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 beingdiscouragedfrom arriving at mathematical perceptions through unorthodox (and uncontrollable!) channels of analogy involving considerabledivergentthinking or through consideration of physical models with which they are familiar.