Teaching to listen, question, and ponder: an investigation into promoting an enquiring atmosphere in a mathematics classroom

This study reports on a classroom-based intervention that lasted eight lessons with the particular focus of exploring whether and how specific activities, strategies, and questions may promote an enquiring atmosphere in a mathematics classroom, i.e., a classroom environment in which students feel safe to investigate new mathematical ideas in order to produce, share, and test their conjectures in search for a proof. Although many researchers agree on the central role that conjectures and proofs should play in all students’ mathematical experiences, many students find it difficult to engage with conjecturing and proving. In this paper we argue that the classroom atmosphere has a crucial influence in helping students to overcome these difficulties and we focus our investigation on an English secondary mathematics classroom taught by the first author. Students’ responses to questionnaires, prompts, tasks, and interview questions were analysed in order to evaluate the impact of the intervention. The analysis suggests that specific activities, strategies, and questions can be used by teachers to facilitate an enquiring classroom atmosphere. However, for these to be effective, the teacher needs to explicitly teach students how to listen, question, and ponder in order to give students the tools to formulate conjectures and proofs