We have done extensive work on developmental changes in mathematical processing. Using an innovative approach to localize underlying mechanisms, we have shown that quantity processes in the intra-parietal sulcus are crucial for procedural calculations in subtraction, whereas the verbal processes in the middle temporal gyrus are important for retrieval of math facts in multiplication. In more recent work, we found a striking developmental dissociation in the neural basis of arithmetic. We observed grade-related increases of activity for multiplication in verbal mechanisms, whereas we found grade-related increases of activity for subtraction in quantity mechanisms. These results suggest that fluency in simple arithmetic may not always be achieved through increasing reliance on verbal retrieval, but also via a greater use of quantity-based procedures. We are extending this work by examining individual differences in the neural basis of arithmetic, including in children with dyscalculia. We are finding that the development of quantity mechanisms may be facilitated by fine-grained finger representations formed though counting and that the quality of these mechanisms are also related to performance on number line estimation. These findings are consistent with the argument that dyscalculia is characterized by a deficit in quantity processing. However, our research shows that children with dyscalculia have deficits in both quantity and verbal mechanisms when solving arithmetic problems.

Our interest in individual differences led to a series of investigations examining the relation of socio-economic differences to the neural basis of arithmetic. We have shown that, at higher SES, better skill is correlated with greater engagement of verbal mechanisms. In contrast, we have shown that, at lower SES, better skill is correlated with greater engagement of spatial mechanisms. Not only were these relationships concurrently predictive, but they also predicted longitudinal math gains over a 2-3 year period. These results support an adaptation model wherein lower and higher SES children engage different neural mechanisms to achieve similar skilled performance. We recently extended this work into the reading domain showing that, at higher SES, better skill is associated with greater white matter integrity in left occipito-temporal regions, whereas better skill is associated with homologous regions in the right hemisphere for lower SES. We are currently extending this work to language and reasoning tasks and also examining more proximal variables of parenting that may be associated with differences in brain function in children.

In our cross-cultural work, we are examining whether differences between countries in educational systems result in different brain networks recruited for solving arithmetic problems. We have shown that Chinese adults engage verbal mechanisms to a greater degree for multiplication problems presumably due to rote teaching methods used in China. In contrast, American adults rely to a greater degree on quantity mechanisms possibly due to greater emphasis on calculation procedures. We are in the process of examining developmental differences in Chinese compared to American children, and expect that the increases in the engagement of verbal mechanisms may be particularly pronounced for Chinese children.

Reasoning is a fundamental aspect of human development, and similar to our work on arithmetic, we are interested in the role of verbal and quantity mechanisms in reasoning. We have shown that relational reasoning involving linear orderings relies on quantity mechanisms (e.g. John is taller than Tom, Tom is taller than Chris, therefore John is taller than Chris), whereas categorical reasoning involving set inclusion relies on verbal mechanisms (e.g. All Tulips are Flowers, All Flowers are Plants, therefore All Tulips are Plants). We have shown this dissociation in both adults and in school age children, suggesting that these forms of reasoning develop early. We are extending our work to examine how individual differences in intelligence are associated with the recruitment of spatial and verbal mechanisms. In the framework of dual process theories, these mechanisms have been called heuristics. Future work will examine whether there is differential developmental trajectories of heuristic versus analytical systems for solving these problems.