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Best Practices in K–12 Math Interventions

With a historic national decline in math scores, K–12 districts must embrace innovative math interventions and instruction. Use these practices to improve student outcomes.

When the National Center for Education Statistics released the 2022 Nation’s Report Card, it confirmed what educators already feared. Decades of lost progress exacerbated by the pandemic had resulted in historic declines in reading and mathematics scores. With math scores taking the largest hit, K12 districts across the country face a critical question. How can they close the widening learning gaps through math intervention programs?

According to the latest data, only 37% of fourth graders and 27% of eighth graders are proficient in math. Of course, much of this decline stems from COVID-19’s disruption of student learning experiences. Yet, in truth, math scores were already declining years before the pandemic. To help all students get a solid foundation in math skills, districts and schools must embrace better math instruction and math intervention programs — ones based on solid research and data. 

School districts face many academic intervention decisions, and choosing a mathematics intervention is critical. In the last decade, a variety of approaches, tools, and technologies for teaching math have popped up with promises to significantly improve students’ abilities. Unfortunately, not all of them work or are implemented in a way that guarantees effectiveness. Many districts have remedial programs or intensive tutoring in place that are helping some students make gains. But more must be done to help all students recover or, better yet, surpass pre-pandemic achievement levels. 

To begin, let’s look at best practices for effective math interventions. These approaches are based on findings from a variety of education national councils, associations, and research centers. 

Common Characteristics of Effective K–12 Math Interventions

Districts with effective math intervention programs share some common characteristics that educators can look to when trying to improve students’ performance in their districts, including:

  • Universal screening. The American Institutes for Research and the What Works Clearinghouse recommend that educators screen all students to identify those in need of supplementary assistance. 
  • Explicit and systematic instructional methods. What Works and the National Council of Teachers of Mathematics found that explicit and systematic instructional methods are also highly effective strategies. 
  • Data‐based decision making. Using data to drive decision-making is another common theme that unites recommendations from research centers, including Institute of Education Sciences, and the National Center on Intensive Interventions. 
  • Consistent retrieval of basic arithmetic facts and a systematic approach to problem types. Regular attention to basic operations and problem-solving strategies (e.g., identifying patterns or clue words, using formulas, drawing, estimating) effectively build competencies. 
  • Early detection and remedy of math difficulties, along with nurturing students’ confidence. Researchers agree that elementary school math interventions are essential to avoiding later challenges. Because math gets increasingly complex and abstract with each grade level, detecting and addressing math difficulties early on is critical to building positive learning experiences and eliminating future struggles.
  • Engaging tactics, such as role‐playing or technology‐assisted learning. While engaging students is viewed as a top priority, best practice interventions typically emphasize distinctive qualities, such as mastering word problems or improving proficiency with fractions. 

To make even more math learning gains, here is a selection of specific practices we’ve seen districts use with success when implemented thoughtfully and with a data-mindset. 

Use data to investigate your district’s achievement gaps with guidance from Hanover’s Academic Equity Workbook. 

Math Intervention Strategy 1: Collective Mathematical Reasoning

Collective reasoning is an approach in which the teacher facilitates discussion about mathematical content. Randomized control studies have found that experimental student groups outperformed control groups in their understanding of number sense in early childhood education settings and algebraic and fractional thinking in elementary settings. Other studies have demonstrated the benefit of collective reasoning in integrating social and emotional learning in preschool mathematics. 

Math Intervention Strategy 2: Developing Math Self-Concept

Math self-concept refers to how people think of themselves in relation to math. Interventions that strengthen math self-concept have proven successful for improving academic engagement and achievement. Cross-sectional and longitudinal studies indicate that the links between math self-concept and achievement are reciprocal and robust across varying age groups. This has been demonstrated around the world, including in Germany, China, Spain, and the U.S.  

Math Intervention Strategy 3: Personalized Learning with Technology-Based Interventions

With technology, many studies have reported success in math interventions that incorporate game-based and personalized learning strategies. Personalized learning empowers students to direct their own learning experiences, with corresponding increases in motivation and achievement. Experimental studies of transitional kindergarteners and kindergarteners and of kindergarteners and first graders found that a personalized learning app increased students’ interest and engagement in learning. Meanwhile, students in the experimental group significantly outperformed the control group in math knowledge and skills.  

In addition, a recent meta-analysis of apps targeting students in pre-K through third grade found that digital apps had significant positive effects on math skills. However, educators caution that successful apps are based on high-quality activities that rest on research-based principles. In particular, the most successful apps foster active, engaged learning. They’re also supported by social interactions and clear learning goals, as well as focused, deliberate practice with regular feedback and varied activities and contexts. 

Math Intervention Strategy 4: Socially and Culturally Responsive Interventions

Some schools have accomplished gains in math performance by shifting to more socially oriented or culturally informed approaches. For example: 

  • Benjamin Franklin Elementary in Meriden, Connecticut, managed to achieve small gains in state test results during the COVID-19 pandemic by moving from lessons dominated by teachers writing problems in front of the class to a peer studying approach in which students wrestle with problems in pairs or small groups.  
  • Math Corps, an AmeriCorps intervention program for fourth through eighth graders, showed promising results in a recent experimental study. It identified higher achievement scores among Math Corps students and greater probability of reaching grade-level benchmarks, although differences in state test scores were not significant. 
  • A 2021 study investigating the effects of culturally informed communal contexts for African American third and fourth graders demonstrated that students who learned fractions in the communal group outperformed those who learned individually. 
  • Another study found that Hispanic/Latino second grade English language learners exhibited improved math problem solving and math vocabulary acquisition when culturally relevant information and their native language was incorporated into instruction. 

As districts downshift from the acute operational crises of COVID-19, there is a terrific opportunity to double down on fundamental math skill-building for students. Look for approaches that not only enhance their mastery of subject-matter fundamentals, but that also help them see themselves as capable, confident, and eager learners, no matter the subject. 

Learn how to launch any new intervention or program with success. Download the Successful Program Implementation Toolkit.

Author Information

Research Consultant, K–12 Education
View All Author Information
Education: BA, Anthropology, Howard University; MA, Anthropology, University of Pennsylvania
Areas of Expertise: Qualitative Research, Anthropology, K–12 Education

Kenya is a trained anthropologist and social services provider with over 14 years of practical experience in the K–12 sector. She has worked extensively with diverse student and parent populations, including developing literacy and STEM curricula, serving on school curriculum and climate committees in the Philadelphia School District, developing and implementing a school-based case management model for at-risk students and families, advocating for students in the juvenile court system, leading parent and community outreach, and creating and overseeing service learning and social and emotional learning initiatives. She has also served as an adjunct faculty at Widener University and Community College of Philadelphia.

"K–12 education is facing unprecedented challenges. I am passionate about using robust qualitative and mixed-methods research to highlight solutions for issues impacting academic equity, school safety and security, educational technology, staff satisfaction and retention, social and emotional learning, and special education."
Math interventions in K–12 schools are critical to overcome pandemic-related learning loss and help students on the road to academic recovery, using innovative mathematic programs and instructional methods.

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