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Impacts of rational number interventions among U.S. students in Grades 3 through 9 with mathematics difficulties are examined using a systematic review and meta-analysis. The primary goal of the meta-analysis was to identify instructional practices that are key drivers of student impacts. From approximately 1,200 published and unpublished study records, we identified 28 studies that met our inclusion criteria and coded the interventions for their instructional practices, intervention characteristics, and study design features. The random-effects mean effect size across all 28 studies (90 effect sizes) was 0.68 ( SE = 0.08, p < .001, 95% confidence interval [CI]: [0.51, 0.85]). The 95% prediction interval was −0.36 to 1.8. Using meta-regression techniques, we found the teaching of mathematical language ( β = 0.50) and the use of the number line ( β = 0.47) during intervention to be significantly associated with positive impacts when adjusted for controls. We discuss implications for intervention practice and study limitations along with the challenges of examining complex, multifaceted interventions.

Using a randomized controlled trial, we examined the effect of a fractions intervention for students experiencing mathematical difficulties in Grade 5. Students who were eligible for the study ( n = 205) were randomly assigned to intervention and comparison conditions, blocked by teacher. The intervention used systematic, explicit instruction and relied on linear representations (e.g., Cuisenaire Rods and number lines) to demonstrate key fractions concepts. Enhancing students’ mathematical explanations was also a focus. Results indicated that intervention students significantly outperformed students from the comparison condition on measures of fractions proficiency and understanding ( g = 0.66–0.78), number line estimation ( g = 0.80–1.08), fractions procedures ( g = 1.07), and explanation tasks ( g = 0.68–1.23). Findings suggest that interventions designed to include explicit instruction, along with consistent use of the number line and opportunities to explain reasoning, can promote students’ proficiency and understanding of fractions.

A formative pilot study of a fractions intervention was conducted to address the intervention's potential for improving fifth‐grade struggling students’ knowledge of fractions, and to identify any logistical or instructional design issues, before scaling up for a randomized control trial. In the first section, we provide details of the formative pilot study and present preliminary data that demonstrate the potential of the intervention. Intervention lessons—adapted from a commercially available program—emphasize consistent use of the number line in conjunction with concrete representations to scaffold learning and facilitate understanding of grade‐level and foundational fractions content. We explain how intervention revisions were guided by the formative evaluation. In the second section, we present key concepts that distinguish understanding fractions principles from understanding whole number principles. These concepts relate to understanding foundations of fractions (e.g., magnitude, equivalence, part‐whole, and measurement) and the four operations. We present these key concepts and show how the fractions intervention addressed them as a guide to practitioners for teaching new and difficult fractions content, as students integrate fractions understanding with their understanding of whole numbers.