Preservice middle school mathematics teachers conceptions of proof

Developing students’ understanding of proof has become an important task of mathematics educators (Hanna & de Villiers, 2008). Teachers’ competence in creating opportunities for their students and enhancing their experiences with proof is considerably affected by their own conceptions of proof (Knuth, 1999). Therefore, this study investigated junior preservice middle school mathematics teachers’ (PST) conceptions of proof through their responses on a written task where conceptions of proof referred to conceptions of what made an argument a mathematical proof (Knuth, 1999). Data were collected from 32 PSTs enrolled in Elementary Mathematics Education program at a Turkish public university. PSTs took algebra and geometry courses, however, geometry courses did not include proof practices. Two mathematical statements (one algebra and one geometry) and three mathematical arguments which were trying to prove these statements were presented for each statement. PST’s were asked to determine whether given arguments were valid proofs for the statements or not and explain their reasoning. Their responses were deductively coded according to Cobb’s (1986) sources of conviction as authoritarian or intuitive, where the former addressed an outside authority (such as a book) as the source and the latter an individual’s “uncritical belief” (Almeida, 2001, p.56) for “a proposition [which] makes intuitive sense, sounds right, rings true” (Cobb, 1986, p.3). Participants’ emphasis on the distinction between empirical and general arguments was validated by the literature, as generality was considered as an important criterion of proof (Balacheff, 1988). Findings showed that PSTs mainly relied on intuitive and authoritarian reasons and general terms in the argument while explaining their reasoning for accepting an algebraic argument as a proof. Some participants stressed that mathematical proofs should not be exemplifying specific cases. PSTs employed intuitive reasons and idea of generality in geometry task. However, they did not mention authoritarian reasons. PSTs relied on similar reasons for evaluating both algebraic and geometric arguments. They were able to transfer their understanding of proof formed in algebra courses to the case of geometry. Not relying on authoritarian sources of conviction in geometry task might be due to the lack of experience of a geometry content course in which they would learn about authorities’ practices and preferences. Mathematics content courses could be enhanced to have more influence on PSTs’ conceptions of proof.
Citation Formats
M. Dilberoğlu, G. Kaplan Can, and Ç. Haser, “Preservice middle school mathematics teachers conceptions of proof,” presented at the Proceedings of the Thirty-Seventh Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education : Critical Responsesto Enduring Challengesin Mathematics Education, November 5-8 2015, 2015, Accessed: 00, 2021. [Online]. Available: