A Study on the Proofs Used by Primary Education Teacher Candidates in Circumference Problem Solutions and Instructional Explanations

Abstract

This study aims to determine the proof schemes used by primary education teacher candidates when solving a given problem and in their instructional explanations. Having a qualitative nature, the study utilized data collected from 277 third-year teacher candidates studying at the primary education department of the education faculty of a state university in Ankara. The study group was selected via criterion sampling. The data were tested by using an open-ended problem case and analyzed via document analysis. The proofs used by students in solving the problem and in instructional explanations were categorized as Proof A, Proof B ... Proof H, and the data were evaluated in these categories. The results obtained were discussed in line with the proof schemes outlined by Harel and Sowder (1998). However, as certain proofs fell into several categories, they could not be evaluated in only one group. The primary education teacher candidates were found to use authoritative, habitual and symbolic proof schemes, albeit to a little extent, in the external proof scheme category as they solved the given problem situation and explained the solution to their students. The majority of the candidates used the empirical proof scheme known as the perceptual proof scheme, and included some sample-based proofs. Analytical proof schemes were used less frequently than others.