Supporting Teacher Proving Practices with Three Phases of Proof

Abstract

Although reasoning and proof in learning and teaching mathematics is crucial and have gained more presence in school mathematics, both students and their teachers face great difficulties when engaging in proving activities. One potential cause for such difficulties might be due to teachers’ conception of proof. However, to date, there are few, if any, studies that have examined how secondary school in-service mathematics teachers learn justification and proof. This study focuses on secondary school in-service teachers’ engagement in proving activities by providing observational data from a master’s level professional development course that focuses on teaching reasoning and proof. The findings from this work highlight the usefulness of framing proving activities as consisting of three phases: exploration; justification; and evaluation. In addition, we discuss the useful role that generic example-based proofs can play when teachers are proving. We illustrate through a specific vignette of teacher proving activities, and discuss the results in the light of using proof-related tasks to engage learning during proving activities.