Relations between numerical, spatial, and executive function skills and mathematics achievement: A latent-variable approach.

Current evidence suggests that numerical, spatial, and executive function (EF) skills each play critical and independent roles in the learning and performance of mathematics. However, these conclusions are largely based on isolated bodies of research and without measurement at the latent variable level. Thus, questions remain regarding the latent structure and potentially shared and unique relations between numerical, spatial, EF, and mathematics abilities. The purpose of the current study was to (i) confirm the latent structure of the hypothesized constructs of numerical, spatial, and EF skills and mathematics achievement, (ii) measure their unique and shared relations with one another, and (iii) test a set of novel hypotheses aimed to more closely reveal the underlying nature of the oft reported space-math association. Our analytical approach involved latent-variable analyses (structural equation modeling) with a sample of 4- to 11-year-old children (N = 316, Mage = 6.68 years). Results of a confirmatory factor analysis demonstrated that numerical, spatial, EF, and mathematics skills are highly related, yet separable, constructs. Follow-up structural analyses revealed that numerical, spatial, and EF latent variables explained 84% of children's mathematics achievement scores, controlling for age. However, only numerical and spatial performance were unique predictors of mathematics achievement. The observed patterns of relations and developmental trajectories remained stable across age and grade (preschool - 4th grade). Follow-up mediation analyses revealed that numerical skills, but not EF skills, partially mediated the relation between spatial skills and mathematics achievement. Overall, our results point to spatial visualization as a unique and robust predictor of children's mathematics achievement.