Lecturers' tools and strategies in university mathematics teaching: an ethnographic study

The thesis presents the analytical process and the findings of a study on: lecturers teaching practice with first year undergraduate mathematics modules; and lecturers knowledge for teaching with regard to students mathematical meaning making (understanding). Over three academic semesters, I observed and audio-recorded twenty-six lecturers teaching to a small group tutorial of two to eight first year students, and I discussed with the lecturers about their underlying considerations for teaching. The analysis of this thesis focuses on a characterisation of each of three (of the twenty-six) lecturers teaching, which I observed for more than one semester. I chose the teaching of three experienced lecturers, due to diversity in terms of ways of engaging the students with the mathematics, and due to my consideration of their commitment to teaching for students mathematical meaning making. The distinctive nature of the study is concerned with the conceptualisation of university mathematics teaching practice and knowledge within a Vygotskian perspective. In particular, I used for the characterisation of teaching practice and of teaching knowledge the notions tool-mediation and dialectic from Vygotskian theory. I also used a coding process grounded to the data and informed by existing research literature in mathematics education. I conceptualised teaching practice into tools for teaching and actions with tools for teaching (namely strategies). I then conceptualised teaching knowledge as the lecturers reflection on teaching practice. The thesis contributes to the research literature in mathematics education with an analytical framework of teaching knowledge which is revealed in practice, the Teaching Knowledge-in-Practice (TKiP). TKiP analyses specific kinds of lecturer s knowing for teaching: didactical knowing and pedagogical knowing. The framework includes emerging tools for teaching (e.g. graphical representation, rhetorical question, students faces) and emerging strategies for teaching (e.g. creating students positive feelings, explaining), which were common or different among the three lecturers teaching practice. Overall, TKiP is produced to offer a dynamic framework for researcher analysis of university mathematics teaching knowledge. Analysis of teaching knowledge is important for gaining insights into why teaching practice happens in certain ways. The findings of the thesis also suggest teaching strategies for the improvement of students mathematical meaning making in tutorials.