Recognising mathematical creativity in schoolchildren

Examples of tasks designed to recognise creative thinking within mathematics, used with 11–12-year-old pupuls, are described. The first construct empoyed in the design of these tasks is the ability to overcome fixation. Sometimes pupils demonstrate content-universe fixation, by restricting their thinking about a problem to an insufficient or inappropriate range of elements. Other times they show algorithmic fixation by continuing to adhere to a routine procedure or stereotype response even when this becomes inefficient or inappropriate. The second construct employed is that of divergent production, indicated by flexibility and originality in mathematical tasks to which a large number of appropriate responses are possible. Examples of three categories of such tasks are described: (1) problem-solving, (2) problem-posing, and (3) redefinition. Examples of pupils’ responses to various tasks are used to argue that they do indeed reveal thinking that can justifiably be described as creative. The relationship to conventional mathematics attainment is discussed-mathematics attainment is seen to limit but not to determine mathematical creativity.