Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers

Abstract

This study examined the subject(s) that elementary mathematics teacher candidates find most suitable for proving in analysis courses, the functional structure of proof they remember most, the level of proof, and the reasons for preferring this proof. For this reason, this research aims to reveal the pre-service teachers' preferences for proof in analysis courses, the proof they keep in mind the most and its functional structure, their level of proof, and their views on proof relationally and holistically. In this study, which was conducted with a qualitative research approach, a form consisting of open-ended questions was applied to teacher candidates. In this form, teacher candidates were asked various questions about the mathematical proofs they made. With descriptive analysis, the answers of the pre-service teachers who participated in the research were systematically defined, and data were tried to be defined through content analysis. Accordingly, while the subject that the pre-service teachers found the most appropriate application of the proof approach to be the subject of trigonometry, it was determined that the proof that remained in their minds the most was also related to the subject of trigonometry. By examining the functional structure of these proofs written by pre-service teachers, it has been seen that they have the function of explanation and systematization. In addition, the reasons for preferring the proof they made were asked of the pre-service teachers, and the answers were gathered on the fact that proof provides the most permanence and causal learning. It was emphasized that theorems that require formula memorization generally become more understandable with the proof method. According to the results of the research, it is stated that the common opinion of the prospective teachers is that teaching how to obtain the proof method of formulas in trigonometry, instead of memorizing them, is beneficial in ensuring both meaningful and permanent learning. In light of the findings of these studies, more sensible suggestions can be made to improve pre-service teachers' knowledge systems and classroom teaching on proof. By determining which topics and theorems students have difficulty in proving in addition to trigonometry, additional learning on these subjects can be recommended.