Using strict and lenient mathematics achievement cutoff scores to define a learning disability, respective groups of children who are math disabled (MLD, n=15) and low achieving (LA, n=44) were identified. These groups and a group of typically achieving (TA, n=46) children were administered a battery of mathematical cognition, working memory, and speed of processing measures (M=6 years). The children with MLD showed deficits across all math cognition tasks, many of which were partially or fully mediated by working memory or speed of processing. Compared with the TA group, the LA children were less fluent in processing numerical information and knew fewer addition facts. Implications for defining MLD and identifying underlying cognitive deficits are discussed.

First- to fifth-grade mathematics and word reading achievement were assessed for children with mathematical learning disability (MLD, n = 16), persistent low achievement (LA, n = 29), and typical achievement (n = 132). Intelligence, working memory, processing speed, and in-class attention were assessed in 2 or more grades, and mathematical cognition was assessed with experimental tasks in all grades. The MLD group was characterized by low school-entry mathematics achievement and poor word reading skills. The former was mediated by poor fluency in processing or accessing quantities associated with small sets of objects and corresponding Arabic numerals, whereas the latter was mediated by slow automatized naming of letters and numbers. Both the MLD and LA groups showed slow across-grade growth in mathematics achievement. Group differences in growth were mediated by deficits or delays in fluency of number processing, the ability to retrieve basic facts from long-term memory and to decompose numbers to aid in problem solving, and by the central executive component of working memory and in-class attention.

Children with a mathematical learning disability (MLD, n = 19) and low achieving (LA, n = 43) children were identified using mathematics achievement scores below the 11th percentile and between the 11th and 25th percentiles, respectively. A control group of typically achieving (TA, n = 50) children was also identified. Number line and speed of processing tasks were administered in 1st and 2nd grade and a working memory battery in 1st grade. In both grades, the MLD children were less accurate in their number line placements and more reliant on a natural numbermagnitude representational system to make these placements than were TA children. The TA children were more reliant on the school-taught linear system in both grades. The performance of the LA children was similar to that of the MLD children in first grade and to the TA children in second. The central executive component of working memory contributed to across-grade improvements in number line performance and to group differences in this performance.Several large-scale population-based, prospective studies and a number of smaller-scale studies have consistently found that between 5% and 10% of children and adolescents will experience a substantive learning deficit-not attributable to low cognitive ability-in at least one area of mathematics before graduating from high school (Badian, 1983;Barbaresi, Katusic, Colligan, Weaver, & Jacobsen 2005;Ostad, 1998;Shalev, 2007;Shalev, Manor, & Gross-Tsur, 2005). These individuals are considered to have a mathematical learning disability (MLD), and are joined by another 5% and perhaps many more children and adolescents who experience more mild and circumscribed learning difficulties in mathematics (for recent reviews see Berch & Mazzocco, 2007). The mathematics achievement of this latter group of low achieving children (LA) is below expectations based on their cognitive ability and reading achievement, and the mechanisms contributing to their difficulties with mathematics learning may differ from those underlying MLD (Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007;Murphy, Mazzocco, Hanich, & Early, 2007). The central executive component of working memory has been implicated as a core mechanism underlying differences in the mathematical cognition of children with MLD but not their LA peers, but this remains to be confirmed. Moreover, the mathematical areas in which these groups may be similar or different are not well understood. HHS Public Access Author Manuscript Author ManuscriptAuthor Manuscript Author ManuscriptChildren with MLD have deficits in a wide range of basic mathematical domains, including a delayed understanding of counting concepts (Geary, Bow-Thomas, & Yao, 1992), difficulties remembering arithmetic facts (Geary, 1993;Jordan, Hanich, & Kaplan, 2003;Jordan & Montani, 1997), and poor conceptual knowledge of rational numbers (Mazzocco & Devlin, in press). The delayed learning of LA children, in contrast, may center on basic numerical representations, including the number line (Geary et al., 20...

Previous research indicates that verbal memory span, the number of words people can remember and immediately repeat, is related to the fastest rate at which they can pronounce the words. This relation, in turn, has been attributed to a general or global rate of information processing that differs among individuals and changes with age. However, the experiments described in this article showed that the rates of 2 processes (rapid articulation and the retrieval of words from short-term memory) are related to memory span but not to each other. Memory span depends on a profile of processing rates in the brain, not only a global rate. Moreover, there appears to be only a partial overlap between the rate variables that change with age and those that differ among individuals.

One in five adults in the United States is functionally innumerate; they do not possess the mathematical competencies needed for many modern jobs. We administered functional numeracy measures used in studies of young adults’ employability and wages to 180 thirteen-year-olds. The adolescents began the study in kindergarten and participated in multiple assessments of intelligence, working memory, mathematical cognition, achievement, and in-class attentive behavior. Their number system knowledge at the beginning of first grade was defined by measures that assessed knowledge of the systematic relations among Arabic numerals and skill at using this knowledge to solve arithmetic problems. Early number system knowledge predicted functional numeracy more than six years later (ß = 0.195, p = .0014) controlling for intelligence, working memory, in-class attentive behavior, mathematical achievement, demographic and other factors, but skill at using counting procedures to solve arithmetic problems did not. In all, we identified specific beginning of schooling numerical knowledge that contributes to individual differences in adolescents’ functional numeracy and demonstrated that performance on mathematical achievement tests underestimates the importance of this early knowledge.