The performance of 223 Grade 4 children, with Average overall IQ and no disability (ND), or reading disability (RD), or math disability (MD), or reading/math disability (RD+MD), was compared on theoretically-derived factors measuring specific cognitive processes underlying reading and math achievement. The processes included automatic visual/orthographic and visual/math fact retrieval, working memory span, phonological and algorithmic processing, and IQ (e.g., verbal/nonverbal reasoning). Good readers and good mathematicians (ND group) showed solid performance across all tasks. Compared to the ND group, achievement and cognitive profiles of single disability (RD and MD), and RD+MD were elucidated. Structural equation models (SEM) for the entire sample confirmed a theoretically-derived four factor READ model and a four factor MATH model, both with identical Working Memory Span and IQ factors. Two other READ model factors were Automatic (RAN/Words) and Phonological Processing. Two additional MATH model factors were Automatic (RAN/Facts) and Algorithmic Processing. Based on the cognitive and functional neurobiological literatures, these models supported a systems view of the unique and collaborative relations among the automatic, processing, working memory, and IQ cognitive processes underlying reading and math achievement. Through regression analyses, the specific factors from both the READ and MATH models predicted each group’s reading and math achievement. Regression results enhanced our understanding of what factors/cognitive processes (strong or weak) contribute to good or poor reading and math achievement. Findings that automatic RAN/Words and RAN/Facts both predict fluent math fact retrieval for all groups suggest potential overlap in basic automatic visual/orthographic and visual/fact routes. Possible overlap in these automatic processes was also seen in the weakest RD+MD group for word reading.

The performance of 223 Grade 4 children, with Average overall IQ and no disability (ND), or reading disability (RD), or math disability (MD), or reading/math disability (RD+MD), was compared on theoretically-derived factors measuring specific cognitive processes underlying reading and math achievement. The processes included automatic visual/orthographic and visual/math fact retrieval, working memory span, phonological and algorithmic processing, and IQ (e.g., verbal/nonverbal reasoning). Good readers and good mathematicians (ND group) showed solid performance across all tasks. Compared to the ND group, achievement and cognitive profiles of single disability (RD and MD), and RD+MD were elucidated. Structural equation models (SEM) for the entire sample confirmed a theoretically-derived four factor READ model and a four factor MATH model, both with identical Working Memory Span and IQ factors. Two other READ model factors were Automatic (RAN/Words) and Phonological Processing. Two additional MATH model factors were Automatic (RAN/Facts) and Algorithmic Processing. Based on the cognitive and functional neurobiological literatures, these models supported a systems view of the unique and collaborative relations among the automatic, processing, working memory, and IQ cognitive processes underlying reading and math achievement. Through regression analyses, the specific factors from both the READ and MATH models predicted each group’s reading and math achievement. Regression results enhanced our understanding of what factors/cognitive processes (strong or weak) contribute to good or poor reading and math achievement. Findings that automatic RAN/Words and RAN/Facts both predict fluent math fact retrieval for all groups suggest potential overlap in basic automatic visual/orthographic and visual/fact routes. Possible overlap in these automatic processes was also seen in the weakest RD+MD group for word reading.

The subject of this study is how pupils in math disabilities communicate and reason during calculations involving fractional numbers. The study comprises eight informants, two from eigth grade (a boy and a girl, 13 to 14 years old) and six from ninth grade (three girls and three boys, 14 to 15 years old) who all were considered to have math disabilities. They were all interviewed alone about their reasoning when solving ten tasks involving fractions to see what knowledge and misconceptions the pupils showed. The conclusion of the study is that the pupils posessed procedural abilities, but were weaker in their concepual abilities. Most pupils in the study were uncertain about the meaning of nominator and denominator. Several of the pupils preferred to think in percent rather than fractions but they had problems in converting from percent to fractions and vice versa.