Do better working memory and higher intrinsic motivation predict greater math achievement? Disaggregating within-person and between-person effects in a birth cohort followed from age 8 to 16

Intrinsic motivation and working memory are widely recognized as important for math achievement, and prior research suggests that each may be involved in reciprocal processes with achievement over time. However, most research relies on Cross-Lagged Panel Models (CLPMs), which confound within- and between-person effects and may result in ambiguous conclusions about intraindividual change. This study therefore compares results from ordinary CLPMs with those from a Latent Curve Model with Structured Residuals (LCM-SR), which separates these levels. Teacher-reported math achievement, child-reported intrinsic motivation, and central executive working memory were assessed biennially in a BLINDED FOR REVIEW (n = 833, 52% girls) followed from ages 8 to 16. Both the CLPM and LCM-SR revealed a reciprocal cycle in which higher math achievement predicted increased intrinsic motivation two years later, and vice versa. In contrast, while the CLPM suggested bidirectional associations between working memory and math achievement, the LCM-SR did not support within-person associations. This suggests that the relation between working memory and math achievement reflects stable individual differences rather than ongoing changes within students. Supporting this, between-person analyses revealed that students with higher initial math performance generally had stronger working memory. Higher initial math achievement was also linked to greater intrinsic motivation and a slower decline in motivation over time. These findings suggest that fostering intrinsic motivation may be an effective approach to improving math achievement across childhood and adolescence, whereas enhancing working memory may not – underscoring intrinsic motivation’s role in a self-reinforcing cycle of academic growth.