For several years the Department of Mathematics at the University of Arizona has been developing its undergraduate course in geometry, a required course for future high school teachers. The goal of the course is to get students solving problems in geometry and doing mathematics on their own, enthusiastic about the ideas that emerge and hooked on the processes that are involved. The purpose of the talk is to describe the ways used to achieve these goals.

We grab students attention by making the problems we work on accessible, attractive, useful, and intriguing. We help them build an arsenal of attack methods by offering problems that lend themselves to students' using (and commenting on) a wide variety of processes for solutions. To keep students involved, we make problems, topics, and solutions connect in surprising and tantalizing ways. To allow time for exploration, making models and discovering things (especially the connections), we don't try to cover every topic in depth. We give students many occasions to work with other students --- to share insights, to communicate ideas, to pump each other up. Finally, there is a culminating experience in which they can show off their involvement in geometry --- in the form of a Geometry Fair for presenting the results of final projects. Topics have been chosen in order to enable all of the above to happen: polyhedra, mirrors, symmetry, minimal paths, efficient shapes, sphere packing. In the talk I will provide specifics of problems, projects, models, topics and curriculum materials.

David A. Gay, University of Arizona