Fraction Arithmetic Development: an Examination of Students’ Patterns of Growth and Errors Across the Intermediate Grades.

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses revealed three empirically distinct growth trajectories: (a) consistently accurate students who displayed high accuracy across time; (b) high-growth students who demonstrated low initial accuracy but made subsequent growth; and (c) low-growth students who demonstrated consistently poor accuracy across time. Age and whole number calculation fluency predicted membership in the consistently accurate and high-growth classes relative to membership in the low-growth class. Language and nonverbal reasoning skills were identified as predictors of student membership in the consistently accurate versus low-growth class. Low-growth students displayed more whole number bias and calculation errors compared with students who demonstrated growth. Findings reveal that a concerning subset of students make little to no progress in simple fraction arithmetic computation, despite several years of fractions instruction in school. Educational Impact and Implications Statement Fraction arithmetic is challenging for many students. The current study addresses fraction arithmetic development during the critical intermediate grades. Identification of predictors of fraction arithmetic growth and related student errors provides insight for why some students persistently struggle with fraction arithmetic and others do not. Identification of barriers to fraction arithmetic learning informs the development of screeners to identify those at risk for persistent fraction difficulties. Furthermore, results from this study indicate that struggling students would likely benefit from interventions that (a) are grounded in both core fraction concepts and procedures, (b) focus on differences and similarities between whole numbers and fractions to help shift students away from a whole number bias perspective of fractions, and (c) provide reinforced practice with calculation fluency and multiplicative reasoning, to help support their future fraction arithmetic success.