Predicting fraction magnitude knowledge and fraction arithmetic

The core assumptions of the integrated theory of numerical development were tested using a cross-sectional sample of 379 fifth-grade students, who were assessed on their understanding of whole numbers and fractions, including arithmetic skills. An additional factor of part-whole knowledge was also assessed and analyzed in four structural equation models. All models showed non-significant chi-square values and good fit indices according to common modelling benchmarks. As hypothesized, whole number magnitude knowledge predicts fraction magnitude knowledge and arithmetic proficiency. Additionally, part-whole knowledge mediates numerical magnitude understanding but does not predict arithmetic outcomes. These findings are in line with the integrated theory of numerical development, suggesting that numerical magnitude knowledge is crucial for both numerical development and arithmetic learning. Our findings also reveal that part-whole knowledge may serve as a bridge to more advanced magnitude understanding. Theoretical and practical implications are discussed.