Examining Proof Schemes of Prospective Mathematics Teachers Towards Countability Concept

In this study it was focused to concept of countability, which compose a part of prospective teachers’ understanding of the infinity concept, and it was aimed to examine prospective teachers proof schemas in proving activities including this concept. Case study method, which is one of qualitative research approaches, was used. Also convenience sampling method was preferred. For that purpose, 100 sophomore prospective mathematics teachers studying a state university included the research. After a course period, they were asked to prove some theorems about equivalence of infinite sets. Their answers were examined both descriptive and content analyses. As a result of these process it was identified that majority part them (%91) couldn't reach the formal proof. Also, it was identified that different proof schemas emerged in relation to proving process. In addition, it was seen that most of the prospective teachers (%51) have Empirical Proof Schemes and Analytical Schemas are least observed (%17) scheme