# Lecturer’s perspectives on students’ participation in university mathematics teaching

mathematics education seminar : Thomais Karavi (RUG).
Thursday the 13th of October, 15:30 – 17:00. Lecturer’s perspectives on students’ participation in university mathematics teaching |

### Abstract

The most common teaching method in advanced mathematics courses is lectures. In this context, the lecturer is in front of a large cohort of students, presenting the mathematical content to them, who listen in a mostly one-sided communication format. Recently, an increase in empirical studies about lecturing in proof-oriented, university mathematics courses appeared, with descriptive studies being the most common among them. However, the participatory aspects of lecturing still need to be explored.

In this seminar, I will discuss the third part of my PhD project which is a single case study with an experienced lecturer, teaching an introductory, proof-oriented, analysis course. We studied the rules in lecturing that encourage students’ participation in the mathematical course using the commognitive framework. Through a multi-layered analysis, a number of metarules concerning students’ participation in the mathematical discourse from the lecturer’s perspective emerged. We focused on three aspects of the meta-level discourse: the development of proof, the advanced mathematical norms, and the expectations of the lecturer for students’ self-study. Examples of the identified metarules relate to the use of the definitions for the beginning of the proving process, the proof production, and the self-conviction. The study offers a micro-level investigation of lecturing and adds to the empirical studies about the participatory aspects of proof lecturing.