Modes of Integration:
1) Enhancing with projects and
assignments within a science course
2) Adding online support for math topics
3) Adding a credit of math onto a science
course
4) Linking or combining math & science
courses
5) Other ideas?
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Edmonds Community College – MAC project
Project description: Integrating mathematics
more explicitly into a non-major, beginning
chemistry course. Students will make direct
connections between mathematical principles
such as equivalent fractions, proportional
reasoning, logarithms, solving linear equations
and direct & inverse proportions and their
applications in basic chemistry.
Often in chemistry there are equations containing more than one variable that need to be
solved for a specified variable. This is equivalent to solving equations in mathematics
using multiplication and addition properties of equality.
Solve the following equations using multiplication and addition property of equality.
“Math You Need” Project – UW Oshkosh and
Highline CC
http://serc.carleton.edu/mathyouneed/index.html
◦ Online “help” modules on mathematical
“sticking places” such as
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Graphing
Slopes
Rearranging equations for variables
Unit conversions
…
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MathBench Biology Modules – U of Maryland
◦ Online modules
http://mathbench.umd.edu/
1. purplemath.com/
Helping students primarily with algebra, it has
free tutoring, worksheets, etc.
2. coolmath.com
This site has everything (fractions to fractals).
The study hints and tutorials are well done.
3. algebrahelp.com
A collection of lessons, calculators, and
worksheets created to assist students and
teachers of Algebra.
AND many many more out there…
Biology with Math-Aid
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Combined Biology 201 (5-credits) with Topics
in Math (2-credits).
◦ Biology 201 is the first-quarter of the 3-quarter
biology majors series
◦ Class met 1 extra hour a day for 5 weeks
◦ Knowledge of math content used in assignments
and labs
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Math topic
Biology examples
Graphing
Photosynthesis
Enzymatic reactions
liter, ml, l,
meter, mm, m …
pH, electrophoresis,
bacterial growth
Units & Scientific
Notation
Logarithms &
exponential
functions
Probability &
Genetics
"DNA math"
Mendelian genetics
restriction maps,
electrophoresis
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Benefits to Students
– Students with minimum Math prerequisites
• appreciated opportunity to practice in an open,
friendly environment
• benefited from learning to self-assess
– Students with more Math (Calculus) prerequisite
• one commented that he found the review helpful for
preparing for professional school exams (PCAT)
• Probability concepts were new for most students
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Benefits to Instructors:
 The math instructor better understood which
mathematical skills are used in biology
courses and how they are used.
 The math instructor now incorporates more
appropriate examples into the mathematical
courses that are prerequisites for biology.
 The Biology instructor continues to use (&
improve) biology student problems,
activities, and worksheets that were first
developed in this MAC-funded project in
2000.
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Exercise developed for Biology
classes
Will be given data, graph paper,
pens/pencils
Make a graph from your data
You will share it with the rest of
the “class”
1. Biology & Sociology
2. Physics & Algebra and Physics & Calculus
3. Chemistry & Algebra
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10-credit coordinated studies (CS) course
◦ Sociology 110 (Introduction to Sociology)
◦ Biology 150 (Biology of Human Disease)
 Prerequisite: Placement into Intermediate Algebra
◦ Fully integrated, interdisciplinary
◦ Both instructors and all students present
 9 hours lecture
 2 hours lab
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MAC3 implementation - Spring 2008
◦ Quantitative epidemiological exercises
 data analysis, calculations, graph & table interpretation
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Objective 1: Students use & understand basic concepts in
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Two worksheets were developed at the 2007 Summer
Institute
epidemiology, especially how rates, such as crude death rate, agespecific death rate, infant mortality rate, cancer rates, etc. are
calculated.
 General Mortality Rate
 Infant Mortality Rate
◦ Worksheets include
 Definition of term
 Equation for calculation of rate
 Example of how rate is calculated
 2-3 Problems that let students calculate rates
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Objective 2: Students read and interpret graphs and tables and
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Students will
generate hypotheses to explain data.
◦ read and interpret the graph or table
◦ explain conceptually how the data (e.g. rates) were calculated
◦ generate 2-3 hypotheses that explain the observed differences
between groups
◦ indicate type of data needed to evaluate one hypothesis
◦ predict what data would look like if the hypothesis were
supported/not supported
◦ make one suggestion on how to reduce differences between
groups assuming that their hypothesis were supported (i.e. a
social or biological solution).
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Students recall
information needed for
Mortality Rate
calculations.
Students interpret graph
& generate hypotheses
to explain differences
between regions.
Students propose types
of data needed to test
hypotheses (e.g. GDP)
Students propose social
or biological solutions
to child mortality.
NSF visit
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Physics & Algebra
◦ Physics for Non-science Majors &
Intermediate Algebra
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Physics & Calculus
◦ Calculus I & Engineering Physics I (fall quarter)
◦ Calc II & Engr Physics II (winter quarter)
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Two teachers together in the same room
Integrated homework, exams, physics labs
and mid-term and final projects
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Using the same math language in the science
class to describe mathematical operations
◦ I.e., In math class the students are asked to
perform certain operations with terminology
specific to math or even the text. Using the same
language in the Physics class helped the students
transfer their math knowledge.
◦ P.S. This is not as trivial for the students as it is
to you!
Making explicit translations between math
symbols and science symbols.
E.g. Math class
vs.
Physics class . . .
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y ( x)  42 x  5 x  6
x(t )  42t  5t  6
y '  84 x  5
dx
 84t  5
dt
2
2
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It is important to know when and why you (as
a scientist) are using math differently than
the students have been taught . . . and to
know how to justify it to the students!
E.g.,
◦ Sometimes leaving off constants in integration
◦ Using tables for integration
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If you know what the math instructors are not
teaching you can address it explicitly.
E.g.,
– Knowing that coefficients and variables have units
and meaning.
– Using variables besides y and x.
– Dividing by zero is meaningful in science
(interpreting asymptotes)
– Understanding there are limitations for
mathematical models to model real data.
– Building equations that are then manipulated by
mathematical operations.
If you know what technology the math
instructors are teaching you can include it to
help the students bridge and extend their
knowledge.
E.g.,
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◦ graphing calculators
◦ Excel, Maple and Mathematica
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Chemath course was created out of lack of math
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General Chemistry Prep & Intermediate Algebra
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10-credit combined course, team- taught
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Students required to do math content, even if
have higher placement.
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Group work, quizzes, and final exam combined
skills in Chemistry class
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See mathematician and scientist “talking”
◦ Different notation, different methods of solving
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“Just in time” mathematics instruction
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A “cohort” naturally gets formed
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10 credits of math/science gets them
prepared for future coursework