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Preservice teacher proficiency with transformations-based congruence proofs after a college proof-based geometry class
Journal article   Peer reviewed

Preservice teacher proficiency with transformations-based congruence proofs after a college proof-based geometry class

Meredith Hegg, Dimitri Papadopoulos, Brian Katz, Timothy Fukawa-Connelly and Maria Delivoria-Papadopoulos
The Journal of mathematical behavior, v 51, pp 56-70
Sep 2018

Abstract

Mathematics teacher education Proof Transformational geometry
•Students trained in transformational geometry successfully completed elementary transformations-based congruence proofs.•Students expressed a preference for using SAS and ASA criteria to write proofs, rather than a transformational approach.•Students typically gave analytic definitions of transformations, despite having experience with synthetic definitions.•Student thinking included both motion and map conceptions of transformations, but appeared dominated by motion conceptions. This report explores pre-service teachers’ proficiency with concepts of transformational geometry at the end of a semester-long advanced geometry course. In the course, the instructor incorporated transformational geometry content, including congruence proofs, in an attempt to prepare the pre-service teachers to teach high school geometry in alignment with the Common Core State Standards for Mathematics. At the conclusion of the course, students expressed a preference for using traditional triangle congruence criteria (SAS, ASA, SSS, and AAS) over using transformations to complete proofs, but were nevertheless generally successful in completing proofs using transformations. Similarly, while the students often described thinking of transformations in terms of analytic forms, they were successfully able to prove triangle congruences in synthetic contexts. Finally, some evidence indicates that students may have motion or process conceptions of transformations, but not map or object conceptions, but this evidence is not conclusive.

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Education & Educational Research
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