Leading students to investigate diffusion as a model of brine shrimp movement. (English) Zbl 1184.92061
Summary: Integrating experimental biology laboratory exercises with mathematical modeling can be an effective tool to enhance mathematical relevance for biologists and to emphasize biological realism for mathematicians. This paper describes a lab project designed for and tested in an undergraduate biomathematics course. In the lab, students follow and track the paths of individual brine shrimp confined in shallow salt water in a Petri dish. Students investigate the question, “Is the movement well characterized as a two-dimensional random walk?” Through open, but directed discussions, students derive the corresponding partial differential equation, gain an understanding of the solution behavior, and model brine shrimp dispersal under the experimental conditions developed in the class. Students use the data they collect to estimate a diffusion coefficient, and perform additional experiments of their own design tracking shrimp migration for model validation.
We present our teaching philosophy, lecture notes, instructional and lab procedures, and the results of our class-tested experiments so that others can implement this exercise in their classes. Our own experience has led us to appreciate the pedagogical value of allowing students and faculty to grapple with open-ended questions, imperfect data, and the various issues of modeling biological phenomena.
We present our teaching philosophy, lecture notes, instructional and lab procedures, and the results of our class-tested experiments so that others can implement this exercise in their classes. Our own experience has led us to appreciate the pedagogical value of allowing students and faculty to grapple with open-ended questions, imperfect data, and the various issues of modeling biological phenomena.
MSC:
| 92D50 | Animal behavior |
| 93A30 | Mathematical modelling of systems (MSC2010) |
| 97M60 | Biology, chemistry, medicine (aspects of mathematics education) |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
project-based learning; undergraduate education; brine shrimp; Artemia Franciscana; diffusion; random walksReferences:
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