DOI: 10.7910/dvn/tb4qvb
title: Replication Data for: A Systematic Review and Meta-Analysis of Rational Number Interventions for Students Experiencing Difficulty with Mathematics

description: Our goal was to provide valuable information, grounded in evidence, on which aspects of rational numbers interventions were associated with positive student outcomes. We examined which instructional components (e.g., visual representations, use of number lines, teaching and using of mathematical language) and study features (e.g., group size, interventionist training) may have contributed to the effectiveness of intervention. In choosing to focus on instructional components and study features, the ﬁndings have the capacity to inform state and district leaders, as well as teachers providing intervention, on which instructional components are necessary for a rational numbers intervention to be effective.

We searched for studies that focused on teaching rational numbers concepts to students experiencing mathematics difficulties in Grades 3 through 9. Approximately 1,500 studies were identiﬁed and screened, leaving 77 reports to be screened more in-depth for relevance. Those still eligible were then screened for rigor by applying the What Works Clearinghouse (WWC) evidence standards. A total of 26 studies with 4,237 unique participants from 30 independent samples were included in the meta-analysis.

Findings indicated that rational numbers interventions are effective. The estimate of the mean effect size was statistically signiﬁcant (g = 0.65; p &lt; .001 ). To assess which specific instructional components were effective, a multivariate meta-regression model with robust variance estimation (RVE) was used. This meta-analytic technique is a contemporary and rigorous method recommended by experts in the ﬁeld. The majority of the instructional components were non-signiﬁcant at p &lt; 0.05, with the exception of the teaching and using of mathematical language (p &lt; .047), indicating that studies including this component were associated with significantly larger positive effects on mathematics outcomes. Using this rigorous approach, the signiﬁcant ﬁnding of teaching and using of mathematical language as a moderator (g = 0.57) can be interpreted with conﬁdence.

When exploring study features, we found that interventions were more effective when they were (a) implemented for students in Grades 3-6, (b) delivered to small groups of 2-6 students, (c) provided by research project personnel, (d) longer than nine hours, and even more effective when 20 hours or longer, and (e) implemented by interventionists who received ongoing training.

The results from this meta-analysis suggest that intervention programs devoting time to teaching and using of mathematical language can substantially enhance outcomes. Mathematical language is a type of abstract academic language (terms such as equivalent, reciprocal, circumference) that helps students learn mathematics concepts more precisely. When students understand and use mathematical language, it is believed that the students will more deeply understand the mathematics they are learning.

Findings from this study provide valuable information that may help educators understand effective intervention components for students experiencing mathematics difﬁculties and the conditions under which intervention is optimal. Speciﬁcally, the positive impact for teaching and using of mathematical language may guide schools and districts in choosing interventions that include this practice. Also, the impact for interventionists receiving high—quality, ongoing training may guide districts when making decisions on how to provide training and professional development to teachers who deliver intervention. Providing evidence-based intervention on rational numbers topics addresses the ever-widening achievement gap in mathematics between low- and high-performing students as they prepare for high-stakes courses like Algebra 1. Findings from this project should be considered as schools make important decisions about the provision of mathematics services to students experiencing difficulties in mathematics.