Kindergarten Domain-Specific and Domain-General Cognitive Precursors of Hierarchical Mathematical Development: A Longitudinal Study

This study examined cognitive precursors of hierarchical mathematical development. Six-year-old children (n = 258) were assessed on number skills, cognitive skills, and arithmetic 1 year prior to school entry. Skills in advanced arithmetic and advanced mathematics were assessed in Grades 3 and 6, respectively. Path analyses were computed and provided longitudinal evidence for a hierarchy of mathematics. During development, the reliance on prior skills at lower, most proximal levels becomes increasingly important in order to acquire and succeed at later and higher levels of mathematics. The study extends the Fuchs et al. (2010b) model as the mechanisms underlying 3 different hierarchical levels of mathematics all involve an interplay between domain-specific number abilities (i.e., sequence knowledge, digit comparison) and general cognitive abilities (i.e., logical reasoning, phonological awareness, working memory). The constellation of domain-specific number and domain-general cognitive mechanisms subserving mathematics at different hierarchical levels showed a high degree of similarity. However, the importance of number abilities decreases during development, whereas the importance of general cognitive abilities remains approximately equal across levels of mathematical learning. Early symbolic number skills (i.e., counting sequence knowledge, digit comparison) are subserved by general cognitive mechanisms such as working memory, phonological awareness, and rapid automatic naming processes.