The Role of Heuristic Proof in Mathematics Teaching

Abstract

Summary With the great emphasis now being placed on the importance of ‘rigour’ in new mathematics programmes, many educators have been led to disparage intuition as the vitally important tool that it is in developing mathematical insights. Increasingly one sees evidence, even in technical schools, of pupils actually being discouraged from arriving at mathematical perceptions through unorthodox (and uncontrollable!) channels of analogy involving considerable divergent thinking or through consideration of physical models with which they are familiar. As a mathematician, this pre‐occupation with ‘purism’ greatly disturbs the author. Mathematicians do not create through the formal apparatus ‐‐ they only apply formalism after ‘guessing’ results intuitionally. We have become overconcerned with the way the package is wrapped and less concerned with what is in it. Especially, the role of heuristic argument is widely misunderstood and misused in schools and colleges. The author hopes that this article will help to...