How Students Think: The Role of Representations

Abstract

The job of a mathematics student is to build up, in his or her mind, a \ncollection of mathematical ideas. But where, really, do these mathematical \nideas come from? In the past, for teachers working from the "transmission" \nmodel of instruction, this was hardly an important question. Mathematical \nideas were presented in books, and were held in the memories of knowledgeable people. Students obtained these same ideas by reading these \nbooks and listening carefully to what teachers told them. This approach \ngave us what has been called "the age of the sage on the stage," and \njustified the name transmission theory of sharing knowledge.

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