The Social Construction of Meaning--A Significant Development for Mathematics Education?.

Abstract

I would like today to direct your attention to what I consider to be a significant new research area for us in mathematics education, and the best way I can do this is to explain not only what it is about, but also how I came to see its value. This talk will therefore be a kind of journey through some ideas and will, I hope, convey something of the flavour, and also the substance, of the new area. However, in order to help you comprehend and evaluate what I have to say you should know that my own working context is in teacher education, at a University Department of Education, and you must also remember that it is within the U.K. system. One consequence is that I start my research from the assumption that the teacher is the most important agent in the whole educational enterprise. Much of the practice of teaching and of teacher education in the U.K. is based on the idea of the autonomous This idea is a myth, of course, in the sense that every teacher is subject to all kinds of pressures but it is a myth that we value and preserve. I am not concerned today with whether or not this is a good or a bad myth, but I will be happy to agree for now that it has its dangers as well as its blessings! My research interests have always been concerned with the mysteries and the complexities of the mathematics classroom the context in which teachers try to acculturate pupils into the mathematician's ways of understanding the world. My research philosophy is that of constructive alternativism [Kelly, 1955] which means that I look for alternative ways of construing and interpreting classroom phenomena in order that the acculturation process can be achieved more successfully than it is at present. One of the first strands of this research to get developed concerned my work on teachers' decisionmaking. The teacher as a decision-maker was a conception designed to catch the process whereby the teacher deals with the many choices occurring both before and during teaching. I was particularly interested in the decisions made during the classroom interactions, now referred to in the research literature as [Shavelson, 1976]. It is a very powerful construct in that it links the work on teachers' knowledge, ideology, attitudes, etc. with the work on teachers' classroom behaviour, methods, language, etc. Various aspects of mathematics teachers' decision-making were learnt [Bishop, 1976a] and many more are waiting to be explored. For example, dealing with pupils' misunderstandings and errors constitutes a large part of a teacher's activity but the decision-making construct forced me to attend to the fact that, in the classroom situation, what is significant is the teacher's perception of the errors and misunderstandings. This is sometimes forgotten by those researchers who study children's errors in a laboratory-like atmosphere away from the interactive classroom. I therefore looked at perrs (teacher perceived errors) and was particularly interested in the teachers' strategies for dealing with these [Bishop, 1976b]. This research developed some very useful activities for teacher education; for example, freezing a moment of decision in a video-tape of a lesson and analysing the choices and criteria open to the teacher. Into such discussion it is possible to inject many constructs from psychological research which would otherwise seem very remote from the classroom.