Longitudinal and reciprocal relationships between physical activity, physical fitness, executive functions, and arithmetic fluency in adolescents

Abstract Background The relationship between physical health and academic outcomes in adolescents is well-established, but the directionality and reciprocal nature of these associations remain unclear. Given the foundational role of mathematical skills in academic success, this study aims to analyze the reciprocal and longitudinal relationships between moderate-to-vigorous physical activity, physical fitness, core executive functions and arithmetic fluency in adolescents over a seven-month lag during a school year. Methods A longitudinal study was conducted with 1,166 Spanish adolescents (12–14 years) over seven months. Moderate-to-vigorous physical activity was measured via accelerometry (ActiGraph GT3X+) over seven consecutive days, physical fitness through the test from the ALPHA-Fitness battery, and executive functions using the NIH Examiner Battery. Arithmetic fluency was assessed with the Woodcock protocol. Data analysis included multiple imputation for missing values and cross-lagged panel models to examine longitudinal relationships. Residualized change models were used to test if improvements in moderate-to-vigorous physical activity, fitness, and executive functions predicted gains in arithmetic fluency, adjusting for sociodemographic covariates. Results A cross-lagged panel model showed that all variables exhibited significant temporal stability (β = 0.240–0.755, p < 0.001). Baseline physical fitness positively predicted executive functions (β = 0.104, p < 0.001) and arithmetic fluency (β = 0.040, p < 0.05) at Time 2. A reciprocal relationship was also observed between executive functions and arithmetic fluency over time (β = 0.074–0.132, p < 0.001). Baseline moderate-to-vigorous physical activity was not significantly associated with physical fitness, executive functions, or arithmetic fluency at Time 2. The model explained 65% of the variance in arithmetic fluency at follow-up. Additionally, analyses of longitudinal change revealed that increases in moderate-to-vigorous physical activity, physical fitness, and executive functions significantly predicted gains in arithmetic fluency. Conclusions These findings underscore the importance of physical fitness and cognitive skills as key predictors of academic success, highlighting the need for educational strategies that integrate the promotion of physical fitness to foster cognitive development and, consequently, enhance mathematical skills in adolescents.