Investigation and analysis of the basic models of reasoning and proof in math education

The purpose of this study was to investigate and analyze mathematical models and important frameworks that researchers and educators have suggested to discuss people’s response to issues related to proof in mathematics. Eight models have been introduced and analyzed. Each of these models categorizes a way of students’ reasoning and proof. Of course, some of these classifications are more accurate and detailed. According to the researcher's explanation for the different classes of models, a table was presented that shows the overlap and distinction between these classes. The results of models’ analysis shows that people’s response to issues related to proof can be classified in two ways: a. regardless of individuals’ opinions on the proof, and solely on the basis of their reasoning methods, and b. depending on the type of thinking during the process of proof and also their reasoning methods for presenting the proof. Using the models under study, a new framework was proposed; so that various mathematical reasoning could be classified using it. In this framework, the reasoning of people during the proof of a proposition was classified based on the type and method of presentation. Using this method, we can demonstrate the ability of students on the process of proof and furthermore we can study the way of their thinking and their views about this process. It seems that the proposed framework could cover different classes of models presented by other researchers.