Ann Dowker (University of Oxford, England)
Karin Kucian (Center for MR-Research, University Children’s Hospital Zurich, Zurich, Switzerland)
Daniel Ansari (University of Western Ontario, Canada)
Roi Cohen Kadosh (University of Surrey, England)
There is increasing interest in the neuroscience of mathematical cognition: in how particular brain areas and functions may be involved in number processing and arithmetic. This may be studied through neuropsychological studies of how brain damage may impair or spare some or all aspects of numerical cognition; studies of developmental disorders of numerical cognition; neuroimaging studies of how patterns of brain activation in different areas of the brain may reflect numerical cognition; and studies of how brain stimulation may influence numerical learning. This symposium presents aspects of all these, with a particular focus on individual differences.
Esther Gosling, Nele Demeyere and Ann Dowker studied 9 chronic stroke patients. They were compared to 11 healthy controls on tasks involving nonsymbolic visual enumeration, symbolic addition, and symbolic multiplication. Three patients showed no impairment compared with controls on any of the mathematics tests. The others showed a variety of specific deficits, not consistently related to specific areas of the brain. The study focused on relationships between visual enumeration and other arithmetical tasks, as it has often been suggested that nonsymbolic visual enumeration is a foundation and prerequisite for arithmetic. In this group, such relationships did not emerge. No overall correlations were found between visual enumeration accuracy or reaction time and either addition or multiplication; and double dissociations were found between visual enumeration and arithmetic.
Karin Kucian and colleagues performed a longitudinal study of about 2,900 children from kindergarten to 5th grade. They found that children at risk of developmental dyscalculia could be identified as early as kindergarten. Early number magnitude competencies predicted future calculation skills. Half of the children at risk received an intervention in kindergarten. These children performed much better in the subsequent years than controls who received no intervention; and were less likely to be diagnosed with dyscalculia. This shows that it is possible and important to identify children at risk for dyscalculia at an early stage, and that early intervention may significantly reduce their risk.
Daniel Ansari and his colleagues carried out a series of neuroimaging studies investigating the processing of Arabic numerals in the brain. The studies indicated that Arabic numerals are represented in the left parietal cortex and that this representation is invariant across handedness, differs from letters and is amodal in nature. In this presentation, Daniel Ansari discusses the differences between brain representation for symbolic and non-symbolic number, and how the left-lateralization of symbolic number might emerge over developmental time.
Roi Cohen Kadosh and colleagues developed a personalized neurostimulation approach to reveal the involvement of qualitatively different neural processes as a function of individual differences, and to use these to successfully optimise arithmetic performance by searching, learning, and recommending parameters for effective neurostimulation. An active machine learning technique demonstrated the potential for this approach to be used to improve mathematical learning and performance and translation to other clinical and non-clinical domains.