Co-development of fraction magnitude knowledge and mathematics achievement from fourth through sixth grade

Fraction magnitude understanding is linked to student achievement in mathematics, but the direction of the relation is not clear. To assess whether fraction magnitude knowledge and mathematics achievement develop in a bidirectional fashion, participants (N = 536) completed a standardized mathematics achievement test and two measures of fraction magnitude understanding-fraction comparisons and fraction number line estimation (FNLE)-twice yearly in 4th-6th grades. Cross-lagged panel models revealed significant autoregressive paths for both achievement and magnitude knowledge, indicating longitudinal stability after accounting for correlational and cross-lagged associations. Mathematics achievement consistently predicted later FNLE and fraction comparison performance. FNLE and fraction comparisons predicted mathematics achievement at all time points, although this relation diminished over time. Findings suggest that fraction magnitude knowledge and broader mathematics achievement mutually support one another. FNLE predicted subsequent mathematics achievement more strongly than did fraction comparisons, possibly because the FNLE task is a more specific measure of fraction magnitude understanding.