Pre-service elementary school teachers' experiences with interpreting and creating proofs

Having an ability to appreciate, understand, and create proofs is crucial in being able to evaluate students’ mathematical arguments and reasoning. As such, the development of this ability in pre-service teachers is imperative. Research, however, has repeatedly shown that the ability to understand and create proofs is difficult for students in general and for pre-service elementary school teachers in particular. This study aimed at extending the views and insights about the difficulties that pre-service elementary school teachers experience in dealing with the notion of mathematical proof. For this purpose I analysed students’ discourses when they attempted to interpret or create proofs for some propositions related to elementary number theory. The communicational approach to learning is the theoretical perspective that I adopted to investigate the difficulties students experience in generating proofs. According to communicational approach to cognition, thinking is a special case of the activity of communication, and learning mathematics is an initiation in a certain type of discourse, which is called literate mathematical discourse. In this study, I have introduced the notion of dialogue as a tool for involving students in the process of creating a proof. Based on the idea that thinking can be considered as an act of communication that one has with oneself, I introduced dialogue as a self-dialogue or a conversation that a person has with oneself while she/he is thinking. I encourage d students to write a dialogue while they were thinking to interpret or create a proof. For this purpose, I designed six tasks. The results revealed that the main difficulty that students experienced in creating a proof is that they do not know how to communicate their idea mathematically. There are several contributions of this study to the field of mathematics education focusing on pedagogy, methodology and theory.