My starting point in this paper is that there is a cultural gap between the mathematics that children do as part of their everyday experience and the mathematics that they learn at school; my thesis is that the computer has (perhaps uniquely) the potential to bridge this divide. The paper will examine the cultural impact—both actual and potential—of the computer on children's mathematical education; at the ways in which the introduction of the computer does and will change the ambient space in which mathematics is learned. I begin with a discussion of the cultural context of mathematics learning and the relationship between informal, everyday mathematical activity, and formal, school mathematics. This perspective leads to a closer examination of what it means to do mathematics, and on the relationship of a technology to the mathematics embedded within a given culture. Discussion is then focussed on the intersection between mathematical learning and the mathematics of the computer culture, and on the challenges for research and curriculum development which are generated by this interplay. Finally, I consider some recent Logo-based studies which illustrate the ways in which the computer is changing the culture in which mathematics is done, learned and taught.
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