Symbolic Processing Mediates the Relation Between Non-symbolic Processing and Later Arithmetic Performance

Anatomical connectivity in children with developmental dyscalculia: A graph theory study

Current theories postulate that numerical processing depends upon a brain circuit formed by regions and their connections; specialized in the representation and manipulation of the numerical properties of stimuli. It has been suggested that the damage of these network may cause Developmental Dyscalculia (DD): a persistent neurodevelopmental disorder that significantly interferes with academic performance and daily life activities that require mastery of mathematical notions and operations. However, most of the studies on the brain foundations of DD have focused on regions of interest associated with numerical processing, and have not addressed numerical cognition as a complex network phenomenon. The present study explored DD using a Graph Theory network approach. We studied the association between topological measures of integration and segregation of information processing in the brain proposed by Graph Theory; and individual variability in numerical performance in a group of 11 school-aged children with DD (5 of which presented with comorbidity with Developmental Dyslexia, the specific learning disorder for reading) and 17 typically developing peers. A statistically significant correlation was found between the Weber fraction (a measure of numerical representations' precision) and the Clustering Index (a measure of segregation of information processing) in the whole sample. The DD group showed significantly lower Characteristic Path Length (average shortest path length among all pairs of regions in the brain network) compared to controls. Also, differences in critical regions for the brain network performance (hubs) were found between groups. The presence of limbic hubs characterized the DD brain network while right Temporal and Frontal hubs found in controls were absent in the DD group. Our results suggest that the DD may be associated with alterations in anatomical brain connectivity that hinder the capacity to integrate and segregate numerical information.

Effects of intelligence and approximate number system on the non-symbolic division ability in preschoolers

Recently, it has become evident that cognitive abilities such as the approximate number system (ANS), number knowledge, and intelligence affect individuals' fundamental mathematical ability. However, it is unclear which of these cognitive abilities have the greatest impact on the non-symbolic division ability in preschoolers. Therefore, in the present study, we included 4- to 6-year-old Korean preschoolers without prior formal education of division in order to test their ability to solve non-symbolic division problems, ANS acuity, and intelligence, and to determine the interrelationships among those functions (N = 38). We used the Panamath Dot Comparison Paradigm to measure the ANS acuity, employed non-symbolic division tasks to measure the ability to solve non-symbolic division problems, and measured the intelligence using the Korean version of the WPPSI-IV (Wechsler Preschool Primary Scale of Intelligence-IV). Our results showed that, in all conditions of the non-symbolic division tasks, the 4- to 6-years old children were able to perform better than chance level. Additionally, in a relatively easy condition, the children's performance showed a significant positive correlation with full-scale intelligence quotient (FSIQ) and ANS acuity; however, in a more complex condition, only FSIQ was significantly correlated with their performance. Overall, we found significant relationships between the children's performance in the non-symbolic division tasks and verbal comprehension, fluid reasoning, and processing speed index. Taken together, our findings demonstrate that preschoolers without formal education on the arithmetic problem solving can solve non-symbolic division problems. Moreover, we suggest that both FSIQ and ANS ability play essential roles in children's ability to solve non-symbolic division problems, highlighting the significance of intelligence on children's fundamental mathematical ability.