The Great Marble Race: An Assignment Gone Wrong
Benny Evans, Jerry A. Johnson · American Mathematical Monthly · 1995
As many educators have discovered, it is not always easy to produce computerrelated activities that are accessible to students and actually contribute to their understanding of mathematics. Occasionally the most carefully designed assignments in the hands of students produce unexpected results. This is not necessarily bad on the contrary, it may be a learning opportunity. The purpose of this note is to discuss an interesting example of this. Before we start, we will say a word about software. We use the computer algebra system DERIVEX in our classes and what follows reflects this fact. There are several other such programs on the market, most notably MapleTM and Mathematica@, with which the exercise we describe below can be analyzed as well. The most important thing is the mathematics, not the software, but users of other programs may observe some differences in the results. As we will see, the essence of the problem we discuss is structural, so any software should ultimately lead to the same difficulty.