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Science One: Integrating Mathematical Biology into a First-year Science Program

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### Science One: Integrating Mathematical Biology into a First-year Science Program

Mark MacLean

Department of Mathematics

The University of British Columbia (Vancouver)

Outline of Talk

- Description of Science One
- Role of Mathematical Biology in the Program
- Some “evidence” that something interesting happens with our students

What is Science One?

- A Learning Community of 72 first-year students and 8 instructors
- A single 27-credit course (of a typical 36-credit load) that integrates biology, chemistry, mathematics, and physics
- Students are selected on the basis of grades and their interest in science.
- Weekly: 12 hours of “lectures”, 2 hours of tutorials (24 students), 2 hours of “small groups”(9 students), 9 hours of labs.
- Faculty share the classroom with their peers
- Students do two independent research projects, one each term
- Research Conference in the spring term

The Role of Mathematical Biology

- First introduction to Mathematical Modeling

The mathematics curriculum is based on calculus and elementary differential equations (primarily ODEs), plus some extras

Most Science One students (70%+) are interested in pursuing a life sciences degree.

- Mathematics is “obvious” in physics and parts of chemistry, but has been hidden from them in biology -- new opportunities to learn to see mathematics in the world.
- One way to help them see biology as more than a collection of factoids, which is one of the goals of UBC’s first-year biology courses.

Goal:

To help students develop mathematical modeling skills, including

- Learning to see mathematical concepts in nature
- Learning to work with ready-made models
- Learning to modify a given model to better capture actual features of a real-world system
- Learning to create their own models

Learning to see mathematical concepts in nature

Example: Elasticity of Nereocystis leutkeana (bull kelp)

Elasticity is the derivative of stress (Force per unit area) with respect to strain (relative change in length)

Photo: Tom Bird

Learning to work with ready-made models

Example: Michaelis-Menten type models

Lewis et al., J. Theor. Biol. 65 (3), 1977, 579--590.

Learning to modify a given model

Example: Metastatic tumors

Creating your own models

Example: SIR epidemic models and HIV/AIDS

Figure from Bearman et al., American Journal of Psychology, 110 (2004), 44-91.

Some thoughts

- The best examples connect to real biological problems -- students know when you have contrived something just to teach them a piece of mathematics
- Embrace your ignorance -- make sure students see how you use your mathematical understanding to build your biological understanding (or vice versa)
- Recognize that learning to become a mathematical modeler takes time -- design a progression of experiences that help students build skills over time and be explicit in showing how you are using prior experience to tackle learning new tools or to building models
- Believe in your students -- even if a student does not seem destined to be a mathematician, they gain a lot by learning how to communicate with mathematics.
- Be in control -- understand your expected learning outcomes for each modeling exercise.

What impact does this have on students?

Some intangibles:

- Science One students in the life sciences take more mathematics courses than their peers.
- Science One students are not afraid to use mathematics in their biology classes, even when it is not expected.
- Science One students question the validity of models (mathematical and otherwise) more than their peers.

How to compare our students to other students?

Problems:

- We have not undertaken a standard controlled experiment (for ethics reasons, amongst others).
- Our students go through a selection -- they chose to apply and we choose them from the applicant pool.

Our approach: (joint with Neil Dryden, UBC-V Chemistry)

- Study performance in courses requiring higher-level problem-solving skills in each discipline. The comparisons are to other selected groups; in the life sciences these are microbiology and immunology, physiology, pharmacology.
- Compare our students’ performance in these courses to their ownoverall sessional average.

Admission Averages

There appears to be little correlation between high school admission averages and first-year averages at UBC.

Organic Chemistry

- The selected group comprises students in Microbiology and Immunology, Physiology, and Pharmacology

Relative Performance in Organic Chemistry

Difference between organic chemistry grade and sessional average:

BSc: -9.95 Selected: -9.07 Science One: -5.47

Relative Performance in Genetics

Difference between genetics grade and sessional average

BSc: -4.81 Selected Life Sciences; -1.57 Science One: +2.67

Acknowledgements

- Martin Adamson, Gordon Bates, Julyet Benbasat, Les Burtnick, Jim Carolan, Neil Dryden, Martin Ehlert, Lee Gass, Tony Griffiths, Mark Halpern, Geoff Herring, Leah Keshet, Celeste Leander, Domingo Louis-Martinez, Barry McBride, Ed Nelson, Rosie Redfield, George Spiegelman, Luis Sobrino, Bob Thompson, David Walker, Chris Waltham
- And our many students!
- And thanks to you for listening.

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