Introduction

Mathematicians and mathematics teachers have been provided with a new tool, the computer. There is no shortage of applications or interesting examples which one can quote. But, like all tools, the computer by itself does not supply the solution to our problems, not least the problems of mathematics education. There is no automatic beneficial effect linked to a computer: the mere provision of micros in a class- or lectureroom will not solve teaching problems.

It is essential, therefore, that we should develop a serious programme of research, experimentation and reflective criticism into the use of informatics and the computer as an aid. It will not suffice to think only in terms of mathematics and the computer, and of the production of software which amuses and interests mathematicians. We must also take into account types of knowledge and the ways in which these can be transmitted, and attempt to study, in a serious epistemologically-based manner, various concepts and the obstacles which they present to learners. We must think of students, their development and the matching of new and old knowledge. We must consider in depth those teaching possibilities created by the computer. It is essential, above all, that we should move beyond the stage of opinions, enthusiasms, and wishful thinking and engage in a true analysis of the issues. Only in this way will we come to a true resolution of certain problems of teaching. Such research, of necessity experimental, will have to be critically evaluated.