Learning and solving more complex problems: the roles of working memory, updating, and prior skills for general mathematical achievement and algebra

We examined the influences of domain-specific and domain-general factors (measured by working memory and updating capacities) on learning and solving mathematical problems. Using both general mathematical achievement and more targeted measures of algebraic skills, we conducted a 4-year longitudinal study that involved 673 children from K2; Grades 2, 4, and 6 (5, 7, 9, and 11 year olds, respectively), tested annually. Domain-general influences are important for general mathematical achievement and relatively more so than prior mathematical achievement for the younger children. Prior achievement plays a more important role for children in higher grades. Learning to solve algebraic problems is influenced largely by domain-specific factors, though domain-general capacities are still associated with performances on a cross-sectional basis. These findings show that the importance of domain-general capacities vary greatly depending on the domain of mathematics under consideration and perhaps the way in which they are measured. Reasons for variations and ideas for future studies are discussed.