This paper uses a structural model with a large random sample of urban children to explain children's competence in math concepts and computation at the time they begin first grade. These two aspects of math ability respond differently to environmental resources, with math concepts much more responsive to family factors before formal schooling begins than is computation. In this sample blacks and whites are equivalent in terms of computational and verbal skills as measured by the California Achievement Test (CAT) at the start of grade one. However, black boys equal white boys and white girls in terms of math concepts (reasoning skills) but black girls are about one quarter of a standard deviation lower than others in terms of math concepts on the CAT. Both black and white children of all socioeconomic levels respond to parents' psychological resources: net of ability or other factors, children score higher if parents expect them to do well. Socioeconomic resources in the home also help both groups. In particular, the parent's being a high school graduate as opposed to a drop-out is important. When parents' material and psychological resources are taken into account, family configuration (solo motherhood vs. other types) has no discernible effects on either type of math performance. There are 48 references listed. (Author/DC)