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An Across-The-Curriculum Approach to Quantitative Literacy in Environmental Studies
Ben Steele, Semra Kilic-Bahi, Nick Baer, Leon Malan, Laura Alexander, Harvey Pine
Colby-Sawyer College
New London, NH
Quantitative Reasoning and the Environment
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Need for Quantitative Skills
• Understanding issues• Careers• Informed citizenry
• Environmental Studies and Environmental Science
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Across the Curriculum Approach
• Encounter different skills and different applications throughout the curriculum
• Use skills in context – Learning advantage– Habit of mind
– But hard to ensure students get all skills– Harder to assess
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Skills• Basic arithmetic
– Proportion; percent– Unit conversions– Rate of change
• Data presentation and analysis– Error – Graphing– Descriptive statistics
Sugar maple (alone)
White Birch (clumped)
3032343638404244
Ave
rag
e P
erce
nt
of
Lea
f M
issi
ng
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Skills (cont.)
• Algebra; Modeling– Manipulating equations– Linear and non-linear functions– Modeling
• Geometry; Trigonometry – Circles– Squares, rectangles, Triangles – Trigonometric functions– Spheres– Cubes and other solid figures
0 20 40 60 80 100
0
100
200
300
400
500
600
Both species P
R
Po
pu
lati
on
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Curriculum Grid Env. Science Aquatic
Basic arithmetic Data presentation AlgebraNumber sense and analysis Modeling
Aquatic track prop
ortio
n; p
erce
nts
Unit
conv
ersio
nsSi
gnifi
cant
figu
res
Rate
of c
hang
eEs
timati
onLo
garit
hms;
scie
ntific
not
ation
Gath
erin
g da
taer
ror
Grap
hing
Desc
riptiv
e st
atisti
cs
Prob
abili
tySt
atisti
cal t
ests
spre
adsh
eet s
kills
Man
ipul
ating
equ
ation
s
Line
ar fu
nctio
nsN
onlin
ear f
uncti
ons (
expo
nenti
al, l
og)
Mod
elin
gGe
omet
ry
ENV 100 Natural HistoryBIO 107 EcologyENV120 Environmental ScienceCHE 101, 102 Chem PrinciplesENV 201 Water ResourcesENV 203 Climate Change SCI 200-level (geology)ENV 300 environmental chemistryBIO317 Aquatic EcologyMAT 220 Statistics
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Curriculum Grid Env. Science TerrestrialBasic arithmetic Data presentation Algebra
Number sense and analysis Modeling
Environmental Science Terrestrial track pr
opor
tion;
per
cent
s
Unit
conv
ersio
nsSi
gnifi
cant
figu
res
Rate
of c
hang
eEs
timati
onLo
garit
hms;
scie
ntific
not
ation
Gath
erin
g da
taer
ror
Grap
hing
Desc
riptiv
e st
atisti
cs
Prob
abili
tySt
atisti
cal t
ests
spre
adsh
eet s
kills
Man
ipul
ating
equ
ation
s
Line
ar fu
nctio
nsN
onlin
ear f
uncti
ons (
expo
nenti
al, l
og)
Mod
elin
gGe
omet
ry
ENV 100 Natural HistoryBIO 107 EcologyENV120 Environmental ScienceENV 201 Water ResourcesENV 203 Climate ChangeENV 204 GISBIO314 Animal BehaviorBIO 318 Terrestrial EcologyBIO 407 Conservation BiologySCI 200 geologyMAT 220 Statistics
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Curriculum Grid Env. StudiesBasic arithmetic Data presentation Algebra
Number sense and analysis Modeling
Environmental Studies prop
ortio
n; p
erce
nts
Unit
conv
ersio
nsSi
gnifi
cant
figu
res
Rate
of c
hang
eEs
timati
onLo
garit
hms;
scie
ntific
not
ation
Gath
erin
g da
taer
ror
Grap
hing
Desc
riptiv
e st
atisti
cs
Prob
abili
tySt
atisti
cal t
ests
spre
adsh
eet s
kills
Man
ipul
ating
equ
ation
s
Line
ar fu
nctio
nsN
onlin
ear f
uncti
ons (
expo
nenti
al, l
og)
Mod
elin
gGe
omet
ry
ENV 100 Natural HistoryBIO 107 EcologyBUS 115 Business IntroBUS 321 Sustainable Org.PSY 101 or SOC 101ENV120 Environmental ScienceENG 215 Env writingENV 201 Water ResourcesENV 203 Climate ChangeENV 204 GISMAT 220 Statistics
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Examples: BIO 107 Ecology• Data collection and presentation• Preference of Fall Web Worms for maple
versus cherry leaves• Spreadsheets, means, standard errors,
graphsDISH LEAF WEIGHT BEFORE WEIGHT AFTER CONSUMPTION
1MAPLE 0.2462 0.1023 0.14392MAPLE 0.2369 0.104 0.13293MAPLE 0.3533 0.164 0.18934MAPLE 0.6266 0.267 0.35965MAPLE 0.4436 0.2132 0.23046MAPLE 0.5503 0.1731 0.37727MAPLE 0.3624 0.1201 0.24238MAPLE 0.3173 0.1583 0.1599MAPLE 0.3436 0.1343 0.2093
10MAPLE 0.7392 0.3976 0.3416 Average 0.23855 std dev 0.090864114 std error Maple Apple
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
amou
nt
con
sum
ed (
g)
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Examples: ENV 201 Water Resources
• Quantifying Stream Discharge– Area calculations– Unit conversions– Data management– Spreadsheet skills – Graphing
0 .5m 1m 1.5m 2m 2.5m 2.9m
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Examples: BIO 318 Terrestrial Ecology
• Matrix model using survival and reproduction in several age classes.
• Stable population and age classes• Effect of survival at different ages
Matrix 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 5total pop 30 40 32.5 35 36.25 33.75
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
5
10
15
20
25
30
35
40
45
total pop
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Does it work: Evaluation• Overall: Basic Q skills and QL skills tests
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Does it work: Evaluation• Pre/post test on module
Pre test Post Test End of semester0
0.5
1
1.5
2
2.5
3
3.5
4
Gra
de
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Challenges
• 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)
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Challenges: basic skills (cont.)• Now design an experiment to answer the
question: – 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.
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Challenges: basic skills (cont.)
• 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?
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Conclusions• Quantitative Literacy skills are weak• Across the curriculum makes sense
– But does it work?
• Projection– Students need to encounter quantitative
issues more often.
