Numerical magnitude processing impairments in genetic syndromes: a cross-syndrome comparison of Turner and 22q11.2 deletion syndromes.

Cross-syndrome comparisons offer an important window onto understanding heterogeneity in mathematical learning disabilities or dyscalculia. The present study therefore investigated symbolic numerical magnitude processing in two genetic syndromes that are both characterized by mathematical learning disabilities: Turner syndrome and 22q11.2 deletion syndrome (22q11DS). We further verified whether the phenotypic outcomes of these syndromes emerged from the same or different cognitive processes and therefore examined whether numerical impairments were related to working memory deficits, often observed in these syndromes. Participants were 24 girls with Turner syndrome, 25 children with 22q11DS and 48 well-matched typically developing control children. All children completed a symbolic numerical magnitude comparison task and four additional working memory tasks. Both groups of children with genetic syndromes showed similar impairments in symbolic numerical magnitude processing compared to typically developing controls. Importantly, in Turner syndrome, group differences in symbolic numerical magnitude processing disappeared when their difficulties in visual-spatial working memory were taken into account. In contrast, the difficulties in 22q11DS were not explained by poor visual-spatial working memory. These data suggest that different factors underlie the symbolic numerical magnitude processing impairments in both patient groups with mathematical learning disabilities and highlight the value of cross-syndrome comparisons for understanding different pathways to mathematical learning disabilities or dyscalculia.

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test).

The ability to compare symbolic numerical magnitudes correlates with children's concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one- and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1-6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single- as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterion-related validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia.

Numerical magnitude processing deficits in children with mathematical difficulties are independent of intelligence.

Developmental dyscalculia (DD) is thought to arise from difficulties in the ability to process numerical magnitudes. Most research relied on IQ-discrepancy based definitions of DD and only included individuals with normal IQ, yet little is known about the role of intelligence in the association between numerical magnitude processing and mathematical difficulties (MD). The present study examined numerical magnitude processing in matched groups of 7- to 8-year-olds (n=42) who had either discrepant MD (poor math scores, average IQ), nondiscrepant MD (poor math scores, below-average IQ) or no MD. Both groups of children with MD showed similar impairments in numerical magnitudes processing compared to controls, suggesting that the association between numerical magnitude processing deficits and MD is independent of intelligence.

Children's mapping between non-symbolic and symbolic numerical magnitudes and its association with timed and untimed tests of mathematics achievement.

The ability to map between non-symbolic numerical magnitudes and Arabic numerals has been put forward as a key factor in children's mathematical development. This mapping ability has been mainly examined indirectly by looking at children's performance on a symbolic magnitude comparison task. The present study investigated mapping in a more direct way by using a task in which children had to choose which of two choice quantities (Arabic digits or dot arrays) matched the target quantity (dot array or Arabic digit), thereby focusing on small quantities ranging from 1 to 9. We aimed to determine the development of mapping over time and its relation to mathematics achievement. Participants were 36 first graders (M = 6 years 8 months) and 46 third graders (M = 8 years 8 months) who all completed mapping tasks, symbolic and non-symbolic magnitude comparison tasks and standardized timed and untimed tests of mathematics achievement. Findings revealed that children are able to map between non-symbolic and symbolic representations and that this mapping ability develops over time. Moreover, we found that children's mapping ability is related to timed and untimed measures of mathematics achievement, over and above the variance accounted for by their numerical magnitude comparison skills.

The development of numerical magnitude processing and its association with working memory in children with mild intellectual disabilities.

The present research examined numerical magnitude processing and its association with working memory in children with mild intellectual disabilities (MID). We investigated the performance of 8-year-old children with MID on a symbolic (Arabic digits) and non-symbolic (dot patterns) magnitude comparison task by means of a chronological-age/ability-level-match design. We also examined whether the predicted problems with numerical magnitude comparison could be explained by working memory by using three working memory tasks. Findings revealed that children with MID performed more poorly than their chronological age-matched peers on both the symbolic and non-symbolic magnitude comparison tasks, suggesting impairments in these children's ability to represent numerical magnitudes. They also performed more poorly on working memory compared to their typically developing age- and ability-matched peers, but when these differences in working memory performance were additionally controlled for, the group differences on the numerical magnitude comparison tasks remained. Both symbolic numerical magnitude processing and central executive functioning predicted addition performance in children with MID.

Numerical magnitude processing in children with mild intellectual disabilities.

The present study investigated numerical magnitude processing in children with mild intellectual disabilities (MID) and examined whether these children have difficulties in the ability to represent numerical magnitudes and/or difficulties in the ability to access numerical magnitudes from formal symbols. We compared the performance of 26 children with MID on a symbolic (digits) and a non-symbolic (dot-arrays) comparison task with the performance of two control groups of typically developing children: one group matched on chronological age and one group matched on mathematical ability level. Findings revealed that children with MID performed more poorly than their typically developing chronological age-matched peers on both the symbolic and non-symbolic comparison tasks, while their performance did not substantially differ from the ability-matched control group. These findings suggest that the development of numerical magnitude representation in children with MID is marked by a delay. This performance pattern was observed for both symbolic and non-symbolic comparison tasks, although difficulties on the former task were more prominent. Interventions in children with MID should therefore foster both the development of magnitude representations and the connections between symbols and the magnitudes they represent.