Teachers' interventions and the growth of students' mathematical understanding
This study explores the ways in which teachers' interventions interact with and occasion the growth of students' mathematical understanding. Two 'cases' were documented, and these form the two strands of my research. The first strand concerns data collected in my own high school classroom at a time when I was a full-time teacher of mathematics in a small, rural secondary school in the United Kingdom. The second strand concerns data collected in a mathematics classroom in a large, urban high
... rge, urban high school in Vancouver, British Columbia. The data consist of videotaped lessons in each of the two classrooms, videotaped interviews with students from both strands of the data, copies of students' work from both strands, videotaped interviews with the Vancouver teacher, and my own journal entries. Analysis of the data, which is described in six stages, resulted in the generation of fifteen themes to describe the teachers' actions-in-the-moment. Three of these themes are distinguished from the others as teaching styles, as contrasted with the remaining twelve teaching strategies, and a number of the teaching strategies are clustered within the three teaching styles. The notion of a 'continuum of telling' is developed, upon which the three teaching styles lie, and this continuum is explored in order to probe the ways in which teachers' interventions interact with the growth of students' mathematical understanding. The ways in which teachers' interventions occasion the growth of students' mathematical understanding is probed through an integration of detailed traces of the students' growth of understanding with contemporaneous considerations of the teachers' strategies and styles. Implications to be drawn from these analyses, both for the research community and for teaching and learning, are discussed. I also share my reflections on my own growth as a teacher and as a researcher that I have experienced as a result of participating in, and conducting, this study.