Definitions play a crucial role in reasoning and proving in geometry, and consequently in the Geometry for Teachers (GeT) course. However, the handling of definitions in the teaching of geometry has been criticized by mathematics education researchers and mathematicians alike. The College Geometry course can therefore be an especially productive site for a course-correction by preparing future secondary mathematics teachers to incorporate knowledge about definitions and defining into their own knowledge-base and practice.
In this seminar, we’ll begin by introducing some of the challenges uncovered by our own and others’ research with respect to working with definitions in geometry. In particular, we will pay special attention to the relationship between the structure and logic of definitions and proving. Research-based activities that have been used to develop specific competencies for proving in geometry will be shared, and some affordances of using such activities within the GeT course will be discussed.