Should Students Learn Integration Rules?

Abstract

In this note we formulate a didactic principle that can govern the use of symbolic computation software systems in math courses. The principle states that, in the treatment of each subarea of mathematics, one must distinguish between a "white-box" and a "black box" phase. In the "white box" phase, algorithms must be studied thoroughly, i.e. the underlying theory must be treated completely and algorithmic examples must be studied in all details. In the black box phase, problem instances from the area can be solved by using symbolic computation software systems. This principle can be applied recursively.