An Across-The-Curriculum
Approach to Quantitative
Literacy in Environmental
Studies
0011 0010
1
Ben Steele, Semra Kilic-Bahi, Nick Baer, Leon
1010 1101
0001Laura
0100 1011
Malan,
Alexander, Harvey Pine
Colby-Sawyer College
New London, NH
2
4
Quantitative Reasoning and the Environment
Need for Quantitative Skills
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• Understanding issues
• Careers
• Informed citizenry
• Environmental Studies
and Environmental
Science
1
2
4
Across the Curriculum Approach
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• Encounter different skills and different
applications throughout the curriculum
• Use skills in context
– Learning advantage
– Habit of mind
1
2
4
– But hard to ensure students get all skills
– Harder to assess
Skills
• Basic arithmetic
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– Proportion; percent
– Unit conversions
– Rate of change
– Error
– Graphing
– Descriptive statistics
Average Percent of Leaf
Missing
• Data presentation and analysis
44
42
40
38
36
34
32
30
1
2
4
Sugar maple
(alone)
White Birch
(clumped)
Skills (cont.)
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Both species
• Algebra; Modeling
• Geometry; Trigonometry
–
–
–
–
–
Circles
Squares, rectangles, Triangles
Trigonometric functions
Spheres
Cubes and other solid figures
R
600
500
Population
– Manipulating equations
– Linear and non-linear functions
– Modeling
P
400
300
200
100
0
0
1
50
2
100
4
Curriculum Grid Env. Science
Aquatic
Basic
arithmetic Data presentation
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1011
and analysis
Aquatic track
ENV 100 Natural History
BIO 107 Ecology
ENV120 Environmental Science
CHE 101, 102 Chem Principles
ENV 201 Water Resources
ENV 203 Climate Change
SCI 200-level (geology)
ENV 300 environmental chemistry
BIO317 Aquatic Ecology
MAT 220 Statistics
pro
po r
tio
n; p
Un
it c
erc
onv
en t
s
e rs
Sig
i
ons
nifi
can
t fig
Rat
u re
eo
s
f ch
ang
Est
im a
e
tion
Log
arit
hm
s; s
Ga
the
cie
nti
ring
fic
err
dat
not
or
a
atio
n
Gra
ph i
ng
De
scr
ipti
ve
Pro
sta
bab
tist
ility
ics
Sta
tist
i ca
l te
spr
sts
ead
she
et s
Ma
nip
kill
s
ula
tin
Lin
g
ear
equ
fun
ctio ations
No
nlin
ns
ear
fu n
Mo
ctio
del
ing
ns
(e x
Ge
pon
om
ent
etr
y
ial,
log
)
Number sense
Algebra
Modeling
1
2
4
Curriculum Grid Env. Science
Terrestrial
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1011
Basic
arithmetic Data presentation
Environmental Science
Terrestrial track
ENV 100 Natural History
BIO 107 Ecology
ENV120 Environmental Science
ENV 201 Water Resources
ENV 203 Climate Change
ENV 204 GIS
BIO314 Animal Behavior
BIO 318 Terrestrial Ecology
BIO 407 Conservation Biology
SCI 200 geology
MAT 220 Statistics
and analysis
pro
po r
tio
n; p
Un
it c
erc
onv
en t
s
e
Sig
r
sio
nifi
n
s
can
t fig
Rat
u re
eo
s
f ch
ang
Est
im a
e
tion
Log
arit
hm
s; s
Ga
the
ci e
nti
ring
fic
err
dat
not
or
a
atio
n
Gra
ph i
ng
De
scr
ipti
ve
Pro
sta
bab
tist
ility
ics
Sta
tist
ica
l te
spr
sts
ead
she
et s
Ma
nip
kill
s
ula
t
ing
Li n
ear
equ
fun
ctio ations
No
nlin
ns
ear
fu n
Mo
ctio
del
ing
ns
(e x
Ge
pon
om
etr
ent
y
ial,
log
)
Number sense
Algebra
Modeling
1
2
4
Curriculum Grid Env. Studies
Basic arithmetic Data presentation
Number sense and analysis
Algebra
Modeling
Environmental Studies
ENV 100 Natural History
BIO 107 Ecology
BUS 115 Business Intro
BUS 321 Sustainable Org.
PSY 101 or SOC 101
ENV120 Environmental Science
ENG 215 Env writing
ENV 201 Water Resources
ENV 203 Climate Change
ENV 204 GIS
MAT 220 Statistics
pro
po r
tio
n; p
Un
it c
erc
onv
en t
s
e
Sig
r
sio
nifi
n
s
can
t fig
Rat
u re
eo
s
f ch
ang
Est
im a
e
tion
Log
arit
hm
s; s
Ga
the
ci e
nti
ring
fic
err
dat
not
or
a
atio
n
Gra
ph i
ng
De
scr
ipti
ve
Pro
sta
bab
tist
ility
ics
Sta
tist
i ca
l te
spr
sts
ead
she
et s
Ma
nip
kill
s
ula
tin
Lin
g
ear
equ
fun
ctio ations
No
nlin
ns
ear
fu n
Mo
ctio
del
ing
ns
(e x
Ge
pon
om
etr
ent
y
ial,
log
)
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1
2
4
Examples: BIO 107 Ecology
• Data collection and presentation
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• Preference of Fall Web Worms for maple
versus cherry leaves
• Spreadsheets, means, standard errors,
graphs
LEAF
1MAPLE
2MAPLE
3MAPLE
4MAPLE
5MAPLE
6MAPLE
7MAPLE
8MAPLE
9MAPLE
10MAPLE
WEIGHT BEFORE WEIGHT AFTER CONSUMPTION
0.2462
0.1023
0.1439
0.2369
0.104
0.1329
0.3533
0.164
0.1893
0.6266
0.267
0.3596
0.4436
0.2132
0.2304
0.5503
0.1731
0.3772
0.3624
0.1201
0.2423
0.3173
0.1583
0.159
0.3436
0.1343
0.2093
0.7392
0.3976
0.3416
Average
0.23855
std dev
0.090864114
std error
0.5
amount consumed (g)
DISH
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
4
Maple
Apple
Examples: ENV 201 Water
Resources
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• Quantifying Stream Discharge
–
–
–
–
–
0
Area calculations
Unit conversions
Data management
Spreadsheet skills
Graphing
.5m
1m
1.5m
2m 2.5m
1
2.9m
2
4
Examples: BIO 318 Terrestrial
Ecology
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• Matrix model using survival and
reproduction in several age classes.
• Stable population and age classes
• Effect of survival at different ages
0
1
2
0.5
0
0
0
0.5
0
year 1 year 2 year 3 year 4 year 5 year 6
10
30
15
20
22.5
17.5
10
5
15
7.5
10 11.25
10
5
2.5
7.5
3.75
5
total
pop
45
40
35
30
25
20
15
10
5
30
40
1
32.5
35
36.25
33.75
0
2
4
total pop
Matrix
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Does it work: Evaluation
• Overall: Basic Q skills and QL skills tests
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1
2
4
Does it work: Evaluation
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• Pre/post test on module
4
3.5
1
Grade
3
2.5
2
1.5
1
0.5
0
Pre test
Post Test
2
4
End of semester
Challenges
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• Only one example of a skill: low retention
• Hindered by basic skills
Task 1. If the island is 267 ha
and each bird needs 0.1 ha,
what is the maximum
population? (A hectare is
100m by 100m)
1
2
4
Challenges: basic skills (cont.)
• Now design an experiment to answer the
question:
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– Is it better for a one year old to produce more
young or to put their energy into survival?
Start by reducing the survival of one year olds
by 10% and see what % change in fecundity is
required to recreated a stable population.
1
2
4
Challenges: basic skills (cont.)
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• Extra credit:
– What is 10% less than 0.7?
– What is 20% less than 200
– What is 5 % more than .01
• Average = 1.7, Range 0-3
• Lack of practice?
• Used to calculators?
1
2
4
Conclusions
• Quantitative Literacy skills are weak
• Across the curriculum makes sense
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– But does it work?
• Projection
1
– [email protected]
2
4
– Students need to encounter quantitative
issues more often.