Since march, 1995 we have been involved with the Southwest Regional Institute for Mathematical Sciences (SWRIMS) at Utah State University, a National Science Foundation funded effort to involve mathematical researchers in educational issues. We focussed on illustrating and enlivening mathematics instruction through its application in biology. Prompted by examples of collaborations between research biologists and applied mathematicians, we developed the Biologist/Applied-Mathematician Instructional Model (BAMIM). The central basis for BAMIM is that the cognitive state of a mathematical researcher creating mathematics for a biological application is the appropriate state of mind for a student who is learning mathematics. To this end, we have explored various collaborative arrangements among students studying mathematics and students studying biology.
Calculus curriculum reform projects [1, 2, 3] as well as the Curriculum and Evaluation Standards for School Mathematics [4, 5] emphasize the need for students to engage in cooperative learning activites for the purpose of creatively applying mathematics to address real-world problems. When appropriately structured and organized, cooperative learning activities have proven extremely successful in leading students to invent and discover mathematics for themselves rather than mimic textbook rules and algorithms [6, 7, 8]. The mathematics instructor applying cooperative learning strategies creates, organizes, and manages an environment in which students learn from one another. In such an environment, students are stimulated to speak in the language of mathematics as they collaboratively address problems. Not only does this enhance their fluency with the language, it also forces them to organize their thoughts well enough to be comprehended by their peers . This organizing-of-thoughts function leads to conceptualization of mathematical relationships [6, 10].
In traditional textbook-and-instructor centered courses, cooperative learning only takes place out of the sight and supervision of the instructor, when students informally gather in small study groups. Most students who survive this educational tradition develop a reliance on passive aids (e.g. textbook recipes). They may develop a talent for manipulating symbols and following recipes but are terrified of applying mathematical knowledge in unknown territory. To use a linguistic analogy, they have knowledge of mathematical grammar, but are scarcely conversational and certainly not colloquial. Modelling and understanding science through mathematics is foreign to the vast majority of traditionally-taught students .
This is the context in which we developed BAMIM. Our goal is to overcome the passivity and isolation perpetuated by traditional mathematical education. The model confronts students with biological circumstances and assists them in group construction of concepts (e.g. continuity, derivative, antiderivative, integral) and discovery of relationships (e.g. the fundamental theorem of calculus). Students also establish a sense of ownership because the constructions and discoveries are built from their own observations and activities.
Application of BAMIM in mathematics courses requires professors to confront students with situations that stimulate them to behave like applied mathematicians collaborating with research biologists. At least five options exist for accomplishing this within the confines of a conventional college or university course structure, most of which we have tested during the SWRIMS activity: