Analysing the quality of real analysis lectures using a structured observation tool

This paper reports a study investigating the quality of advanced mathematics lectures following three goals. First, we present our conceptualisation and operationalisation concerning the quality of mathematics lectures. Second, we test the reliability of a structured observation tool that is based on the aforementioned conceptualisation. Third, we describe the quality of mathematics lectures based on data collected with the observation tool and illustrate its use. The results show that our observation tool is suitable for collecting data about characteristics of mathematics lectures observed on-site and from video recordings. The analysis of the data shows that our findings are in line with previous research: formal aspects of mathematical statements are presented in verbal and written forms mostly correctly; informal aspects of mathematical statements (such as examples, visual or mental representations) are, if they are presented, usually presented only verbally. Furthermore, students have the opportunity to participate during lectures, but there are seldom presentations of alternative solutions, examples or proofs and only a few opportunities for formative assessment. Finally, we discuss implications for future research.