ABSTRACT
The graphical representation of functions is an important topic for several reasons. Historically, it is a key development in mathematics that has paved the way for other important discoveries including calculus. In the mathematical education of school children, it has long represented a key and often difficult leap in understanding. Today, computer graphing software and graphing calculators have added a dimension to this topic that has attracted the interest of many researchers and curriculum developers in mathematics education. The rapidly growing body of research in this area is the subject of three recent reviews from different perspectives (Herscovics, 1989; Kaput, 1989; Leinhardt, Zaslavsky, & Stein, 1990). Not another research review, this chapter focuses rather on the graphical content of school mathematics. It begins with an analysis of the content on graphing in typical mathematics textbooks prior to algebra—that is, Grades 1–8 —and argues that many common student difficulties with graphing can be understood in light of the inadequacy of this content. Then a discussion of techniques that can be used to introduce graphing in the primary grades is presented. Finally, the ways in which graphing utilities have begun to change the role of graphing in the school curriculum and in mathematics itself and the adjustments in content in prealgebra and algebra required by this change are analyzed.
