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

1. Science One: Integrating Mathematical Biology into a First-year Science Program Mark MacLean Department of Mathematics The University of British Columbia (Vancouver)

2. Outline of Talk • Description of Science One • Role of Mathematical Biology in the Program • Some “evidence” that something interesting happens with our students

3. 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

4. Field trip to Bamfield Marine Sciences Centre in the fall term J

5. 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.

6. 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

7. 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

8. Learning to work with ready-made models Example: Michaelis-Menten type models Lewis et al., J. Theor. Biol. 65 (3), 1977, 579--590.

9. Learning to modify a given model Example: Metastatic tumors

10. Creating your own models Example: SIR epidemic models and HIV/AIDS Figure from Bearman et al., American Journal of Psychology, 110 (2004), 44-91.

11. 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.

12. 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.

13. How do you satisfy the Dean?

14. 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.

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

16. Organic Chemistry • The selected group comprises students in Microbiology and Immunology, Physiology, and Pharmacology

17. Relative Performance in Organic Chemistry Difference between organic chemistry grade and sessional average: BSc: -9.95 Selected: -9.07 Science One: -5.47

18. Genetics

19. Relative Performance in Genetics Difference between genetics grade and sessional average BSc: -4.81 Selected Life Sciences; -1.57 Science One: +2.67

20. 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.