are similar in nature
that may impact student achievement.
Summary
Further study is needed to ascertain why school size has not demonstrated a
significant relationship with student achievement in South Carolina, which is in contrast
to Howley and Bickel’s (2001) studies. Possibly, research conducted longitudinally may
indicate a significant relationship between the two. Poverty was demonstrated to be a
highly influential variable of student achievement in South Carolina. Research should
seek to ascertain why poverty is such a powerful predictive variable. Additionally, the
variable from the South Carolina Department of Education Annual School Report Card
percent objectives met has demonstrated to be a new, highly predictive variable of
student achievement. Further study should be conducted on this variable and its
relationship with student achievement to ascertain strategies that policy makers,
educators, and researchers may implement to increase student achievement in spite of
the powerful effects of poverty.
273
Chapter V provided a brief summary of this study’s purpose, a discussion of the
study’s findings in the context of related research, conclusions, and recommendations
for policy makers, educators, and researchers. The focus of this study was to examine
the relationship between elementary school size and student achievement in South
Carolina, as well as determine whether any South Carolina Department of Education
Annual School Report Card variable, or combination of variables, indicated a
relationship with student achievement. This study has provided policy makers,
educators, and researchers with additional information on the relationship between
school size and student achievement, the effects of poverty, and presented a new
avenue of research into the study of the relationship between percent objectives met
and student achievement.
274
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