Chapter 7 - Interpolative approximation

Summary

Introduction

In the spirit of the mathematical laboratory, special attention is accorded to the elimination of traditional mathematical tables, which students have always used as “black boxes,” without the faintest understanding of their origin and construction. Thus, these tables were antieducational tools that the students aquired without any mathematical enlightenment and used as “cookbook recipes.” Now that calculators and microcomputers are used in mathematical education, the danger arises of replacing one set of black boxes with another. Of course, we are not advocating the introduction of these new electronic black boxes merely for using, say, the logarithmic built-in function of the computer (or pressing the “log” key on a pocket calculator). What we do advocate is to teach students what is behind such built-in functions as part of the material covered in the mathematical laboratory. This subject fits naturally into the environment of the laboratory and reveals the “story behind the key.” The attainment of this objective is the subject of this chapter and the next.

We might ask whether students should be allowed to use the built-in functions before (and during) learning how they were built in. We feel that no harm can result from such a practice, so long as the students are told expressly that their “ignorant” use of the built-in functions is temporary. Before long, the secrets held by the computer keys will be revealed.