Comparing performance of pupils with high spatial-low numerical and high numerical-low spatial scores on a standardized mathematics test in the United Kingdom

Questions from a national mathematics test taken by over a 1,000 12- and 13-yr.-olds in the United Kingdom were perused for heavily loaded spatial and numerical items. Pupils' answers to the two types of item were examined, and those who answered well in one of the categories but poorly in the other were selected to form two groups, those high in spatial thinking but low in numerical thinking and those high in numerical thinking but low in spatial thinking to assess whether the approaches to solve the item used by each group were different. The two groups did indeed utilize different thinking strategies to solve the questions. For example, questions involving angle and volume, items thought to require a high spatial facility, were answered correctly by the predominantly numerical thinkers as often as by the predominantly spatial thinkers. This would indicate that one of the samples, i.e., numerical thinkers, used a different strategy than the other, i.e., spatial thinkers. This was verified by examination of students' work in the test booklets and personal interviews of them. Also, the same proportion of boys in each group was recorded, but a higher percentage of girls was recorded in the spatial group than in the numerical. This reflected the large number of boys who scored high on the spatial measures also doing moderately well on the numerical items and so, being moved out of the solely spatial group. Since the tests used by mathematics educators to assess learning are so heavily laden with linguistic/analytical rather than holistic/spatial types of questions, pupils high in spatial but low in numerical thinking face a severe handicap in schools.