As I have mentioned briefly in Chapter 1, my research into an investigative approach to the learning and teaching of mathematics is theoretically based in constructivism. My own perceptions of constructivism have developed considerably over and beyond the period of research, that is from 1985 until 1994. In 1994, as this book approaches publication, arguments are rife in the mathematics education community regarding constructivism as a theory of learning mathematics, its status and underpinnings (Ernest, 1994; Lerman, 1994). The perspective which I present in this chapter will largely trace the development of my own thinking, related to what others have written, up to and including the period of the research. Further reflections on my own developing thinking will occur throughout the book. I shall leave it until my final chapter to face some of the current controversies and their relation to my research.
Constructivism is a philosophical perspective on knowledge and learning. It has been argued (See, for example von Glasersfeld, 1984; Richardson, 1985.) that modern constructivism has its origins in the thinking and writing of Vico and of Kant in the eighteenth century, owes much of its current conception to the works of Piaget and Bruner in the twentieth century, is evident in the writing of current influential educational psychologists such as Donaldson, and underpins an important influence for primary classroom practice in the United Kingdom—the Plowden Report.
Constructivism is internationally recognized as a theory which has much to offer to mathematics education. 1 In this respect it has had a grounds well in the United States during the 1980s, initially from a mainly theoretical position (for example von Glasersfeld, 1984; Cobb, 1988), but latterly in terms of the practice of teaching mathematics (for example Davis, Maher and Noddings, 1990). The NCTM Mathematical Standards (NCTM, 1989), which many mathematics curricula in the US are now designed to uphold, can be seen to be grounded in constructivism. In the UK, and in other parts of the world, many educators now believe that constructivism has significant implications for mathematics teaching (for example, Malone and Taylor, 1993). There is international debate about the nature of these implications. My study of mathematics teaching, I believe,