Individual differences in children's mathematical competence are related to the intentional but not automatic processing of Arabic numerals.

In recent years, there has been an increasing focus on the role played by basic numerical magnitude processing in the typical and atypical development of mathematical skills. In this context, tasks measuring both the intentional and automatic processing of numerical magnitude have been employed to characterize how children's representation and processing of numerical magnitude changes over developmental time. To date, however, there has been little effort to differentiate between different measures of 'number sense'. The aim of the present study was to examine the relationship between automatic and intentional measures of magnitude processing as well as their relationships to individual differences in children's mathematical achievement. A group of 119 children in 1st and 2nd grade were tested on the physical size congruity paradigm (automatic processing) as well as the number comparison paradigm to measure the ratio effect (intentional processing). The results reveal that measures of intentional and automatic processing are uncorrelated with one another, suggesting that these tasks tap into different levels of numerical magnitude processing in children. Furthermore, while children's performance on the number comparison paradigm was found to correlate with their mathematical achievement scores, no such correlations could be obtained for any of the measures typically derived from the physical size congruity task. These findings therefore suggest that different tasks measuring 'number sense' tap into different levels of numerical magnitude representation that may be unrelated to one another and have differential predictive power for individual differences in mathematical achievement.