Constructive and instructive representation

Abstract Beginning teachers of mathematics are likely to have noted the development of powerful multiple representation software which offers children access to the many modalities through which mathematics is expressed. We argue that embedded, even hidden, within such software are many mathematics conventions, which the naive learner has to unravel in order to construct meaning for those representations. We contrast such representations, which we label as instructive, with those children construct through the use of expressive software; this contrast is seen as analogous to aspects of literacy. We identify various characteristics of these two distinctive forms of representation.

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