Prospective High School Mathematics Teachers' Uses of Diagrams and Geometric Transformations While Reasoning about Geometric Proof Tasks

The purpose of this study was to examine prospective teachers' uses of diagrams and approaches to congruence while solving proof tasks. Eight prospective high school mathematics teachers were given three proof tasks to solve at the beginning and end of a mathematics education course. The course used the history of mathematics as the context for assisting teachers in making connections between important mathematical ideas. A unit of instruction used technology-based activities to support a transformational approach to congruence. Analysis revealed that at the beginning of the course teachers approached congruence proofs using perceptual or correspondence approach and used a descriptive mode of interaction with diagrams. At the end of the course, their approaches to congruence included more instances of transformations and measures and their interactions with diagrams included fewer uses of the descriptive mode and more instances of representational, generative, and functional modes.