Towards a Theory of Symbol Use in Mathematics

This chapter begins to outline a theory of mathematical symbol systems promised in Chapter 2 . In the long term such a theory should (1) help frame a systematic discussion of mathematics symbol use by individuals, including correct, partial, inappropriate, and primitive use, (2) clarify the interactions between natural language and imagistic representations on one hand and synthetic symbol systems on the other, (3) enhance our understanding of the roles of symbolic representations in mathematics growth and change, and (4) guide the development of new symbol uses made possible by new information technologies. (The reader recognizes this chapter as a companion to John Mason’s decidedly more poetic contribution “What Do Symbols Represent?” in Chapter 8 . Virtually every issue raised there through a range of concrete examples is addressed in this chapter. As points of parallel occur, we point them out.)