Functions and Associated Learning Difficulties

Summary

In this chapter we have surveyed some of the learning difficulties students have with function concepts, and why they occur from historical and psychological points of view. Perceived helplessness and anxiety seem to hinder learning, and literature has been cited which studies these psychological barriers. But the major theme of this chapter is that functions and their associated notions are not conceived visually, and that this non-visual approach hinders one’s development of having a sense for functions. Students seem to think of function concepts in only a symbolic representational mode. Indeed, not only are functions thought of this way, but this seems symptomatic of the fact that the majority of topics constituting mathematics are considered non-visual. It is the conclusion of the author that this unwillingness to stress the visual aspects of mathematics in general, and of functions in particular, is a serious impediment to students’ learning.