Evidence-Based Instructional Principles and Sequences for Effective Fraction Instruction

Abstract

Fraction proficiency is a critical milestone for students to reach, as fraction knowledge strongly predicts later math achievement. However, fractions are notoriously difficult for students to learn. The first study in this dissertation reviewed commonly used math curricula to determine if their fraction lessons used evidence-based instructional strategies. The results showed several strengths of the curricula, including sufficient prerequisite skill practice, instructional examples of fraction concepts, and practice opportunities. However, the curricula also needed more explicit instruction of fraction concepts and procedures. In addition to using evidence-based instructional principles, the order of conceptual and procedural instruction may also affect students’ learning and generalization of fraction skills. The second study in this dissertation compared the effect of two instruction sequences, concepts-first and iterative, on fraction performance during a classwide intervention. Fourth-grade students (N=114) were randomly assigned to the concepts-first, iterative, or control group. The primary conceptual assessment showed that the iterative and concepts-first groups performed similarly, demonstrating medium effect sizes compared to control. The primary procedural assessment again demonstrated that both intervention groups outperformed the control, this time with large to very large effects. Additionally, the iterative group outscored the concepts-first group with a medium effect size, though it was not statistically significant. Generalization assessments measuring skill transfer found no differential effects. Overall, iterative instruction was at least as effective as a concepts-first sequence during a fraction intervention. The implications of these findings for fraction instruction and the sequencing of conceptual and procedural instruction more generally are discussed.