Children's made-up mathematics problems — a new perspective on talented mathematicians

Abstract

As part of a large scale mathematics study, students were asked to make up a mathematics problem that would be difficult for a friend to solve. They were also asked to solve the problem themselves. A sub-sample of 11- to 13-year-olds was interviewed while they worked through the items in the study.

The problems made up by a group of eight more able and eight less able children from this sub-sample are reported here, together with the comments the children made during the interviews about their respective problems.

The results highlight features of the problems made up by the two groups of children. In general, the more able children made up problems of greater computational difficulty, with more complex number systems and with more operations than their less able peers. In addition, there is evidence to suggest that the more able students planned their problems and were able to work out the answer, while their less able peers had difficulty with both the planning and the solution of their own problems.

As the substance and style of the problem made up by each child uniquely reflects that child's mathematical experiences and ideas, the made up problem is a particularly useful tool for studying mathematically talented children for whom routine tasks are usually completed quickly and accurately.