Abstract: The ways in which mathematics educators think about the learning of mathematics have changed over the last ten years. The image of children waiting, open-mouthed (or was it open-minded?) to accept whatever knowledge the teacher was going to transmit is anachronistic. We know that children do not simply ‘soak up’ the knowledge around them but that they must actively construct this knowledge. How they do this and what effect the social milieu in which this action takes place has on the construction is much more problematic. Beyond this, the implications for teachers of acceptance of a theory of learning which relies on the children’s own constructions are only just being investigated.

The purpose of this paper is to provide some background for teachers on the theory of knowing which has been recognized as ‘constructivism’, particularly ‘social constructivism’, and to investigate possible implications for teachers of mathematics in schools. The paper concludes with a description of an approach to teaching bases on social constructivist principles which has proved successful for the author in both schools and tertiary environments.