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Arithmetic and cognitive skills of children with mathematical difficulties (MD-only), with comorbid reading difficulties (MD-RD), with reading difficulties (RD-only), and normally achieving children were examined at 3 points from Grades 3-4 to Grades 5-6 (age range, 9 -13 years). Both MD groups displayed severe weaknesses in 4 domain-specific arithmetic components (factual, conceptual, procedural, and problem-solving skills) during all 3 measure points. Telling time and approximate arithmetic were also problematic for children with MD. Both MD groups displayed a small weakness related to visual-spatial working memory, and the MD-RD group also displayed small weaknesses related to verbal short-term memory, processing speed, and executive functions. The 4 groups developed at similar rates within all domain-specific components as well as basic cognitive functions. These findings demonstrate that children identified as having MD when they are 9 years old do not catch up with their normally achieving peers in later school grades, when they are 13 years old. They also continue to lag behind their peers with respect to the domain-general cognitive system.

The mathematical performance of 182 third and fourth graders in 8 different areas of mathematics was examined. The children belonged to 4 achievement groups: children with mathematic difficulties (MD only), children with both mathematic and reading difficulties (MD-RD), children with reading difficulties (RD only), and normally achieving children (control group). Both MD groups performed worse than the normally achieving children in all but 1 area, place value knowledge. The MD-only and the MD-RD children performed equally in all areas of mathematics. The RD-only group performed at the same level as the control group on all areas of mathematics. The study provides further evidence that fact retrieval deficits are a cardinal characteristic of children with MD. The MD children's substantial difficulties with mathematic word problem solving can be attributed to several processes involved in problem solving. Besides poor skills in multidigit calculation, arithmetic fact retrieval, and poor understanding of calculation principles, children with MD might have deficits related to specific problem-solving processes such as establishing a problem representation and developing a solution plan.

The present findings demonstrate that working memory, in general, and the central executive, in particular, contribute to children's arithmetical skills. It was hypothesized that monitoring and coordinating multiple processes, and accessing arithmetical knowledge from long-term memory, are important central executive functions during arithmetical performance. The contribution of the phonological loop and the central executive (concurrent processing and storage of numerical information) indicates that children aged 9-10 years primarily utilize verbal coding strategies during written arithmetical performance.

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