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. In this study, which was conducted with a qualitative research approach, a form consisting of openended questions was applied to teacher candidates. In this form, teacher candidates were asked 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 determined through content analysis. Accordingly, while 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 topic 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, the common opinion of the pre-service 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 pre-service teachers have difficulty in proving in addition to trigonometry, additional learning on these subjects can be recommended.