Proving routines in a lecturer’s mathematical discourse for proof teaching: a case of analysis lecturing

This study focuses on the characterisation of proof teaching in university lectures on mathematical analysis using the commognitive framework. The case is set around a lecturer with experience in teaching this course and a good reputation among university students. Six lectures of the course were analysed using discourse and thematic analysis. The analysis resulted in a range of characteristics of the mathematical discourse for proof teaching of a lecturer. Then, by exploring the proving routines within the characteristics, we produced a typology of teaching characteristics in the lecturer’s discourse; that typology gave us insights into a pattern of proving specific to our case study. The exploration of the proving routines in the lecturer’s discourse offered an in-depth understanding of teaching proof beyond the macro-level descriptions of lectures in the extant literature. We conclude the study with implications for research and education.