9/3/2010
Assessment Seminar for Mathematics Teachers
Jointly organised by: Association of Mathematics Educators &
Singapore Polytechnic
Speaker:
Magdalena Mo Ching Mok, HKIEd
Venue:
Singapore Polytechnic Auditorium
Date:
Monday 6 September 2010
2
1. Self-directed Learning Oriented
Assessment
2. Implementation: How to use SLOA to
Enhance Teaching & Learning in Math
3. Q & A
Acknowledgement: Thanks to Baptist (STW) Lui Ming Choi Primary School
3
4
Assessment as Learning
 Develop self-directed learner
Assessment
should support
current & future
Dr. David Carless
 Engender & sustain motivation
 Build metacognition
 Empower with self-assessment
1. Assessment …learning tasks
2. Assessment … engage students;
3. Feedback …feedforward
“Classroom Assessment for the Hong Kong Tertiary Context” Project,
UGC Teaching Development Grant 2002 –2005 (HK$2,000,000) ,
The Hong Kong Institute of Education
5
Assessment of Learning
Assessment for Learning
 How much has been
learned?
 Inform Learning
 Standard
 Goal, Achievement, & Gap
 Reliable & valid
assessment tools
 How to close the Gap?
 Provide Feedback
6
1
9/3/2010
Self-directed Learner:
Metacognition
• Funded by EDB under the
University-School
Partnership scheme
Ability to set learning goals
Self-motivated
• 3-year project (2005-8)
&
Capability to Self-monitor
• 100 schools
• Extended to other schools
in China, Hong Kong and
Macau since 2008
Perseverance in face of difficulties
Acknowledgement: 100
Partner Schools of the
Assessment Project
• P1 to S4
Self-regulation capabilities
7
• Effect of schooling: Growth
8
Son
Mum
Son
Mum
• Questions to address:
– Do we have evidence of growth?
: Mum, I got 80 marks in my math!
: Wow! How about the others?
: M…m about 98, 99… 95 in general.
: What?! You must work harder!!!
Son
Mum
Son
Mum
: Mum, I got 98 marks in my math!
: Wow! How about the others?
: M…m about 98, 99.
: That’s my good boy! …
Who got the highest mark?
Son : M…m John did. He’s 200 & that’s the max.
Mum : What?! You must work harder!!!
– What is the rate of growth of this student?
– Is the rate of growth of this student
comparable to an average student of
similar background?
– Will this rate of growth lead to reaching the
standard in due course?
Juhoo Leever10
Mathematics Vertical Scale
9
You scored 80 last year
and 70 this year. Why
have you gone
backwards?
Targeted Instruction
Instruction
80 marks
P2
11
P3
P4
P5
P6
Year Level
S1
S2
S3
S4
Figure 1. Schematic Representation of the ARC Mathematics Scale
12
2
9/3/2010
The Mathematics Scale by CARD, Hong Kong Institute of Education
Acknowledgement: Lau, D. C. H., Yan, Z., & Mok, M. M. C. (2008)
A2
06-07
07-08
A3
A4
166
165
66
A5
A6
166
170
68
64
177
178
170
106
110
115
110
101
161
627
683
A7
174
67
67
180
180
A8
104
105
614
614
83
100
183
14
08-09
A6b
174
64
172
Acknowledgement: Lau, D. C. H., Yan, Z., & Mok, M. M. C. (2008)
421
421
0
Total
348
336
331
134
132
130
360
355
342
225
216
160
262
209
198
3738
Sample
3,728 primary students
from 53 classes
from 5 schools
Procedures
Intensive site-based
teacher development from
Oct 2005 to Jun 2009.
Summative assessment
every 6 months at the end
of Semester
Acknowledgement: CH Lau, AWC Leung, Z Yan, MMC Mok (2009)
15
Mathematics Vertical Scale
05-06
No. of
School Level Classes A1
R
P4
5
P3
5
P2
5
S
P4
2
P3
2
P2
2
T
P4
5
P3
5
P2
5
U
P6
3
P5
3
P4
2
77
V
P6
3
P5
3
P4
3
98
Total
53
175
13
Acknowledgement: CH Lau, AWC Leung, Z Yan, MMC Mok (2009)
16
Change in Math Ability from A6B (Oct 2008) to A7 (Feb 2009)
120
100
1. What is the desired learning goal?
f(logit)
80
2. Where are we in the learning?
60
3. Is there a gap between the desired
goal and the achievement?
40
20
0
P2
P3
P4
P5 (Expt)
P6
A6b (logit)
42.16
48.19
63.29
73.80
101.14
A7 (logit)
46.59
61.36
73.99
91.77
107.01
Change:
4.43
13.17
10.71
17.97
4. How can we close the gap?
5.87
N = 1,324 students from 46 classes from 4 schools
Experimental group: 318 students from 10 P5 classes from 4 schools
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18
3
9/3/2010
Object of learning:
meaning of equal
parts in fractions
Focus on Learning
Error is part of
learning
Question & Feedback
6/7
Wait time
6/8
Classmates as
resource
6/8
Acknowledgement: Thanks to Ms Doris Lau, Centre for Assessment Research &
Development, HKIEd, & Ms Jenny Li, Chai Wan Faith Love Primary School
Acknowledgement: Thanks to Ms Doris Lau, Centre for Assessment Research &
Development, HKIEd, & Ms Jenny Li, Chai Wan Faith Love Primary School
19
20
Rasch Model
C
Candidate and item squaring off
George Rasch
e.g. High Jump:
Zone of
Proximal
Development
athlete – the bar
B
A
22
21
STUDENTS
ITEMS
STUDENTS
ITEMS
Most able student
Most difficult item
Zone of Proximal Development
Least able students
Least difficult item
23
24
4
9/3/2010
“…We can identify a
Zone of Proximal
Development (ZPD)
of each student in
the map of the
RASCH model.
0 < MCI < 1
We found that if we
teach around this
Zone, students
learned most
effectively. …”
Acknowledgement: Thanks to Mr Ngan Kwong Kwai,
Chinese Language Teacher, Buddhist Ho Nam Kam College
26
25
100%
Performance
High
High Performance,
Low Caution
High Performance,
High Caution
Maintenance
Luck? Cheating?
50%
Low Performance,
Low Caution
Low Performance,
High Caution
Insufficient Readiness;
Need Remediation
Careless?
Lack Test-taking Skills?
Low
0%
0.0
0.3
1.0
Low
Acknowledgement: Doris C K Lau (2009)
27
School W
Class A
School W
Class B
High
Modified Caution Index
28
School X
Class B
School X
Class A
Acknowledgement:
Doris C K Lau (2009)
Acknowledgement:
Doris C K Lau (2009)
School W
Class D
School Y
MCI by Performance of Student
School Z
1.0
0.9
0.8
0.7
0.6
Performance
School W
Class C
0.5
0.4
0.3
0.2
0.1
29
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
301.0
MCI
5
9/3/2010
Most
difficult
S3
results
Highest ability
Difficult
Items
12.5%
11.1%
62.5%
11.1%
If A = C, what is the value of
x?
A
Zone of Proximal Development
Average
Items
45.8%
9.7%
12.5%
26.4%
Find the value of x.
Easy Items
Lowest ability
Least
difficult
31
5.6%
79.2%
12.5%
1.4%
32
Set learning goals
Self-assessment
1. Metacognition
2. Self-assessment
Articulate learning strategies
3. Self-motivation
Self-regulation: change to improve
4. Self-regulation
Attribution and motivation
Self-identified Gap
Teacher-, peer-, parent-feedback
34
35
Self-assessment
I failed
because…
Attribution
Self-regulation: change to improve
I succeeded
because…
In the next test, I
will work harder
Synchronised
Effort, Strategy, Ability, Luck, ….
Acknowledgement: Chai Wan Faith Love Primary School
36
Acknowledgement: Chai Wan Faith Love Primary School (Primary 2)
37
6
9/3/2010
Metacognition
Ability to Articulate Learning Strategies
I succeeded because I revised according
to plan. During test, I read the items
seriously and carefully; I responded
clearly and strategically; when I met with
items that I did not know how to answer, I
tried my best to answer; I seriously
checked the script and modified my
response to get the correct answer.
I failed because I have not mastered
revision skills; haven’t remembered
the main points so that my results
were very poor. Further, I did not
study in a quiet environment and I
was too nervous at the time so that I
did not reach my full potential.
Acknowledgement: Chai Wan Faith Love Primary School (Primary 6)
38
1. Involvement of key stakeholders at all levels
 Principal, Teachers, Parents, Students, Staff
2. Management & Implementation infrastructure at all
levels for:
 Design & decision of assessment system
 Communication of expectations
 Obtaining assessment feedback
 Communication of feedback
 Follow up action to make use of feedback
3. Systematic review plan and action at all levels
39
About 3,200 professional
development activities for
~22,000 teachers in 20052008.
11,478
86 Open
Seminars
7,438
103 Parent
Education
sessions
11,836
2,942
6,756
169 Whole-school
Development
sessions
Site-based
Professional
Development
1098
32 Day
Camps
830
Whole-school approach offers a vision for a
sustainable education (Shallcross & Robinson,
2008)
10 Joint-school
Development
40
930
22 Other
Seminars
41
What will happen to the liquid level
in a glass if a large piece of ice
melts in the drink?
Rise
Fall
No change
Rigor, Relevance, Relationships
Whole school involvement
Outcomes, Evidence, Feedback
Build strategic partnership
42
Why do you think this is the case? You
may choose more than one option.
 The mass of liquid displayed is the
same as the mass of the ice.
 The volume of liquid displayed is the
same as the volume of the ice.
 The volume of ice is larger than the
volume of liquid .
 The density of liquid is higher than
the density of ice.
 The temperature of liquid is higher
than the temperature of ice.
43
7
9/3/2010
A bee farmer wants to know
how many bees there are in one
of the beehives. He took out 200
bees and label each of them
with a tag. He put the tagged
bees back in the beehive.
Next day he took out 250 bees in a random
manner, and found that 25 of them were tagged.
1. How many bees did the
farmer tag?
2. How many bees did the
farmer catch in total?
3. Estimate how many bees
were in the beehive?
4. Explain how you made
your estimate.
Acknowledgement: Dr Rosemary Callingham, University of Tasmania;
200
25
250
Acknowledgement: Dr Rosemary Callingham, University of Tasmania
Yaumati Catholic Primary School (Hoi Wan Road)
How many bees did the farmer catch
in total?
How many bees did the farmer tag?
A.
25 (confusing the sample)
B.
175 (200 – 25)
C.
200 *
B. 425 (recognises that 25 bees were
caught twice)
D.
250 (confusing the sample)
C. 450*
A. 250 (not understanding question)
D. 475 (add all numbers)
Acknowledgement: Dr Rosemary Callingham, University of Tasmania
Acknowledgement: Dr Rosemary Callingham, University of Tasmania
Estimate how many bees were in the
beehive?
A. 475 (Add all numbers)
B. 425 (200 + 400 – 25)
C. 2000*
1.
4
3

5
5
Attribute:
 subtraction of fractions with same denominator
2.
7
5

4
4
Attributes:
 subtraction of fractions with same denominator
 Simplification of fractions
What are the attributes in the
subtraction of fractions?
D. 2500 (used wrong base for estimation)
Acknowledgement: Dr Rosemary Callingham, University of Tasmania
Reference:
Torre, J. d.l. (2009). DINA Model and parameter estimation: A didactic.
Journal of Educational and Behavioral Statistics, 34(1), 115-130.
49
8
9/3/2010
Item
Same
denominator
subtraction
Fraction
Simplification
Borrowing


1.
4
3

5
5

2.
7
5

4
4

3.
1
1

3
6
1
3
4.
4 3
2
2


3
1
+
=?
5
10
…
Addition of
Fraction

Same
denominator

Y
Different
denominators
x
Proper
Fraction








Whole
Number
Improper
Fraction
Largest Common
Denominator
…
Fraction
…
51
50
There are 4 bags that each carries 3 books. Each book weighs 20 g.
What is the fraction that best represents
the shaded parts in the figure?
Mary took out all the books from the bags and put the books in a box
which weights 50 g. How heavy is the box now?
Possible Distracters
A. 60 g
(3 x 20 g)
B. 80 g
(4 x 20 g)
C. 110 g
(3 x 20 g + 50 g)
D. 140 g
(4 x 3 x 20 g)
E. 190 g * (4 x 3 x 20 g + 50 g) *
(a) 4/8
Cognitive Demands:
(b) 1/2
 Know what is being asked
 Identify useful numeric information
 Multiplication (of 3 numbers)
Whole number /
fraction distinction
 Addition
 Comprehensive skills
52
(c) 4
(d) 8
Shaded parts
Acknowledgement: Thanks to Ms Doris C. H. Lau,, CARD,
HKIED; Ms Jenni Li, Chai Wan Faith Love Primary School
53
During the holidays, I read 18 books. My sister read 3 times as many
books as I did. My brother read 26 more books than the total of what my
sister and I read. How many books did my brother read?
What is the fraction that best
represents the shaded part in the
figure?
 Each part must
be equal in size
(a) 4/8
 Proper fraction
(b) 1/2
Whole
number /
fraction
distinction
 Each part must
be equal in size
 Proper fraction
(c) 4
(d) 8
Shaded part
1.4/8 is not proper fraction. After
simplifying 4/8 &½ are the same.
2. The parts are not equal in size.
3. 1/2 is the answer. No need to consider 4/8.
Learning Goal: read and highlight all relevant information
4. Will not consider 4 or 8 because they are whole numbers (and not fractions).
Acknowledgement: Thanks to Ms Doris C. H. Lau,, CARD, HKIED; Ms
Jenni Li, Chai Wan Faith Love Primary School
54
Acknowledgement:
Ms Doris Ching Heung LAU, CARD, HKIed, and
Ms Lok Wah CHEUNG, Yau Ma Tei Catholic School (Hoi Wang Road),
Apr 2009.
55
9
9/3/2010
20.5
=
500
%
20.5
X 100 %
500
20.5 x 10
205
=
500 X 10
5000
20.5 x 2
41
=
500 X 2
1000
I like group work, and sharing on difficulties
and view points because “I can seek help from
my classmates and I can also teach them.”
20.5
4.1
=
500
100
divide numerator &
denominator by 5
Acknowledgement: Thanks to Ms Jennie Li, Chai Wan Faith Love Primary School
56
•
•
•
•
•
•
•
At first, I was skeptical about my child being asked
to write journals. After 2 years, I saw major changes
in him. Now I understand and hope other parents
can understand too. Now I can see writing journals:
Is a way to develop his thinking
Is a form of training in writing
Enables the teacher to adjust her teaching
Gives a platform for teacher-child communication
Can consolidate learning
Helps my child to have early reflections upon his
learning errors
Is a basic training
Acknowledgement: Thanks to Chai Wan Faith Love Primary School
57
Generous donation from WoFoo Social
Enterprises
Generous support from Winsteps, Yaumati Catholic Primary
School (Hoi Wan Road), Canossa Catholic Primary School,
Carmel Holy Word Secondary School, Dr. Kong, Pearson
Longman HK, Nestle, Seagate, and Transcend.
Thank you, Ms Cheung!
3A Parent, Ms Tang
58
Generous book
donation from
Pearson Longman HK
to 5 schools including
Yaumati Catholic
Primary School (Hoi
Wan Road)
Professor Harvey
Goldstein (University of
Bristol) & Dr. Alan
Cheung (HKIEd)
Dr Guanzhong Luo, Hong Kong Examinations &
Assessment Authority, and visitors from North-West
University, Shaanxi (陜西省西北大學)
Donation, sponsorship, advice, support
59
80% success rate; 10% no change; 10% failure
• Conceptual change about assessment in teachers
• Teachers impressed by significant change in students’
attitudes, approaches to learning, & knowledge levels
• Statistically significant improvement in students
achievement
• Greater parent satisfaction
• Strengthened learning culture of schools
• Strengthened University-school partnership
Acknowledgement
Prof Frederick KS LEUNG, Faculty of Education, Hong Kong University
60
• Rich empirical data for re-evaluation, enhancement, and
re-development of assessment system in school
• Provide a platform for group reflection & change
61
10
9/3/2010
 New lens to reconceptualise
assessment
 New tools to redesign
pedagogy
 Renew teacher commitment
 Advance learning
 Transform the learner
62
63
1. Embed assessment in the daily activities
2. Plan and set long-term & short-term goals
 SLOA framework
3. Link assessment with learning
 Electronic Assessment &
4. Give formative feedback
Reporting
5. Set informative math items
 Multidimensional
6. Create mathematics vertical scale
Computerised Adaptive
7. Use math learning log for reflection & metacognition
Testing
8. Involve students as partners
9. Partner with parents and other teachers
 Cognitive Diagnostic
10. Make good use of Rasch model & SP chart
Assessment
11. Regulate on basis of assessment feedback
64
65
66
11