Rhetorical aspects of the flow of a proof – A shared basis of agreement between lecturer and students

We adapt Perelman's New Rhetoric to assess rhetorical aspects of classroom proof presentation, focusing on the notion of ‘Basis of Agreement’ (BoA). We relate a BoA analysis of episodes from a lesson in number theory to the flow of the proof. Such an analysis puts in evidence lecturer premises while trying to communicate mathematical ideas, student premises and gaps between them. The lecturer's attempts to build a shared BoA with the students by mending gaps became a process of classroom discussion and shared work with the students. Our findings shed light on how content and presentation are intertwined, and suggest how to make classroom communication about proof and its flow more productive.