A framework for example usage in proof presentations

•Four interrelated case studies of mathematics faculty members teaching proof courses.•Observations of actual teaching are combined with interviews of the instructors.•The framework developed in this paper describes example usage in proof presentations.•The uses of examples are classified by the instructors’ pedagogical intentions.

The use of examples has been identified as a pedagogical tool for proof presentations, however, the types and uses of examples in the context of proof presentations in advanced mathematics courses has not been described in detail. This study will organize the types of examples that were used in the proof presentations of four instructors into a coherent descriptive framework that is grounded in observation and interview data. This framework will present an integrated approach for when and how different types of examples are used during proof presentations.