Publication 5280

Excerpt: Why, despite the many sources of difficulty, is successful communication of mathematics among individuals possible? Why is it that to apply mathematical ideas, one must inevitably choose one or more notations in which to materialize those ideas? And why the large variation in the ways that these notations support and/or constrain our thinking processes? In this chapter I will not presume to answer such questions, but rather will attempt to provide some means for others, hopefully including the reader, to gain insight into them. Central to this task will be to describe the twin mediating roles of notation systems, in mediating between what is normally regarded as “pure mathematics” and one’s experienced world, and in mediating communication processes among individuals. In so doing, I hope also to show how a representational framework for mathematical cognition and learning is consistent with constructivism.