Metarules in university mathematics lectures: A commognitive analysis of proof-oriented mathematics teaching

In lectures delivered to large cohorts of students, it is challenging for a lecturer to develop a two-way communication with students. This study explores the tacit aspects of a lecturer’s communicational activity of proof teaching in mathematical analysis. We used a multi-layered commognitive analysis to discern the lecturer’s communicational actions and to connect these actions with metarules that regulate students’ participation from the lecturer's perspective. We discussed two themes of metarules: metarules about the development of proof and metarules governing proof as shaped by advanced mathematical norms. The identified metarules indicate pedagogical orientations for participation in the discourse when focusing on the introduction of proof. The study shows how lectures serve as a medium for disseminating the mathematical norms, potentially facilitating students' participation in the mathematical discourse. We conclude by calling for further research into the metalevel aspects of lecturing. • Identifying metarules sheds light on what the lecturer intends to communicate within the Definition-Theorem-Proof format. • Two metarule themes in the introduction of proof concern its development and its regulation by advanced mathematical norms. • The metarules identified indicate pedagogical orientations for facilitating participation in the mathematical discourse. • Lectures operate as a medium for communicating the norms of mathematics through the lecturer's discourse.