Scaling a Mountain — A study of the use,discrimination and generalisation of some mathematical concepts in a LOGO environment

The paper will describe pupils’ engagement in mathematical activity, in collaboration with a partner, in an exploratory LOGO programming environment. It will focus on how initial pupil conceptions become progressively more differentiated and generalised. An attempt will be made to describe levels at which pupils, in this particular context, tend to operate with respect to a range of mathematical concepts and processes embedded within the activity, and situations which have provoked ‘changes in level’ that is, where pupils have modified or reorientated their initial conceptions, extended their range of applicability or made new links or syntheses. The general role of conflict, both cognitive and socio cognitive will be considered together with the particular roles of teacher intervention, pupil discussion and computer interaction in both promoting the conflict and aiding in its resolution. Illustrations will also highlight the specificity of cognitive structures constructed within the activity and the crucial importance of the nature of pupil representation of the activity and its relation to the practices from which it emerged.