PROJECT SUMMARY/ABSTRACT Math achievement is one of the strongest predictors of college and career attainment, lifetime earnings, and health outcomes. However, much of what comprises later math achievement is decided by the time children enter school. Thus, it is essential to better understand environmental and cognitive determinants of early math skills to close stubborn math achievement gaps. One way to consider these varied determinants is within the Opportunity-Propensity (O-P) model. This model suggests characteristics can be organized into three factors predicting achievement: antecedents represent distal variables which influence the context into which the child is born (e.g., socioeconomic status); opportunities represent features of learning environments (e.g., educational and extracurricular activities); and propensities represent proximal processes that facilitate learning (e.g., executive function). This project aims to better understand ways in which opportunities and propensities independently and interactively contribute to the development of early elementary math skills. Individual differences in children's exposure to math language predict children's math skills. Prior studies have described relations between math language input and math skills in homes and classrooms separately, but little research has explored unique and/or complementary influences of these inputs. Furthermore, some children have a greater propensity to learn from opportunities than do others and this might in part be explained by variations in executive function (EF), skills recruited for goal-directed cognitions and behaviors. Previous research has demonstrated robust relations between EF and math and suggests that EF might serve as a compensatory mechanism for children who enter school with low levels of math skills. Further research is needed to test whether EF interacts with math language to predict math skills. The O-P model provides a useful framework for understanding the development of skills and a basis for developing interventions. Antecedents are difficult to intervene upon and often require systemic policy change, whereas propensities might be more easily affected at the child level. As observational data have suggested propensities fully mediate relations between both antecedent and opportunity factors and achievement, propensity factors might be an ideal target for intervention. As such, this investigation seeks to understand whether modifying propensities affects achievement and/or relations between opportunities and achievement. The primary goals of this research are to (1) examine relations between learning opportunities indexed by math language and child skills; (2) test the role of EF in relations between math language and math skills; and (3) train child propensities to elucidate mechanisms that lead to improvements in math. Findings will have implications for intervention and learning science, policy, and practice. The proposed researc...