ABSTRACT
This chapter is divided into two parts. The first part provides a conceptual backdrop for discussing research on the teaching and learning of functions and their representations. It includes the following: a comparison between set-theoretic and dependency notions of functions; an overview of the historical development of the concept of function; a detailed description of a “process-object” model that explains past student learning of functions; and an examination of the skills students need in order to translate not only between various representations of functions and the underlying situation but also between one representation and another. The second part of the chapter looks at recent projects involving functions and graphing in technology- supported environments. These projects have been classified according to the extent to which graphs are related to algebraic representations: the use of graphs before the teaching of algebra or in activities that do not require a knowledge of algebra; the use of graphs in first-year algebra courses; and the use of graphs with students who have already completed at least one course in algebra. The chapter concludes with some questions for further research on graphing and functions.
