This book is about mathematics, teaching and learning and how these are affected by a constructivist philosophy. It charts my own exploration of what might be involved in an investigative approach to mathematics teaching. This was a concept which had started to form in my mind while I was still a classroom teacher, and which my move into university education offered me a chance to explore more fully. My introduction to constructivism was a timely experience, and much of my exploration involved rationalizing classroom issues with this theoretical perspective.
The research involved a qualitative study of mathematics teaching through close scrutiny of the practice of a small number of mathematics teachers. It’s purpose was to try to characterize the nature of an investigative approach to mathematics teaching. It involved many hours of observation in classrooms and of conversations with teachers and pupils. An essential part of the study was a clarification of what an investigative approach might mean in terms of teaching practices and issues for teachers. It led to a recognition of issues in the development of teaching, and also to a critiquing of the research process and the involvement of the researcher, myself.
In 1994, as I write this, it is hard to perceive the person I was in 1985 when the research began. Indeed it is only possible to look back through the lens of my current knowledge based on experience which includes the last nine years as well as all those before that. As I reflect now on that research, on the questions I addressed about teaching and learning, and about the research process itself, I recognize that it involved a deep learning experience for me, of which my observations of, and interactions with, the other teachers were merely a part, albeit a very important part.
In 1991 I gained my PhD from the Open University with a thesis which took the form of a research biography. In it I tried to set out in a style acceptable to the examiners the theory, research and conclusions of five year’s work and thinking. It proved impossible to do this from any position other than that of the centrality of the researcher to the research. I saw the research then as being ethnographic, or interpretivist, but I realize now that an alternative term is constructivist. I took constructivism as the central tenet of my theoretical position on teaching and learning, and tentatively recognized its internal consistency with the way my research evolved. There are some problems in labelling the research itself as ‘constructivist’ just as there are in talking about constructivist teaching. Ways in which constructivism as a philosophy can be seen to influence research and teaching are a major focus of the book.