Integrating Computer Explorations into College Geometry

Cardinal Stritch University, Milwaukee WI

Investigators

Abstract

This project is a follow-on of a proof-of-concept project where preliminary materials for activity-based college geometry using The Geometer's Sketchpad were produced. Addressing DUE themes of teacher preparation and integration of technology, this project is developing a textbook and supporting CD. Various institutions are testing the textbook and conducting a comprehensive evaluation of its effectiveness. Intellectual merit is in the pedagogic design. The textbook incorporates exploratory activities using Sketchpad to develop intuitive understanding. The text (a) engages students in explorations leading to making and testing conjectures; (b) improves geometric reasoning, encouraging transitions from concrete visualization to abstract conceptions to axiomatic thinking; (c) develops skill in constructing mathematical proofs; and (d) encourages articulation of mathematical observations and ideas. Course materials support cooperative learning, and offer an introduction to mathematical reasoning. Since most geometry students are future teachers, this course models strategies recommended by NCTM (National Council of Teachers of Mathematics) and includes exploratory activities, cooperative learning, and mathematical software. Broader impacts include dissemination of course materials through publication, workshops, and presentations. Key College Publishing, The Geometer's Sketchpad distributor, is publishing the book. Faculty development workshops model the pedagogy through computer explorations and small group discussions, influencing faculty's teaching in geometry and beyond. The course is valuable for any mathematics student, particularly for future mathematics teachers.