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Familial Aggregation Patterns in Mathematical Ability 61 mathematics education, or some other factor—is out- side the scope of this study. The significant sex effects found in the individual-based regressions for MRATE also may reflect persistent differential social effects and opportunities for men and women in the mathematical domain, although biological variables are not ruled out. The differences in correlations between the two SAT scores in the female math probands vs. the other probands may also reflect such social trends, possibly by resulting in more stringent ascertainment of mathe- matically talented girls from the pool of all seventh- grade girls, relative to ascertainment of the other three groups of probands. However, the numbers are small, and additional studies would be needed to replicate this observation. This study admittedly has its shortcomings. The sample sizes are too small to estimate the size of some parameters of interest. The data were derived from the report of one or two informants about members of their kinship who were sometimes not well known to them. In individuals in prior generations—some now deceased—youthful educational and vocational attain- ments had sometimes occurred before the birth of the informant. The educational, vocational, and avocational variables we measured were, at best, proxy stand-ins for underlying mathematical ability. As mentioned pre- viously, however, had we attempted direct measures of mathematical ability in the fewer individuals available for direct testing, their varying educational experience and the unknown results of disuse and of social, gen- der, and age-specific effects on current procedural knowledge and mathematical reasoning would have complicated the picture at least as seriously as the mea- sures we used. It might be possible to develop process- based rather than content-based measures, but none exists at this time with the very wide range needed in a study of the mathematically talented across the age span. An alternative strategy—making use of data such as archived SAT scores across generations— would present still further complications in that only family members who actually had taken the SAT or the equivalent ACT could be included, thereby excluding those who had not spent their high-school years in the United States, those who had not applied to college, and older individuals who had completed their educa- tions before the widespread use of the SAT or ACT. CONCLUSION This preliminary study provides encouragement for the development of methods to measure and study the genetic basis of mathematical talent. Despite the limitations of the proxy measures used here and the small sample size, we were able to obtain some indi- cation that there may be a genetic basis that is specific to mathematical talent. The case-controlfamily design used here has the potential to control for some of the confounding variables that make study of specific tal- ent difficult. A larger and more complete data set stud- ied with more direct measures may shed further light on the etiology of mathematical talent. ACKNOWLEDGMENTS This work was partially supported by funding from the University of Washington Royalty Research Fund and NIH HD33812. Some of the results of this paper were obtained by using the program package S.A.G.E., which is supported by a U.S. Public Health Service Resource Grant 1 P41 RR03655 from the National Center for Research Resources. REFERENCES Alarcón, M., DeFries, J. C., Light, J. C., and Pennington, B. F. 1997. A twin study of mathematics disability. J. Learn. Disabil. 30:617–623. Alarcón, M., Knopik, V., and DeFries, J. 2000. Covariation of math- ematics achievement and general cognitive ability in twins.

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