Conditions for change in pre-service teachers’ beliefs about proof and proof teaching

Abstract Many educators suggest that proof is essential for the learning of mathematics and should be placed at the centre of school mathematics. However, research has indicated that many teachers have counterproductive beliefs about proof which limit students’ learning opportunities of proof. A design-based research study was carried out to develop an intervention aiming to promote pre-service teachers’ beliefs about proof and proof teaching. The study involved four research cycles; each cycle consisted of design, implementation, evaluation and revision of the intervention. The intervention evolved over cycles. This paper focuses on the analysis of the fourth research cycle, regarding the conditions for change in pre-service teachers’ beliefs about proof and proof teaching. Twenty-seven Hong Kong pre-service primary and secondary school mathematics teachers participated in the intervention and experienced cognitive conflict, leading to the development of more productive beliefs about proof and proof teaching. Drawing on the analysis of the data from a subset of the participants ( n = 12), this paper argues that pre-service teachers must have positive emotions about proof and a sense of practicality as necessary conditions of adopting ideas of implementing proof in their classrooms, suggesting the importance of affective aspects of cognitive conflict in belief change. Implications for initial teacher education are discussed in this article.