No abstract

Developmental dyscalculia (DD) is a deficit in number processing and arithmetic that affects 3-6% of schoolchildren. The goal of the present study was to analyze cerebral bases of DD related to symbolic number processing. Children with DD aged 9-11 years and matched children with no learning disability history were investigated using fMRI. The two groups of children were controlled for general cognitive factors, such as working memory, reading abilities, or IQ. Brain activations were measured during a number comparison task on pairs of Arabic numerals and a color comparison task on pairs of nonnumerical symbols. In each task, pairs of stimuli that were close or far on the relevant dimension were constituted. Brain activation in bilateral intraparietal sulcus (IPS) was modulated by numerical distance in controls but not in children with DD. Moreover, although the right IPS responded to numerical distance only, the left IPS was influenced by both numerical and color distances in control children. Our findings suggest that dyscalculia is associated with impairment in areas involved in number magnitude processing and, to a lesser extent, in areas dedicated to domain-general magnitude processing.

An ongoing debate in research on numerical cognition concerns the extent to which the approximate number system and symbolic number knowledge influence each other during development. The current study aims at establishing the direction of the developmental association between these two kinds of abilities at an early age. Fifty-seven children of 3–4 years performed two assessments at 7 months interval. In each assessment, children's precision in discriminating numerosities as well as their capacity to manipulate number words and Arabic digits was measured. By comparing relationships between pairs of measures across the two time points, we were able to assess the predictive direction of the link. Our data indicate that both cardinality proficiency and symbolic number knowledge predict later accuracy in numerosity comparison whereas the reverse links are not significant. The present findings are the first to provide longitudinal evidence that the early acquisition of symbolic numbers is an important precursor in the developmental refinement of the approximate number representation system.

a b s t r a c tThe present study assessed the relationships between approximate and exact number abilities in children with little formal instruction to ask (1) whether individual differences in acuity of the approximate system are related to basic abilities with symbolic numbers; and (2) whether the link between non-symbolic and symbolic number performance changes over the development. To address these questions, four different age groups of 3-to 6-year-old children were asked to compare pairs of train wagons varying on numerical ratio, as well as to complete exact tasks including number words or Arabic numbers. When correlation analyses were conducted across age groups, results indicated that performance in numerosity comparison was associated with mastery of symbolic numbers, even when short-term memory, IQ and age were controlled for. Separate analyses by age group revealed that the precision in numerosity discrimination was related to both number word and Arabic number knowledge but differently across the development.

A specific instance of the association between numerical and spatial representations is the SNARC (Spatial Numerical Association of Response Codes) effect. The SNARC effect describes the finding that during binary classification of numbers participants are faster to respond to small/large numbers with the left/right hand respectively. Even though it has been frequently replicated, important inter-individual variability has also been reported. Mathematical proficiency is an obvious candidate source for inter-individual variability in numerical judgments, but studies investigating its influence on the SNARC effect remain scarce. The present experiment included a total of 95 University students, divided into three groups differing significantly in their mathematical proficiency levels. Using group analyses, it appeared that the three groups differed significantly in the strength of their number-space associations in a parity judgment task. This result was further confirmed on an individual level, with higher levels in arithmetic leading to relatively weaker SNARC effects. To explain this negative relationship we propose accounts based on differences in access to qualitatively different numerical representations and also consider more domain general factors, with a focus on inhibition capacities.