University Mathematics Lecturing as Modelling Mathematical Discourse

The lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from first-semester lectures given by seven mathematics lecturers at three Swedish universities, all concerning various aspects of the function concept. Analysis was carried out from a commognitive perspective, which distinguishes between object-level and meta-level discourse. Here I focus on two aspects of meta-level discourse: introducing new mathematical objects; and what counts as valid endorsement of a narrative. The analysis reveals a number of metarules concerning the modelling of mathematical reasoning and behaviour, both more general rules such as precision and consensus, and rules more specifically concerning construction and endorsement of narratives. The paper contributes to a small but growing body of empirical research on university mathematics teaching, and also lends empirical support to previous claims about the modelling aspect of mathematics lecturing, thus contributing to a deepened understanding of the lecture format and its potential role in future university mathematics teaching