An investigation of proof images of prospective elementary mathematics teachers about equivalence of infinity sets

When mathematics education literature reviewed it could be seen that there are various studies which examine individuals' proving activities. However, there are few studies which examine the transition from intuitive thinking to formal proof in the context of equivalence of infinity sets. Thus, in this study it is aimed to research that how to this process shaped by using The Proof Image theoretical framework which was introduced by Dreyfus & Kidron (2014). The concept of Proof Image comprises Cognitive Understanding and Affective Feeling components. Thus, images which produced in the individuals' proving activities was analyzed in the context of these components. This research is a qualitative study. The Case Study method which is one of qualitative techniques was used. The data were gathered from second grade students who enrolled a state university by using multi-sampling method. Also triangulation technique was included in data collection process. In this context, students were observed for 5 weeks and also general group studies were executed. On the other hand, to execute detailed analyses of proof image task based interviews which included proving activities for equivalence of infinity sets was conducted with 3 participants for 12 times. As a result of general group studies it was observed that prospective teachers frequently used intuitive approachment to determine equivalence of infinity sets. Also it was identified that individuals faced se deficiencies for executing proof. On the other hand, detailed analyses were conducted for cognitive and affective behaviors of individuals who joined individual studies. Consequently, it was identified that these individuals had images oriented to proof.