Estimating the co-development of executive functions and math achievement throughout the elementary grades using a cross-lagged panel model with fixed effects

•Showed bidirectional relationship between executive function and math achievement.•Predictive values in both directions decreased as children grow older.•Cross-lagged panel model with fixed effects accounting for unobserved confounders. Executive functioning (EF) is associated with children’s math skill development, both concurrently and longitudinally. However, it is not known how components of EF might be related to mathematics skills and vice versa over the course of elementary school. The present study addresses this issue by investigating relations between math achievement and two key components of EF -- working memory (WM) and cognitive flexibility (CF) -- from kindergarten to 5th grade, using the large-scale nationally representative dataset (N = 18,174) from the Early Childhood Longitudinal Study-Kindergarten (ECLS-K: 2011). Results from cross-lagged panel models with fixed effects support a transactional theoretical model, demonstrating a long-term reciprocal relationship between WM and math achievement from kindergarten to 5th grade and between CF and math achievement from 2nd grade to 5th grade. However, we found that reciprocal relations decrease as children grow older, suggesting that their math achievement relies less on EF and more on prior math knowledge over time.