In the United States, children from families of lower socioeconomic status (SES) generally enter kindergarten with significantly less mathematical knowledge than children from families of middle SES. Research reveals that this discrepancy is present, although to a lesser degree, at age three years, the age many children enter preschool for the first time (Starkey & Klein, 2008). This mixed-methods correlational study explores relationships between elements of the home learning environment and the mathematical knowledge of three- and four-year-old children from lower and middle SES families in order to better understand the potential reasons for this discrepancy. First, I compare responses from 179 parents, balanced for child's age and family's SES, on a questionnaire designed to capture aspects of the quantity and quality of mathematical support children receive in the home. The questionnaire contained items about the frequency and range of activities children engage in to support the development of informal mathematics, parent practices supporting their children's mathematical development, and parents' beliefs and knowledge about typical early mathematical development in the United States. Next, I analyze videos obtained for a subset of the sample (n = 26) of parents and children engaging in activities at home, believed by parents to support early mathematical development. Specifically, I examine differences in the amount, type, and complexity of math content included in each activity, as well as differences in parents' teaching behavior as they assist their children with mathematical tasks. Correlational relationships between both the questionnaire and video data are and children's scores on a comprehensive mathematical assessment are explored.

Results from the questionnaire component indicate very few differences in the amount and types of mathematical support three- and four-year-old children in both SES groups receive in the home, but very clear SES differences in parents' beliefs about early mathematical development and how it is best supported, as well as SES differences in parents' knowledge about early mathematical development. Compared to lower SES parents, middle SES parents of children at both ages hold higher expectations in terms of skills they expect children to possess by age 5, as well as a more accurate understanding of which mathematical skills are within the developmental range of most children by age 5. Both of these constructs have predictive value, as evidenced by multiple regression models, for children's mathematical knowledge as measured by the math assessment. Middle SES parents are also more likely to provide support for the development of these skills by embedding math in the home routine, encouraging made-up games involving math, and by reading books with mathematical content to their children.

The video analyses suggest that parents of children in both age and SES groups focus on similar mathematical concepts when engaging in math activities with their children, but there are qualitative differences in parents' teaching behavior that are predictive of children's performance on the math assessment when the child's age and family SES is held constant. Specifically, middle SES parents tend to structure the demands of activities in such a way that the children successfully respond to approximately 80% (three-year-olds) or 90% (four-year-olds) of the math included independently, compared to lower SES parents, who tend to structure the demands of activities such that children are only responding to approximately 50% (three-year-olds) or 70% (four-year-olds) of the math independently. Furthermore, the type of assistance provided for the problems or tasks that children do not respond to independently, appears to both vary by age and SES, and predicts unique variance in children's mathematical knowledge.