This is the summary of a presentation given at the Joint Mathematics
Meetings, January 1013, 1996, Orlando, Florida.
The Undergraduate Geometry Course: Problems, Models and Projects
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
