The relationship among geometry, working memory, and intelligence in children.

Although geometry is one of the main areas of mathematical learning, the cognitive processes underlying geometry-related academic achievement have not been studied in detail. This study explored the relationship among working memory (WM), intelligence (g factor), and geometry in 176 typically developing children attending school in their fourth and fifth grades. Structural equation modeling showed that approximately 40% of the variance in academic achievement and in intuitive geometry (which is assumed to be independent of a person's cultural background) was explained by WM and the g factor. After taking intelligence and WM into account, intuitive geometry was no longer significantly related to academic achievement in geometry. We also found intuitive geometry to be closely related to fluid intelligence (as measured by Raven's colored progressive matrices) and reasoning ability, whereas academic achievement in geometry depended largely on WM. These results were confirmed by a series of regressions in which we estimated the contributions of WM, intelligence, and intuitive geometry to the unique and shared variance explaining academic achievement in geometry. Theoretical and educational implications of the relationship among WM, intelligence, and academic achievement in geometry are discussed.