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Elementary School Math Interventions
October 2019


What does the research say about effective elementary math interventions for students who are not meeting standards?

Ask A REL Response

Thank you for your request to our Regional Educational Laboratory (REL) Reference Desk. Ask A REL is a collaborative reference desk service provided by the 10 RELs that, by design, functions much in the same way as a technical reference library. Ask A REL provides references, referrals, and brief responses in the form of citations in response to questions about available education research.

Following an established REL Northwest research protocol, we conducted a search for evidence- based research. The sources included ERIC and other federally funded databases and organizations, research institutions, academic research databases, Google Scholar, and general Internet search engines. For more details, please see the methods section at the end of this document.

The research team has not evaluated the quality of the references and resources provided in this response; we offer them only for your reference. The search included the most commonly used research databases and search engines to produce the references presented here. References are listed in alphabetical order, not necessarily in order of relevance. The research references are not necessarily comprehensive and other relevant research references may exist. In addition to evidence-based, peer-reviewed research references, we have also included other resources that you may find useful. We provide only publicly available resources, unless there is a lack of such resources or an article is considered seminal in the topic area.


Clarke, B., Doabler, C., Strand Cary, M., Kosty, D., Baker, S., Fine, H., & Smolkowski, K. (2014). Preliminary evaluation of a tier 2 mathematics intervention for first-grade students: Using a theory of change to guide formative evaluation activities. School Psychology Review, 43(2), 160–177.

From the Abstract:
"This pilot study examined the efficacy of a Tier 2 first-grade mathematics intervention program targeting whole-number understanding for students at risk in mathematics. The study used a randomized block design. Students (N = 89) were randomly assigned to treatment (Fusion) or control (standard district practice) conditions. Measures of mathematics achievement were collected at pretest and posttest. Treatment and control students did not differ on mathematics assessments at pretest. A series of random-effects models were estimated to compare gains between treatment and control conditions. Gain scores of intervention students were significantly greater than those of control peers on a proximal measure of mathematics achievement. The role of a strong theory-of-change model in the development and evaluation of mathematics interventions is articulated. Implications for researchers and educators designing and delivering instruction for at-risk students in a response-to-intervention model are discussed."

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

From the Abstract:
"Students struggling with mathematics may benefit from early interventions aimed at improving their mathematics ability and ultimately preventing subsequent failure. This guide provides eight specific recommendations intended to help teachers, principals, and school administrators use Response to Intervention (RtI) to identify students who need assistance in mathematics and to address the needs of these students through focused interventions. The guide provides suggestions on how to carry out each recommendation and explains how educators can overcome potential roadblocks to implementing the recommendations. Each recommendation is rated strong, moderate, or low based on the strength of the research evidence for the respective recommendation. Specific recommendations include: (1) Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk; (2) Committee-selected instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8; (3) Instruction during intervention should be explicit and systematic, and should include models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review; (4) Interventions should include instruction on solving word problems that is based on common underlying structures; (5) Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas; (6) Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts; (7) Monitor the progress of students receiving supplemental instruction and other students who are at risk; and (8) Include motivational strategies in tier 2 and tier 3 interventions."

Jitendra, A. K., Rodriguez, M., Kanive, R., Huang, J. P., Church, C., Corroy, K. A., & Zaslofsky, A. (2013). Impact of small-group tutoring interventions on the mathematical problem solving and achievement of third-grade students with mathematics difficulties. Learning Disability Quarterly, 36(1), 21–35. Retrieved from

From the Abstract:
"This intervention study compared the efficacy of small-group tutoring on the mathematics learning of third-grade students at risk for mathematics difficulty using either a school-provided standards-based curriculum (SBC) or a schema-based instruction (SBI) curriculum. The SBI curriculum placed particular emphasis on the underlying mathematical structure of additive problems to represent and solve word problems. At-risk students (N = 136) from 35 classrooms scoring below a proficiency level on their district accountability assessment were assigned randomly to treatment groups. Results indicated interaction effects on the word problem-solving (WPS) posttest and retention tests such that SBI students with higher incoming (pretest) WPS scores outperformed SBC students with higher pretest scores, whereas SBC students with lower pretest scores outperformed SBI students with lower pretest scores. No effects were found on number combinations automaticity, and mathematics and reading achievement. Implications to improve the problem-solving performance of at-risk students are discussed."

Powell, S. R., & Fuchs, L. S. (2015). Intensive intervention in mathematics. Learning Disabilities Research & Practice, 30(4), 182–192.

From the Abstract:
"Students who demonstrate persistent mathematics difficulties and whose performance is severely below grade level require intensive intervention. Intensive intervention is an individualized approach to instruction that is more demanding and concentrated than Tier 2 intervention efforts. We present the elements of intensive intervention that teachers should consider when planning for, implementing, and monitoring intensive intervention in mathematics. Each of these elements is based on evidence from validated interventions. We also highlight strategies for intensifying instruction. We provide two examples of intensive intervention, one of which launches from a Tier 2 intervention platform and the other which is completely generated by a teacher. We conclude with considerations for intensive intervention in mathematics."

Smith, T. M., Cobb, P., Farran, D. C., Cordray, D. S., & Munter, C. (2010). Evaluating math recovery: Assessing the causal impact of Math Recovery on student achievement. Society for Research on Educational Effectiveness.

From the Abstract:
"The authors' goal was to evaluate the potential of Math Recovery (MR), a pullout, one-to-one tutoring program that has been designed to increase mathematics achievement among low-performing first graders, thereby closing the school-entry achievement gap and enabling participants to achieve at the level of their higher-performing peers in the regular mathematics classroom. Specifically, the research questions were as follows: (1) Does participation in MR raise the mathematics achievement of low performing first-grade students?; (2) If so, do participating students maintain the gains made in first grade through the end of second grade? The two-year evaluation of Math Recovery was conducted in 20 elementary schools (five urban, ten suburban and five rural), representing five districts in two states. Students were selected for participation at the start of first grade based on their performance on MR's screening interview and follow-up assessment interview. The authors recruited 18 teachers to receive training and participate as MR tutors from the participating districts--all of whom had at least two years of classroom teaching experience. The findings of this study have theoretical, practical, and policy significance. Practically, the positive causal effect of MR tutoring demonstrates that programs that are diagnostic rather than scripted in nature can overcome fidelity concerns and have an impact on student early mathematics performance. Theoretically, the findings indicate that investing in tutors' knowledge of student reasoning and pedagogical content knowledge can pay off in terms of improvement in student's mathematical learning, particularly if tutors use carefully designed tools such as the MR Learning and Instructional Frameworks that codify and schematize this knowledge. With regard to policy, the authors' finding that the MR program can reduce some of the pre-K mathematics achievement gap provides an initial indication that the cost of the program per student might be justified, although further work is needed to understand why initial gains made by participants appear to diminish after tutoring ends. It is possible that the forms of arithmetic reasoning that MR develops needs to be further supported in the regular classroom to see the full benefit of this form of tutoring. Longitudinal studies that track MR students and their initially higher performing peers until the end of elementary school are needed to address this question adequately."

U.S. Department of Education, Institute of Education Sciences, What Works Clearinghouse. (2013). Elementary School Mathematics intervention report: Peer-Assisted Learning Strategies. Washington, DC: U.S. Department of Education, Institute of Education Sciences. What Works Clearinghouse

From the Abstract:
"Peer-Assisted Learning Strategies" is a peer-tutoring program for grades K-6 that aims to improve student proficiency in math and other disciplines. This report focuses on "Peer-Assisted Learning Strategies" for math. The math program supplements students' existing math curriculum and is based on peer-mediated instruction, a process whereby students work in pairs or small groups to tutor each other. During tutoring sessions, students work together on worksheets that target specific math skills, with one student designated to correct his or her partner's errors, award points for correct responses, and provide consistent encouragement and feedback. The program uses videos and teacher-provided scripted instruction to train students to engage in peer tutoring. Developers recommend that students participate in peer-tutoring sessions two to three times a week for approximately 30 minutes per session. The What Works Clearinghouse (WWC) identified 13 studies that investigated the effects of "Peer-Assisted Learning Strategies" on the math performance of elementary school students. The WWC reviewed all of those studies against group design evidence standards. One study (Fuchs, Fuchs, Yazdian, & Powell, 2002) is a randomized controlled trial that meets WWC evidence standards without reservations. The study is summarized in this report. Four studies do not meet WWC evidence standards. The remaining eight studies do not meet WWC eligibility screens for review in this topic area. Appended are: (1) Research details for Fuchs et al. (2002); (2) Outcome measures for each domain; (3) Findings included in the rating for the mathematics achievement domain; and (4) Description of supplemental findings for the mathematics achievement domain. A glossary of terms is included. (Contains 4 tables and 4 endnotes.)"

Woodward, J., Beckmann, S., Driscoll, M., Franke, M. L., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

From the Abstract:
"The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these challenges. The authors rate the strength of the research evidence supporting each of their recommendations. The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of improving mathematical problem solving in grades 4 through 8. The guide provides practical, clear information on critical topics related to improving mathematical problem solving and is based on the best available evidence as judged by the authors. Appended are: (1) Postscript from the Institute of Education Sciences; (2) About the Authors; (3) Disclosure of Potential Conflicts of Interest; and (4) Rationale for Evidence Ratings. (Contains 9 tables, 21 examples and 303 endnotes.)"

Other Resources

Coe, K. (2019). Mathematics: Menu of best practices and strategies. Washington Office of Public Instruction. Retrieved from

From the Abstract:
"This report contains not only the menu of best practices, but also foundational content describing Washington state's mathematics landscape and other initiatives designed to improve mathematics concepts and skills for all students. It describes how a Multi-Tiered System of Supports (MTSS) framework is critical for implementing a high-achieving educational system. It also explains how assessment data and reporting serve to continuously improve LAP and student outcomes. We have included a rich set of resources and references for those who wish to further explore the identified best practices."

Hanover Research. (2014). Best practices in math interventions. Washington, DC: Hanover Research. Retrieved from

From the Document:
"In the following report, Hanover Research examines best practices in math interventions across all grade levels. This report provides an overview of common practices, summarizes rigorous academic evaluations of math interventions, and concludes with profiles and evaluations of seven math intervention programs."

Pellegrini, M., Lake, C., Inns, A., & Slavin, R. E. (2018). Effective programs in elementary mathematics: A best evidence synthesis. Best Evidence Encyclopedia. Retrieved from

From the Abstract:
"This article reviews research on the mathematics achievement outcomes of all programs with at least one study meeting inclusion criteria. 78 studies evaluated 61 programs in grades K-5. The studies were very high in quality, with 65 (83%) randomized and 13 (17%) quasi-experimental evaluations. Programs were organized in 8 categories. Particularly positive outcomes were found for tutoring programs. One-to-one and one-to-small group models had equal impacts, as did teachers and paraprofessionals as tutors. Technology programs showed modest positive impacts. Professional development approaches focused on helping teachers gain in understanding of math content and pedagogy had no impact on student achievement, but more promising outcomes were seen in studies focused on instructional processes, such as cooperative learning. Whole-school reform, social-emotional approaches, math curricula, and benchmark assessment programs found few positive effects, although there were one or more effective individual approaches in most categories. The findings suggest that programs emphasizing personalization, engagement, and motivation are most impactful in elementary mathematics instruction, while strategies focused on textbooks, professional development for math knowledge or pedagogy, and other strategies that do not substantially impact students' daily experiences have little impact."

Slavin, R. E., & Lake, C. (2007). Effective programs in elementary mathematics: A best evidence synthesis. Review of Educational Research, 78(3), 427–515. Retrieved from

From the Abstract:
"This article reviews research on the achievement outcomes of three types of approaches to improving elementary mathematics: mathematics curricula, computer assisted instruction (CAI), and instructional process programs. Study inclusion requirements included use of a randomized or matched control group, a study duration of at least 12 weeks, and achievement measures not inherent to the experimental treatment. Eighty-seven studies met these criteria, of which 36 used random assignment to treatments. There was limited evidence supporting differential effects of various mathematics textbooks. Effects of CAI were moderate. The strongest positive effects were found for instructional process approaches such as forms of cooperative learning, classroom management and motivation programs, and supplemental tutoring programs. The review concludes that programs designed to change daily teaching practices appear to have more promise than those that deal primarily with curriculum or technology alone."


Keywords and Search Strings: The following keywords, subject headings, and search strings were used to search reference databases and other sources: Mathematics interventions OR math interventions, One-on-one, Small group, Elementary school

Databases and Resources: We searched ERIC for relevant resources. ERIC is a free online library of more than 1.6 million citations of education research sponsored by the Institute of Education Sciences (IES). Additionally, we searched Google Scholar and EBSCO databases (Academic Search Premier, Education Research Complete, and Professional Development Collection).

Reference Search and Selection Criteria

When we were searching and reviewing resources, we considered the following criteria:

Date of publications: This search and review included references and resources published in the last 10 years.

Search priorities of reference sources: Search priority was given to study reports, briefs, and other documents that are published and/or reviewed by IES and other federal or federally funded organizations, as well as academic databases, including ERIC, EBSCO databases, and Google Scholar.

Methodology: The following methodological priorities/considerations were given in the review and selection of the references:

  • Study types: randomized control trials, quasi experiments, surveys, descriptive data analyses, literature reviews, and policy briefs, generally in this order
  • Target population and samples: representativeness of the target population, sample size, and whether participants volunteered or were randomly selected
  • Study duration
  • Limitations and generalizability of the findings and conclusions

This memorandum is one in a series of quick-turnaround responses to specific questions posed by stakeholders in Alaska, Idaho, Montana, Oregon, and Washington, which is served by the Regional Educational Laboratory (REL) Northwest. It was prepared under Contract ED-IES-17-C-0009 by REL Northwest, administered by Education Northwest. The content does not necessarily reflect the views or policies of IES or the U.S. Department of Education, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government.