Are Functions Real?

Some think that the calculus reform movement, consisting of computers, calculators, hands-on, interactive and applications, is going to make calculus and other mathematical analyses understandable and accessible to high school and college students. I remain skeptical and hope that many others share my skepticism. The reason students have problems learning math is that the explanations they receive and the organization of the their texts and other teaching materials are not clear. Many students do not see that functions are real and that functions are central to the study of calculus. This paper will be a discussion of scientific reality as well as mathematical reality. Of course, functions are real, and it is our responsibility as math teachers to guide every student to the awareness that the study of functions is worthwhile and to provide a framework, which will enable students to manage their study. This paper is intended to serve students who may find themselves adrift in their studies of algebra and calculus.