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Prospective high school mathematics teachers’ uses of diagrams and geometric transformations while reasoning about geometric proof tasks

The purpose of the 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 two proof tasks to solve at the beginning and end of a mathematics education course. Analysis revealed that at the beginning of the course preservice teachers’ approached congruence proofs using a perceptual or correspondence approach and interacted and used a descriptive mode of interaction with diagrams. At the end, 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 and functional modes.