Early fraction relational reasoning uniquely predicts later algebraic thinking in children: A longitudinal study

• This study examined longitudinal predictors of algebraic performance. • Fraction relational reasoning made independent contribution. • Magnitude knowledge of fractions and decimals were unique predictors. • Fraction arithmetic fluency was also an independent predictor. • Working memory and attention were also important. The association between children’s fraction relational reasoning and their algebraic thinking has not been explored longitudinally. This study used incremental importance analysis and relative weight analysis to examine the extent to which fourth-grade ( M= 112.3 months, SD= 2.25) fraction relational reasoning predicted sixth-grade algebraic performance, compared to an extensive set of cognitive factors. Multiple linear regression revealed that fraction relational reasoning, fraction and decimal magnitude knowledge, fraction arithmetic, attentive behavior, counting recall, and listening recall were significant predictors in the final model. Relative weight analysis indicated the contribution of fraction relational reasoning to algebraic performance did not differ significantly from fraction magnitude knowledge and fraction arithmetic, but was a stronger predictor than the other variables. This suggests the central executive component of working memory, attention, fraction relational reasoning, magnitude knowledge of fractions and decimals, and fraction arithmetic may warrant focused attention when preparing children for algebra.