An examination of primary school mathematics pre-service teachers' proof images regarding equivalence relations

An Examination of Primary School Mathematics Pre-Service Teachers' Proof Images Regarding Equivalence Relations The aim of this research was to investigate proving processes about equivalence relations of pre-service mathematics teachers using by Proof Image theoretical framework which was introduced by Dreyfus and Kidron (2014). Proof image has two components: the cognitive understanding and affective feeling. Therefore, this study is focused on prospective elementary mathematics teachers proving processes in the context of these components. In this qualitative case study, data were gathered from first grade students by using multi- sampling method. Participants of the research are first-year elementary school mathematics teacher candidates who take abstract mathematics courses at a state university. Three forms of open-ended questions were developed in the study. Firstly, a form which includes equivalence questions is applied to 102 student (Appendix - 1). The second form is applied after the 'equivalence relation' had been processed (Appendix - 2). After that, 3 pre-service elementary mathematics teachers selected based on the skills of using mathematical language and semi-structured interviews were conducted in the direction of the proof form in order to reveal proof images about equivalence relations (Appendix -3). In addition, students were observed during the study for 3 weeks and all lessons are taken in video recording. Analyzes were made on individual studies proving processes and proof images when examining general approaches to the subject with in-class observations. As a result of the research, similarity and difference in proof images were determined by in depth analysis of prospective teachers' information and proving processes. Keywords: Proof, Proof Image, Equivalence, Equivalence Relations, Pre-Service Elementary Mathematics Teacher