Individual Differences in Arithmetical Abilities: The Componential Nature of Arithmetic
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.