Critical Theorising from Studies of Undergraduate Mathematics Teaching for Students' Meaning Making in Mathematics

This paper focuses directly on mathematics teaching practice at university level, exploring "what teachers do and think daily, in class and out, as they perform their teaching work" (Speer et al. in "The Journal of Mathematical Behavior," 29, 99-114, 2010, p. 99). It is based on a small corpus of research conducted from sociocultural perspectives with qualitative and interpretative studies into mathematics teaching and the meanings it promotes for students learning mathematics. Two settings of teaching are explored: lectures and small group tutorials in which teachers are research mathematicians or mathematics educators. Analyses make use of a range of theoretical perspectives to interpret the complexities of teaching based on observations of teaching activity and interviews with teachers. Critical Theorising is seen through critical use of existing theory and construction of new theory: through the analytical process it provides insights into teaching and ways in which teaching does or can develop to promote students' meaning making in mathematics. The paper draws attention to the finer details of teaching practice and teachers' thinking that lie behind judgments such as 'traditional' or 'transmissionist'.