Mathematics

A relatively new aspect of our research is an examination of the developmental changes in mathematical processing. Using an innovative approach to localize underlying mechanisms, we have confirmed that that the intra-parietal sulcus is crucial for quantity comparison as required by subtraction, whereas the middle temporal gyrus is important for the verbal representation of math facts as required by multiplication. Using this approach, we have also shown cross-cultural differences in that Chinese adults engage verbal mechanisms to a greater degree for multiplication problems presumably due to rote teaching methods in China. We have also extended our work to show that transitive reasoning involving linear orderings relies on quantitative mechanisms, whereas transitive reasoning involving set inclusion relies on verbal mechanisms. In terms of our developmental work, our basic hypothesis is that acquisition should be characterized by age-related increases in parietal cortex for tasks demanding quantity comparison (e.g. subtraction), but that there should be shift to the temporal cortex for tasks demanding verbal retrieval of math facts (e.g. multiplication). The shift may be particularly for Chinese children, and would indicate greater reliance on memory-based systems for tasks that can rely on verbal mechanisms. As with other developmental disorders, children with dyscalculia do not represent a homogeneous group. Our work is testing the hypothesis that the central deficit in children with dyscalculia will be in the quantity comparison system, whereas children with co-morbid dyscalculia and dyslexia will have additional abnormalities in the verbal system because of an underlying deficit semantic memory. Our future work will examine the cognitive precursors of mathematical thinking in preschoolers to determine the critical building blocks of calculation.