We investigated whether and to what extent U.S. kindergarten children ' s executive functions, oral vocabularies, and early literacy skills mediate relations between their sociodemographic background characteristics (i.e., family socioeconomic status, race or ethnicity, biological sex) and stable between-individual levels of mathematics and science achievement across kindergarten to 4th grade. We did so by fitting a random intercept crosslagged panel model to nationally representative data ( N = 9081, M age = 92.4 months). Cross-lagged relations were relatively stronger from mathematics to science achievement than from science to mathematics achievement. These relations were weaker in earlier grades and stronger in later grades. Autoregressive coefficients were stronger for mathematics than for science and much stronger for each domain during the upper elementary grades. Children ' s working memory abilities and early literacy skills were the strongest mediators of the relations between their socioeconomic backgrounds and over-time mathematics or science achievement. Educational relevance statement: We observed cross-lagged relations between mathematics and science achievement, particularly during the upper elementary grades and from mathematics to science achievement. We also observed that kindergarten children ' s executive functions, oral vocabularies, and early literacy skills mediate relations between their sociodemographic background characteristics and mathematics and science achievement. Results suggest that multi-component interventions designed to facilitate learning of both mathematics and science skills might be especially effective if introduced by the upper elementary grades. These multi-component interventions might also be designed to support children ' s executive functions, oral vocabularies, and early literacy skills instead of only teaching mathematics and science skills. Our findings add to the limited existing work examining over-time relations between mathematics and science achievement and the extent to which executive functions, oral vocabularies, and early literacy skills help to explain sociodemographic gaps in elementary schoolchildren ' s mathematics and science achievement.

We analyzed a population-based cohort (N = 10,922) to investigate the onset and stability of racial and ethnic disparities in advanced (i.e., above the 90(th) percentile) science and mathematics achievement during elementary school as well as the antecedent, opportunity, and propensity factors that explained these disparities. About 13% to 16% of White students versus 3% to 4% of Black or Hispanic students displayed advanced science or mathematics achievement during kindergarten. The antecedent factor of family socioeconomic status and the propensity factors of student science, mathematics, and reading achievement by kindergarten consistently explained whether students displayed advanced science or mathematics achievement during first, second, third, fourth, or fifth grade. These and additional factors substantially or fully explained initially observed disparities between Black or Hispanic and White students in advanced science or mathematics achievement during elementary school. Economic and educational policies designed to increase racial and ethnic representation in STEM course taking, degree completion, and workforce participation may need to begin by elementary school.

Prior nonexperimental studies have been used to conclude that children's reading and mathematics achievement bidirectionally influence each other over time, with strong paths from (a) early reading to later mathematics and (b) early mathematics to later reading. In the most influential study on the topic, the early math-to-later-reading path was reported to be stronger than the early reading-to-later-math path (Duncan et al., 2007). Yet prior estimates may be confounded by stable environmental and personal factors influencing both reading and mathematics achievement. We reexamined the bidirectional relations between reading and mathematics achievement using both traditional models and extensions intended to account for unmeasured confounding. Results based on a large nationally representative sample of children from kindergarten to 3rd grade (N = 9,612) indicated that the estimated effects between reading and mathematics achievement differ substantially after accounting for the confounding effects of stable unmeasured factors. In these models, autoregressive and cross-lagged paths were substantially reduced. The finding that early mathematics predicts later reading more strongly than early reading predicts later math disappears and sometimes reverses, suggesting that larger paths from math to reading than from reading to math in previous related analyses are not causally informative. Stability in early mathematics and reading achievement resulted from substantially overlapping time invariant factors that correlate above.90.