David C. Geary

Mathematical disabilities: cognitive, neuropsychological, and genetic components.

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.

Mathematics and Learning Disabilities

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.

The Science of Sex Differences in Science and Mathematics

Amid 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 mid-range 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 ability—including 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 are no single or simple answers to the complex questions about sex differences in science and mathematics.

Evolution and proximate expression of human paternal investment.

In more than 95% of mammalian species, males provide little direct investment in the well-being of their offspring. Humans are one notable exception to this pattern and, to date, the factors that contributed to the evolution and the proximate expression of human paternal care are unexplained (T. H. Clutton-Brock, 1989). The nature, extent, and influence of human paternal investment on the physical and social well-being of children are reviewed in light of the social and ecological factors that are associated with paternal investment in other species. On the basis of this review, discussion of the evolution and proximate expression of human paternal investment is provided.

Reflections of Evolution and Culture in Children's Cognition: Implications for Mathematical Development and Instruction.

: An evolution-based framework for understanding biological and cultural influences on childrens cognitive and academic development is presented. The utility of this framework is illustrated within the mathematical domain and serves as a foundation for examining current approaches to educational reform in the United States. Within this framework, there are two general classes of cognitive ability, biologically primary and biologically secondary. Biologically primary cognitive abilities appear to have evolved largely by means of natural or sexual selection. Biologically secondary cognitive abilities reflect the co-optation of primary abilities for purposes other than the original evolution-based function and appear to develop only in specific cultural contexts. A distinction between these classes of ability has important implications for understanding childrens cognitive development and achievement.

Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study.

The studys goal was to identify the beginning of 1st grade quantitative competencies that predict mathematics achievement start point and growth through 5th grade. Measures of number, counting, and arithmetic competencies were administered in early 1st grade and used to predict mathematics achievement through 5th (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence and processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning.

Cognitive Addition: A Short Longitudinal Study of Strategy Choice and Speed-of-Processing Differences in Normal and Mathematically Disabled Children

This study provided a longitudinal assessment of skill development in addition for 26 normal and 12 mathematically disabled firstor second-grade children. At the first time of measurement, the children solved 40 simple addition problems. Ten months later, all subjects were readministered the addition task and a measure of working memory resources. Across times of measurement, the normal group showed increased reliance on memory retrieval and decreased reliance on counting to solve the addition problems, as well as an increase in speed of counting and of retrieving addition facts from long-term memory. The math-disabled group showed no reliable change in the mix of problem-solving strategies or in the rate of executing the counting or memory retrieval strategies. Finally, reliable differences, favoring the normal group, were found for the index of working memory resources.

Cognitive addition : strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children

This study assessed strategy choice and information-processing differences in gifted, normal, and mathematically disabled third- or fourth-grade children. Fourteen gifted, 12 normal, and t 5 math disabled (MD) children solved 40 simple addition problems. Strategies, and their solution times, used in problem solving were recorded on a trial-by-trial basis, and each was classified in accordance with the distributions of associations model of strategy choices. Group differences were evident for the developmental maturity of the strategy mix and for the rate of verbal counting. The gifted group showed the most mature distribution of strategy choices, followed by the normal and MD groups. In terms of speed of processing, the gifted group showed a verbal counting rate that was at adult levels and less than 50% of the rate of counting for the two remaining groups, but group differences were not evident in the rate of retrieving answers from long-term memory. The results were interpreted within the context of the strategy choice model and suggested that a single dimension spanned group differences in the level of mastery of early numerical skills: the maturity of the long-term memory organization of basic facts. Finally, implications for the mental and strategic processes contributing to academic achievement are discussed.

Sexual selection and sex differences in mathematical abilities

The principles of sexual selection were used as an organizing framework for interpreting cross-national patterns of sex differences in mathematical abilities. Cross-national studies suggest that there are no sex differences in biologically primary mathematical abilities, that is, for those mathematical abilities that are found in all cultures as well as in nonhuman primates, and show moderate heritability estimates. Sex differences in several biologically secondary mathematical domains (i.e., those that emerge primarily in school) are found throughout the industrialized world. In particular, males consistently outperform females in the solving of mathematical word problems and geometry. Sexual selection and any associated proximate mechanisms (e.g., sex hormones) influence these sex differences in mathematical performance indirectly. First, sexual selection resulted in greater elaboration in males than in females of the neurocognitive systems that support navigation in three-dimensional space. Knowledge implicit in these systems reflects an understanding of basic Euclidean geometry, and may thus be one source of the male advantage in geometry. Males also use more readily than females these spatial systems in problem-solving situations, which provides them with an advantage in solving word problems and geometry. In addition, sex differences in social styles and interests, which also appear to be related in part to sexual selection, result in sex differences in engagement iii mathematics-related activities, thus further increasing the male advantage in certain mathematical domains. A model that integrates these biological influences with sociocultural influences on the sex differences in mathematical performance is presented in this article.

A Componential Analysis of an Early Learning Deficit in Mathematics

This study was designed to assess strategy choice and information-processing differences in normal and mathematically disabled first and second grade children. Twenty-three normal and 29 learning disabled (LD) children solved 40 computer-presented simple addition problems. Strategies, and their associated solution times, used in problem solving were recorded on a trial-by-trial basis and each was classified in accordance with the distributions of associations model of strategy choices. Based on performance in a remedial education course, as indexed by achievement test scores, the LD sample was reclassified into a LD-improved group and an LD-no-change group. No substantive differences comparing the normal and LD-improved groups occurred in the distribution of strategy choices, strategy characteristics (e.g., error rates), or rate of information processing. The performance characteristics of the LD-no-change group, as compared to the two remaining groups, included frequent counting and memory retrieval errors, frequent use of an immature computational strategy, poor strategy choices, and a variable rate of information processing. These performance characteristics were discussed in terms of the strategy choice model and in terms of potential long-term memory and working memory capacity deficits. In addition, implications for remedial education in mathematics were discussed.