Project Summary - Research There is substantive variation in preschooler’s understanding of the core number concepts (e.g., cardinality) and associated skills (e.g., counting; Geary & VanMarle 2016) that are predictive of later individual differences in readiness to learn formal math at school entry (Geary et al. 2018) and risk of math LD (Chu et al. 2019). Child-centered interventions reduce these gaps (Dumas et al. 2019) but suffer from fade out and thus do not typically confer long-term benefits (Bailey, 2019). Similar fade out is found with individual therapy with young offenders, but sustained gains can be achieved with multisystemic interventions involving the child, home environment, and school (Henggeler et al. 2009), and it is time to consider this approach for LD. The proposed project will provide a unique and much-need foundation for the development of multisystemic – including child, parents, home, and school – interventions for preschoolers who are at risk for long-term math difficulties, including math LD. The home component will provide the most thorough assessment ever conducted of the numeracy-related home environment, including assessment of parent’s math achievement and the complexity of the math-talk with their children, as related to preschoolers’ core conceptual number development (Zippert & Rittle-Johnson 2020). The classroom component will include teacher-report and direct observation of students’ engagement in learning opportunities and the complexity of the math presented in classrooms. The child- centered assessments will focus on the longitudinal development of the core number knowledge and quantitative skills that predict later school readiness for math learning and risk of math LD (Chu et al. 2019; Geary et al. 2018). This ambitious combination will enable the first-ever dynamic assessment of the multiple contextual and child-centered factors that contribute to children’s early math development, including factors that indicate risk of later math LD. Unique features include direct assessment of parents’ math competencies; assessments of child-evocative effects (e.g., does children’s number knowledge predict longitudinal change in the complexity of parent-child number talk?); and assessments of students’ engagement in preschool classrooms. In all, the focus on core quantitative knowledge and skills, combined assessments of parents, the home environment, classroom engagement and learning experiences, and child characteristics will provide the broadest and most thorough study to date of the multiple influences on early mathematical development and preparation for school entry and risk of math LD. The combination will provide the foundation for early multisystemic interventions to better prepare at-risk children for math learning.