Direct and indirect influences of executive functions on mathematics achievement.

Achievement in mathematics is predicted by an individual's domain-specific factual knowledge, procedural skill and conceptual understanding as well as domain-general executive function skills. In this study we investigated the extent to which executive function skills contribute to these three components of mathematical knowledge, whether this mediates the relationship between executive functions and overall mathematics achievement, and if these relationships change with age. Two hundred and ninety-three participants aged between 8 and 25years completed a large battery of mathematics and executive function tests. Domain-specific skills partially mediated the relationship between executive functions and mathematics achievement: Inhibitory control within the numerical domain was associated with factual knowledge and procedural skill, which in turn was associated with mathematical achievement. Working memory contributed to mathematics achievement indirectly through factual knowledge, procedural skill and, to a lesser extent, conceptual understanding. There remained a substantial direct pathway between working memory and mathematics achievement however, which may reflect the role of working memory in identifying and constructing problem representations. These relationships were remarkably stable from 8years through to young adulthood. Our findings help to refine existing multi-component frameworks of mathematics and understand the mechanisms by which executive functions support mathematics achievement.