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