Assisted mathematics: the case of discrete probabilities

Abstract

In this paper, we describe computer environments designed or used to assist learning in discrete probability theory: some with no ‘intelligence’, some with a lot. The degree of assistance ranges from a sophisticated dumb tool to a general problem solver. The main difference between the environments lies in the division of quality and quantity of work between the user and the computer. This leads to a discussion of what one is expected to learn in a certain field and what kind of tools should be provided to students. In particular, we are interested in what happens to the human/computer team when the computer ‘solves’ all the problems.

The field of discrete probabilities has a number of features that suggest this kind of discussion: a strong experimental component that can be easily linked to everyday experience, a simple and powerful theoretical background, and difficult problems for the novice. But the discussion is also intended to raise similar questions in other fields of mathematics and science: the mathematical problems that can be effectively solved by automatic means already include most of the problems non-mathematicians are expected to solve.