Modes of Integration:1)Enhancing with projects and

assignments within a science course2)Adding online support for math topics3)Adding a credit of math onto a science

course4)Linking or combining math & science

courses5)Other ideas?

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 Graphing Slopes Rearranging equations for variables Unit conversions …

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 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

11

12

Math topic Biology examples

Graphing PhotosynthesisEnzymatic reactions

Units & ScientificNotation

liter, ml, l,meter, mm, m …

Logarithms &exponentialfunctions

pH, electrophoresis,bacterial growth

Probability &Genetics

Mendelian genetics

"DNA math" restriction maps,electrophoresis

• 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

13

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.

14

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

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

MAC3 implementation - Spring 2008◦ Quantitative epidemiological exercises

data analysis, calculations, graph & table interpretation

17

Objective 1: Students use & understand basic concepts in epidemiology, especially how rates, such as crude death rate, age-specific death rate, infant mortality rate, cancer rates, etc. are calculated.

Two worksheets were developed at the 2007 Summer Institute

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

18

Objective 2: Students read and interpret graphs and tables and generate hypotheses to explain data.

Students will◦ 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).

19

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 20

Physics & Algebra◦ Physics for Non-science Majors &

Intermediate Algebra Physics & Calculus

◦ Calculus I & Engineering Physics I (fall quarter)◦ Calc II & Engr Physics II (winter quarter)

Two teachers together in the same room Integrated homework, exams, physics labs

and mid-term and final projects

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 . . .

2( ) 42 5 6

' 84 5

y x x x

y x

2( ) 42 5 6

84 5

x t t t

dxt

dt

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

• 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., ◦ graphing calculators◦ Excel, Maple and Mathematica

• Chemath course was created out of lack of math skills in Chemistry class

• General Chemistry Prep & Intermediate Algebra

• 10-credit combined course, team- taught

• Students required to do math content, even if have higher placement.

• Group work, quizzes, and final exam combined

See mathematician and scientist “talking”

◦ Different notation, different methods of solving

“Just in time” mathematics instruction

A “cohort” naturally gets formed

10 credits of math/science gets them prepared for future coursework