Ann Dowker

Wales uses languages with both regular (Welsh) and irregular (English) counting systems. Three groups of 6- and 8-year-old Welsh children with varying degrees of exposure to the Welsh language—those who spoke Welsh at both home and school; those who spoke Welsh only at home; and those who spoke only English—were given standardized tests of arithmetic and a test of understanding representations of two-digit numbers. Groups did not differ on the arithmetic tests, but both groups of Welsh speakers read and compared 2-digit numbers more accurately than monolingual English children. A similar study was carried out with Tamil/English bilingual children in England. The Tamil counting system is more transparent than English but less so than Welsh or Chinese. Tamil-speaking children performed better than monolingual English-speaking children on one of the standardized arithmetic tests but did not differ in their comparison of two-digit numbers. Reasons for the findings are discussed.

Many studies have indicated that mathematics anxiety, and other negative attitudes and emotions toward mathematics, are pervasive and are associated with lower mathematical performance. Some previous research has suggested that working memory is related to both mathematics anxiety and mathematics. Moreover, both gender and chosen course of study appeared likely to influence students’ attitudes to mathematics. In the present study, 40 university undergraduates completed a battery of assessments investigating working memory, attitude to mathematics, test anxiety. and mental and written arithmetic. Attitudes to mathematics were significantly associated with the other variables: working memory, test anxiety, and both measures of mathematical performance. The other variables were not strongly associated with one another. There were no gender differences in mathematical performance, but females exhibited more negative attitudes to mathematics and higher test anxiety than males. After controlling for test anxiety, there ceased to be significant gender differences in attitudes to mathematics. Science students had more positive attitudes to mathematics than humanities students, but the groups did not differ in test anxiety, Science students were better at written but not mental arithmetic. They were also better at working memory, but this was not a significant covariate when the groups were compared on mathematical performance and attitudes to mathematics The results are discussed, with particular focus on implications for future research on influences on mathematics anxiety.

This chapter discusses individual differences in arithmetic. It deals relatively briefly with the findings about the general large extent of such differences in both children and adults. It then discusses findings that indicate that it is inadequate to speak of arithmetical ability as a single characteristic. Rather, it is made up of many components, which may correlate, but also show significant functional independence. Discrepancies between any two such components, in both directions, can be frequently observed. There is evidence for this from many sources, including studies of patients with acquired dyscalculia, brain imaging studies, cross-cultural studies, and studies of both typically developing children and those with mathematical difficulties. The chapter then discusses questions about when such between- and within-individual differences begin, and whether numerical ability is componential from infancy or starts as a single ability and then differentiates. There is certainly evidence that it is already componential in preschoolers. The need for more longitudinal and intervention studies is emphasized, if we are to understand whether differences in specific components are consistent over time, and whether specific components at an early age have specific predictive relationships to specific components found later on.