The Proof Schemes of Preservice Middle School Mathematics Teachers and Investigating the Expressions Revealing These Schemes

Abstract

The aim of this study is to investigate preservice middle school teachers’ proof schemes and how they presented their proof schemes. Clinical method was used to identify the proof schemes of preservice teachers.  For this purpose, clinical interviews about the nature of proof and task based interviews were conducted with the participants in the field of numbers. The Task Based Interview Questions Form and Interview Questions Form about the Nature of Proof were conducted with three female preservice teachers in a single session. Using the content analysis report, it was found that preservice teachers used external proof schemes more frequently than analytic proof schemes, and they used empirical proof schemes less often. It was determined that showing responses on analytical proof schemes was higher in those preservice teachers when compared to the ones with lower level achievements. It was found that the external based opinions of the preservice teachers were found to be related with their characteristics which revealed external based proof scheme. It was also noticed that there could be a relationship between already acquired opinions which were memorized and superficial and the ones which block transforming ideas while making proofs.