CONVERSA TION AS A METAPHOR FOR MA THEMA TICS AND LEARNING

Much can be learned about theories in mathematics education and elsewhere by exarrumng their underlying metaphors. Elsewhere I have compared the underlying metaphors of mind of various learning theories (Ernest, 1993). For example, I have argued that the metaphor of mind for information processing constructivism is that of a computer, an unfeeling thinking machine; that of radical constructivism is an evolving and adapting but isolated organism, a cognitive alien in an unknown or hostile environment; and that of social constructivism is that of persons-in-conversation. It is this last metaphor that I wish to pursue (and extend) here. For some years I have been developing a social constructivist theory of mathematics and learning (Ernest 1991a), and persons-in-conversation plays the part of the central metaphor in this theory in a number of ways. In this paper I wish to indicate how this metaphor can be developed to describe mathematics itself, mind and the teaching and learning of mathematics. The term 'social constructivism ' is used in a variety of ways by different people (and indeed, by myself, over time). My view of the problematique of social constructivism is twofold. It comprises,. first, an attempt to answer the question: How to account for the nature of mathematical knowledge as \ scrcially constructed? Second, How to give a social account of the individual's learning and construction of,. mathematics? This account must accommodate both the personal reconstruction of knowledge, and. personal contributions to accepte