Teachers’ Views about the Role of Examples in Proving-related Activities

Abstract

Examples play a critical role in mathematical practice, in general, and in proving-related activities (e.g., developing conjectures, exploring conjectures, justifying conjectures), in particular. Yet, despite the critical role examples play in proving-related activity, we contend that students typically receive very little, if any, explicit instruction on how to become more deliberate and strategic in their use of examples. The goal of the study reported here was to explore teachers’ beliefs about the role examples play in proving-related activities, and the instructional practices they implement to foster the development of students’ abilities to strategically think about and productively use examples. Fifty-four middle school mathematics teachers responded to a series of on-line survey questions that focused on the role and use of examples during proving-related classroom activities. We found that many teachers have limited views of what it means to use examples strategically during proving-related activities, and that they tended not to provide explicit instruction designed to help students learn to strategically think about and productively use examples during their engagement in proving-related activities. The findings suggest the need for both professional development and curricular resources to support teacher efforts to help their students learn to strategically think about and productively use examples during proving-related activities.