A Computer Activity Approach to College Geometry

Cardinal Stritch University, Milwaukee WI

Investigators

Abstract

Mathematical Sciences (21) Materials are being developed for an activity-based college geometry course using Geometer's Sketchpad. The project addresses the DUE themes of teacher preparation and integration of technology into education. Subsequent work will develop a textbook for the geometry course required for teacher candidates at various institutions. This idea has been discussed with the acquisitions' editor at Key College Publishing, the distributor of Geometer's Sketchpad. More than ten years experience each using an activity-based approach, cooperative learning, and mathematical software to teach calculus, discrete mathematics, and abstract algebra has demonstrated the effectiveness of these approaches. This project applies these pedagogical strategies to college geometry. The course materials are engaging students in exploratory activities designed to develop their intuitive understanding of geometric concepts. Students use interactive geometry software to construct geometric figures, make and test conjectures about these constructions, and create proofs based upon their constructions. Through productive group interactions, students are being guided toward constructing increasingly robust mathematical proofs. Most students served by this course are future teachers. Since teachers often teach as they were taught, it is important to model pedagogical strategies consistent with the recommendations of the National Council of Teachers of Mathematics (NCTM). The project materials model such strategies, and are suitable for an introduction to formal mathematical reasoning in a first or second proof-course. This is a valuable course for any mathematics student, but particularly so for those intending to become teachers of mathematics.