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.
