Considers the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum, such as children's arithmetic shows divergence in performance. Explains how students cope with the transition to advanced mathematical thinking in different ways, leading once more to a diverging…

A cognitive or internal representation refers to an organized system of information which reflects certain, but not all, of the information about reality being represented. This paper considers various opinions, controversies, and debates about what representation is, how it comes about, and what forms of representation can be distinguished. The…