Identifying the types of mathematics content knowledge that are most predictive of students’ long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.

The current study analyzed maternal and paternal differential influences on numeracy performance in kindergarten children. Participants were 180 Chilean children from backgrounds of low and high socioeconomic status (SES), their mothers, and their fathers. A path analysis was used to explore the influences of both maternal and paternal numeracy practices on children’s numeracy performance and the influences of maternal and paternal expectations and anxiety on those activities. Research Findings: Results showed that mothers and fathers who endorse higher numeracy expectations for their children and who report lower levels of math anxiety also report engaging more frequently in advanced numeracy practices with their children. Mothers’—but not fathers’—engagement in numeracy practices at home predicted children’s numeracy performance. Also, low-SES mothers engaged more frequently in numeracy practices with their children, and mothers in general engaged more often in numeracy activities with girls than with boys. Practice or Policy: These findings improve understanding of how maternal and paternal processes relate differently to numeracy performance in kindergarten children. Moreover, these results highlight the need to take into account parents’ numeracy attitudes and practices, as well as their SES, when designing interventions directed at increasing family support for math achievement.

Research Findings: The current study analyzed the relation between the amount of mathematical input that preschool children hear (i.e., math talk) from their mothers in their homes and their early math ability a year later. Forty mother–child dyads recorded their naturalistic exchanges in their homes using an enhanced audio-recording device (the Language ENvironment Analysis System). Results from a sample of naturalistic interactions during mealtimes indicated that all mothers involved their children in a variety of math exchanges, although there were differences in the amount of math input that children received. Moreover, being exposed to more instances of math talk was positively related to children’s early mathematical ability a year after the recordings, even after we controlled for maternal education, self-regulation, and recorded minutes. Practice or Policy: These findings improve the understanding of how mothers use math with their preschool children in naturalistic contexts, providing some insight for parents into how to foster children’s math skills through verbal input in their normal routines. Moreover, these findings inform kindergarten teachers and practitioners about the math input that children receive at home, which may encourage them to adapt their practice by considering the home environment.