Tracking fraction knowledge development using grade-appropriate assessments

Fraction knowledge is foundational for later mathematics achievement, yet its developmental organization remains debated and is constrained by the limited availability of grade-appropriate measures with established psychometric properties. We developed and evaluated the Fraction Knowledge Assessment (FKA), a set of grade-specific instruments for 2^nd, 3^rd, 5^th, and 6^th grades, and examined changes in fraction knowledge across two adjacent-grade transitions. Using an accelerated longitudinal design, we followed 342 children in two cohorts (2^nd-3^rd grade; 5^th-6^th grade). Participants completed standardized mathematics and cognitive measures at baseline and grade-appropriate FKAs across two consecutive years. Confirmatory factor analysis and Item Response Theory were used to examine dimensional structure, item functioning, and to link FKA versions across grades prior to developmental analyses. Results provided no strong evidence for a robust separation between conceptual and procedural fraction knowledge, with two-factor solutions showing comparable fit to one-factor models and highly correlated factors. Item-level analyses revealed developmental shifts: fraction magnitude items differentiated ability more strongly in earlier grades, whereas fraction arithmetic items were more discriminative in later grades. Using equated ability scores, significant gains were observed in both cohorts, with larger improvements from 2^nd to 3^rd grade than from 5^th to 6^th grade. Baseline mathematics achievement and working memory were longitudinally associated with later fraction knowledge. These findings support an integrated account of fraction knowledge development and illustrate how psychometrically linked, grade-appropriate assessments can be used to characterize developmental change.