As noted in RFA HD-07-005, the extent to which mathematics difficulties are attributable to deficits in domain-general cognitive mechanisms and/or impairments in math-specific processes involving numerical processing is a matter of considerable debate as is the definition of math disability. The goal of the proposed study is to bring a quantitative genetic perspective to both issues, building on an ongoing systematic behavioral genetic examination of psychometric math skills (HD046167, funded via RFA HD-02-031), the only effort of its kind in the literature. These efforts have been based on two complementary samples of twins, one in the U.S. and the other in the U.K. The U.S. sample includes 500 same-sex pairs of unselected twins who were previously recruited as part of an NICHD-funded study of reading and related cognitive skills (HD38075). As part of HD-02-031, these children were assessed in their homes at 8.5 years on psychometric mathematics skills, spatial skills, and reading skills. The U.K. sample includes 7500 pairs of unselected twins participating in an MRC-funded study of learning disabilities and behavior problems (G0500079). As part of HD-02-031, 2665 pairs of twins have been assessed at age 10 using web- and teacher-based measures of mathematics and reading. Using both samples, the PIs propose to conduct the first quantitative genetic examination of domain-general and math-specific cognitive skills underpinning psychometric math ability and disability. Given their preliminary data, the PIs predict that domain general measures will account for genetic and shared environmental influences on mathematics that overlap with reading outcomes. They also predict that measures of numerical processing will reflect independent genetic and environmental influences on math outcomes above and beyond that explained by general cognitive ability, reading ability, and domain-general skills such as working memory. The proposed study will also provide a unique opportunity to examine the core cognitive mechanisms of math across multiple definitions of disability within the context of a genetically sensitive design. Furthermore, because this proposal is embedded in an ongoing program of research, data emanating from this proposal can be put into the context of previously (and separately) funded longitudinal genetic studies of reading and psychometric math ability and disability. The proposed research is innovative in that it will move beyond estimating genetic and environmental influences on psychometric measures of mathematic ability to understanding how genes and environments influence the fundamental cognitive skills underpinning mathematic ability and disability in the context of reading skills during middle childhood and adolescence. Developing a model of how genes and environments work together to affect the development of math ability and disability has important implications on how to foster math development as well as to detect, ameliorate and prevent math difficulties.