Cognitive, neuropsychological, and genetic correlates of mathematical achievement and mathematical disability (MD) are reviewed in an attempt to identify the core deficits underlying MD. Three types of distinct cognitive, neuropsychological, or cognitive and neuropsychological deficits associated with MD are identified. The first deficit is manifested by difficulties in the representation or retrieval of arithmetic facts from semantic memory. The second type of deficit is manifested by problems in the execution of arithmetical procedures. The third type involves problems in the visuospatial representation of numerical information. Potential cognitive, neuropsychological, and genetic factors contributing to these deficits, and the relationship between MD and reading disabilities, are discussed. Finally, suggestions for the subtyping of mathematical disorders are offered.

Between 5% and 8% of school-age children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlying memory and cognitive deficits and potential neural correlates. The deficits are discussed in terms of three subtypes of mathematics learning disability and in terms of a more general framework for linking research in mathematical cognition to research in learning disabilities.

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.

SummaryAmid ongoing public speculation about the reasons for sex differences in careers in science and mathematics, we present a consensus statement that is based on the best available scientific evidence. Sex differences in science and math achievement and ability are smaller for the midrange of the abilities distribution than they are for those with the highest levels of achievement and ability. Males are more variable on most measures of quantitative and visuospatial ability, which necessarily results in more males at both high-and low-ability extremes; the reasons why males are often more variable remain elusive. Successful careers in math and science require many types of cognitive abilities. Females tend to excel in verbal abilities, with large differences between females and males found when assessments include writing samples. High-level achievement in science and math requires the ability to communicate effectively and comprehend abstract ideas, so the female advantage in writing should be helpful in all academic domains. Males outperform females on most measures of visuospatial abilities, which have been implicated as contributing to sex differences on standardized exams in mathematics and science. An evolutionary account of sex differences in mathematics and science supports the conclusion that, although sex differences in math and science performance have not directly evolved, they could be indirectly related to differences in interests and specific brain and cognitive systems. We review the brain basis for sex differences in science and mathematics, describe consistent effects, and identify numerous possible correlates. Experience alters brain structures and functioning, so causal statements about brain differences and success in math and science are circular. A wide range of sociocultural forces contribute to sex differences in mathematics and science achievement and abilityincluding the effects of family, neighborhood, peer, and school influences; training and experience; and cultural practices. We conclude that early experience, biological factors, educational policy, and cultural context affect the number of women and men who pursue advanced study in science and math and that these effects add and interact in complex ways. There

Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade ϭ 82 months), children with IQ scores in the low-average to high-average range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD). These children (n ϭ 42), a group of children who showed variable achievement test performance across grades (n ϭ 16), and a control group of academically normal peers (n ϭ 35) were administered a series of experimental and psychometric tasks. The tasks assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, the ease of activation of phonetic representations of words and numbers, and spatial abilities. The children with variable achievement test performance did not differ from the academically normal children in any cognitive domain, whereas the children in the LD groups showed specific patterns of cognitive deficit, above and beyond the influence of IQ. Discussion focuses on the similarities and differences across the groups of LD children.