This is an innovative project establishing an interactive modeling course at the lower division level for culturally diverse students. The course will focus on the modeling process using examples based on (systems of) difference and differential equations. The first part of the course will introduce basic terminology and background necessary for continuous models: the notions of derivative as rate of change and as slope of the tangent line. With this background students can derive model equations and qualitatively analyze the solution using slope field and phase plane graphs created by Mathematica. The course will be taught in the Macintosh laboratory, using Joy of Mathematica as a user-friendly, menu-driven interface to Mathematics. In the second part of the course, students will work on applications from biology, chemistry, economics and physics. Collaborators from these disciplines will identify "standard models" based on difference and differential equations with interesting applications from their area of expertise. These models will be implemented as interactive Mathematica texts; a library of models will thus be created for student exploration. Students will present their final projects at a poster session. The emphasis of the proposed course on visual components for understanding will make it possible to offer the course as a lower division course. The course will be aimed at students with weak mathematics background who would not take the advanced courses needed for a traditional modeling course, science majors in preparation for modeling applications in their disciplines, and prospective teachers in preparation of a curriculum based on the NCTM Standards. Students should leave the course with a solid understanding of the modeling process, improved critical thinking and writing skills, and an appreciation of the importance of mathematics for modeling across the disciplines. It is our hope that they will be less intimidated by mathematics, and view mathematics as an integral part for their understanding of the world.
