Pre-Service Elementary Teachers’ Proof and Counterexample Conceptions
AbstractThis study aimed to document pre-service elementary teachers’ (PSTs’), who are going to teach K-5, ability to construct as well as evaluate justifications varied in terms of levels of sophistication. Additionally, this study aimed to investigate how PSTs’ knowledge of content in which they were being asked to prove influenced their ability to construct and evaluate mathematical justifications. Participants were a sample of PSTs who enrolled in one section of a geometry and measurement course and one section of a mathematics methods course at a large Mid-western University in the U.S. The participants were selected based on their responses to a written questionnaire, which consists of various open-ended proof questions. Then,task-based interviews were conducted at the beginning as well as near the end of the semester in order to detect whether there were any differences in PSTs’ conceptions of proof as a result of taking these courses. The results of this study showed differences in what constitutes as proof in the eyes of the PSTs who participated in this study. Furthermore, this study also demonstrated that the restriction of PSTs’ construction and evaluation of proofs/counterexamples was indeed a result of their limited conceptions of the concepts in which they were asked to prove.