The article was co-authored with Dr. Tommy Dreyfus of Tel Aviv University’s School of Education

ABSTRACT: The term “flow of proof” describes various aspects of the way in which a proof is presented in a mathematics classroom (e.g., the proof’s logic structure, informal aspects of the proof’s presentation, and contextual considerations such as the syllabus and prior knowledge). Using an argumentation theory called New Rhetoric (Perelman & Olbrechts-Tyteca, 1969), we analyze rhetorical aspects of flow, while focusing on the creation of a “Basis of Agreement” (BoA) between the lecturer and students. Such a BoA is essential to the process of deeply convincing students of the correctness of the arguments presented.

The study described in the article was conducted at a number theory course for student teachers. Several course lessons featuring proofs were recorded, and the lecturer was interviewed. In the article, we analyze episodes from one of the lessons recorded; and specifically analyze the lecturer and the students’ premises, demonstrate various types of gaps between them, and show how the lecturer’s attempt to bridge those gaps created a process of effective classroom communication. We demonstrate how the theoretical framework that we’ve created can be used to analyze and improve flow of proof.