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This study examined whether parents who lack numeracy, literacy, or writing skills transmit their difficulty to their children. The study also sought to determine whether other family or child characteristics relate to children's basic skills; if child outcomes or predictors display between-family variation; and if child outcomes display any differing variability as a function of child or family characteristics. The study used a multivariate multilevel analysis to evaluate intergenerational transmission of literacy and numeracy for a sample of 2,647 children (ages 5 to 17 years) born to 2,150 33-year-old cohort members of the fifth sweep of the National Child and Development Study conducted in 1991. Child level data were obtained from interviewing the child's mother and through the Mathematical Assessment and Reading Recognition subtests from the Peabody Individual Achievement Test. Results revealed a steady decrease in variance of mathematics and reading up to 11 years of age followed by an increase in variance. Even with age standardized scores, the effect of age on the outcomes must be considered. Substantive conclusions reflected the power of a multilevel approach to reveal variation in parameter estimates beyond a conventional regression approach. Parental qualifications and social class were influential determinants of children's achievement. Parent's difficulty in writing had a direct effect on child outcomes. There were a number of interactions within and between families involving preschooling, learning difficulties, age, and gender. (Contains 26 references.) (KDFB)