Behavioral Sciences Curriculum Enhanced with Mathematical Modeling

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The Bio2010 report of the National Research Council identifies integration of mathematics into biology as an important part of modernizing the undergraduate curriculum. We propose to advance this goal in the behavioral sciences by producing a CD of interactive simulations and experiments in mathematical modeling. The behavioral sciences rely on mathematics not only for data analysis, but for models that explain behavior and its origins. However, undergraduate texts typically gloss over modeling, and there are few resources for those who would teach it. We are developing prototypes of modules covering a range of topics. They are intended to be used together in a course on behavior or singly in introductory biology, ecology, and evolution. Each starts with a video of a behavior and prompts students to consider the questions it raises. Next, students are led (both verbally and mathematically) through development of a model. Students then form hypotheses about the behavior and test their predictions with a graphical simulation of the model. While the mathematics behind these models does not go beyond algebra, the effect of varying parameters is often not obvious. Interactive simulations allow students to explore on their own as they develop understanding of modeling and a feel for the link between model parameters and behavior. The intellectual merits of this project are the improvement of the undergraduate biology curriculum by introducing mathematical modeling in a context that is accessible and interesting to students and the use of technology to advance teaching goals that cannot otherwise be met. This project is having an immediate impact in Cornell's large animal behavior course, where we are doing initial testing. Broader impact will come from publication of the material and usenationwide in other colleges and universities. Faculty from departments of biology, psychology, anthropology, and mathematics at a variety of other institutions have indicated need for this material and willingness to test it in their classes as part of our evaluation plan. Several publishers, including that of the most widely used animal behavior text, have shown interest, making nationwide dissemination certain.