Surface-to-structure shifts in rational number categories

Experts organize and generalize knowledge in different ways than novices, and conceptual development is often characterized by a surface-to-structure shift in attention and categorization. We explored a surface-to-structure shift in rational number arithmetic. Children and adults sorted arithmetic equations with fractions and whole numbers in three separate studies. In all studies, children were more likely to sort by number type, conceptualizing fraction problems as distinct from whole number problems. In two studies, adults were more likely to sort equations by operation, suggesting integrated rational number categories. Across studies, some older children and adults sorted into highly differentiated categories. Evidence for a surface-to-structure shift in arithmetic categories suggests changes in knowledge organization in addition to content with increasing expertise.