The Nature of Middle School In-Service Teachers’ Engagements in Proving-Related Activities

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. Thus, in order to fill this gap, this study examines 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 show that teachers were very successful at engaging in exploration of the proving tasks, but they fail to produce complete-deductive arguments. Some reasons behind this failure were teachers’ lack of a perceived need for justification and proof after exploring the task, and their lack of seeing algebraic symbolization as a viable means of expressing mathematical ideas