Sources of individual differences in fraction skills.

The purpose of this investigation was to evaluate a conceptual model of relations between two kinds of mathematical knowledge (simple arithmetic and conceptual knowledge), two kinds of child characteristics (working memory and on-task related classroom behavior), and individual differences in three kinds of fraction outcomes (fraction computation, estimation, and word problems) in 105 fifth grade students. Structural equation modeling provided consistent evidence that conceptual knowledge independently contributes to individual differences in the three fraction outcomes. Simple arithmetic knowledge was uniquely related only to variability in fraction computation skills. Mathematical knowledge was found to mediate some of the contributions of both working memory and classroom behavior on variability in fraction outcomes. These supported mediating processes extend the current literature by explication of the pathways via which characteristics of children may affect individual differences in fraction outcomes.