Sources of Individual Differences in Children’s Understanding of Fractions

Longitudinal associations of domain-general and numerical competencies with individual differences in chil-dren’s understanding of fractions were investigated. Children (n = 163) were assessed at 6 years of age on domain-general (nonverbal reasoning, language, attentive behavior, executive control, visual-spatial memory) and numerical (number knowledge) competencies; at 7 years on whole-number arithmetic computations and number line estimation; and at 10 years on fraction concepts. Mediation analyses controlling for general math-ematics ability and general academic ability revealed that numerical and mathematical competencies were direct predictors of fraction concepts, whereas domain-general competencies supported the acquisition of frac-tion concepts via whole-number arithmetic computations or number line estimation. Results indicate multiple pathways to fraction competence. Competence with fractions is an integral part of overall mathematical proficiency, laying the founda-tion for learning the advanced mathematics that is critical for obtaining full economic opportunity and meaningful participation in society (e.g., Moses & Cobb, 2001; National Mathematics Advisory Panel, 2008). Yet fractions represent a primary source of difficulty for many students (Hecht, Close, & Sant