Research: Defining High-Quality Instructional Materials for Math

July 14, 2025

Math achievement in K-12 education is closely tied to graduation rates, college enrollment, and future earnings. Early math skills provide a critical foundation for success in careers, college, and technical training. Research by Johns Hopkins University’s Robert Balfanz and colleagues shows that 81% of students who fail a math class in sixth grade do not graduate from high school. According to the Federal Reserve Bank of Cleveland, the more math students take in high school, the more they earn on average, and the more likely they are to have a job.

However, the 2023 Trends in International Mathematics and Science Study (TIMSS) results reveal troubling gaps in U.S. student performance. Only 13% of U.S. fourth graders reached or exceeded the advanced international benchmark in math, compared to 49% in Singapore and 32% in Japan. Meanwhile, about 17% of U.S. fourth graders scored below the low international benchmark—far higher than rates in Japan (1%), Norway, Sweden, and Denmark (5%), and Finland and Germany (6%).

According to the U.S. Department of Education’s Institute of Education Sciences (IES), “on average, disadvantaged students received less effective teaching than other students, equivalent to about four weeks of learning for reading and two weeks for math, or about 2 to 4 percent of the student achievement gap between these groups.” These disparities underscore the urgent need for educators and policymakers to intensify efforts to help disadvantaged students reach or exceed grade-level expectations in math.

DEFINING HIGH-QUALITY INSTRUCTIONAL MATERIALS

The shortage of effective math teachers, weak early childhood math foundations, low expectations, and the lack of rigorous, well-designed instructional materials all contribute to poor math achievement among students. Research by the Council of Chief State School Officers consistently shows that high-quality instructional materials (HQIM) can strengthen teaching practices and improve student outcomes in both reading and math. However, access to effective instruction—particularly for disadvantaged students—varies widely across school districts, according to IES.

A key reason for this disparity is that many school and district leaders lack a shared understanding of what qualifies as HQIMs. A 2024 Gallup survey of nearly 1,500 principals and district leaders found that only one in four reported their school or district has an official definition of HQIM.

Nearly 4 in 10 said they were “not very” or “not at all familiar” with the term. When asked what resources they use to judge instructional materials, leaders cited a mix of sources: 83% referenced state guidelines, 58% relied on teacher feedback, 55% used district guidelines, and 54% turned to independent curriculum reviewers.

Without a clear and consistent understanding of HQIM, education leaders may struggle to help teachers implement research-based, standards-aligned curricula and ensure all students receive rigorous math instruction. For this reason, establishing a clear definition of HQIM—especially for math—should be a top priority for school and district leaders.

DEFINITIONS OF HQIM FOR MATH

Many states have developed their own definitions of HQIM. For example, Maryland defines it as “grade-level, standards-aligned materials designed to build knowledge for all students in a language-affirming and culturally responsive way.” In Massachusetts, they are described as comprehensive, core teaching and learning resources that are aligned with grade-level standards, evidence-based, and intended to support culturally and linguistically responsive instruction for all learners.

While there is broad agreement that alignment to state standards is a key foundation for identifying these materials, researchers at the advocacy organization EdTrust emphasize that a truly robust definition goes beyond this. In mathematics, HQIM should:

• Align with state grade-level standards and be both rigorous and evidence-based.
• Provide a range of supports that help all students access grade-level content, including daily opportunities to build conceptual understanding, develop procedural skills and fluency, and apply their knowledge to real-world problems.
• Offer clear guidance for effective implementation and include high-quality assessments that measure both conceptual understanding and application skills.

SCHOOL BOARDS PLAY A ROLE

School boards play a crucial role in shaping HQIM by working closely with superintendents, principals, and district curriculum experts. Drawing on the comprehensive findings of the National Mathematics Advisory Panel, the latest HQIM research, and state-level definitions, NSBA’s Center for Public Education (CPE) recommends that school boards lead discussions in the following 10 key areas to strengthen the selection and use of HQIMs:

1. Alignment to standards: Do the materials align with rigorous, grade-level math standards, ensuring content is appropriate and builds on prior knowledge?
2. Conceptual understanding: Does the curriculum promote deep understanding of mathematical concepts—not just rote procedures—using clear explanations, visual models, and real-world applications?
3. Coherence: Does the curriculum support instructional coherence by ensuring that materials, assessments, and professional learning align with the district’s broader instructional strategy and goals?
4. Engagement and relevance: Do the materials feature engaging, culturally responsive, and relevant tasks that motivate students and connect math to their daily lives?
5. Differentiation: Does the curriculum provide scaffolds for struggling learners and enrichment opportunities for advanced students, meeting diverse learning needs?
6. Practice and application: Do the materials include varied and purposeful practices such as fluency exercises, problem-solving tasks, and opportunities to apply concepts in new contexts?
7. Assessment tools: Does the curriculum offer both formative and summative assessments to monitor progress, provide feedback, and inform instruction?
8. Teacher support: Do the resources provide clear guidance for teachers, including lesson plans, instructional strategies, and access to professional development?
9. Evidence-based design: Are the materials grounded in research on how students learn math?
10. Accessibility: Are the materials designed for all learners, with features such as clear fonts, multilingual support, and compatibility with assistive technologies?

In short, while there is no one-size-fits-all curriculum, defining HQIM is a crucial first step for school leaders to set a clear vision for improving math outcomes. By asking thoughtful questions, school boards can help educators to build a shared understanding of what truly qualifies as HQIMs. 

CPE will release a full report on this topic during the Council of Urban Boards of Education (CUBE) Annual Conference in September, where there will be a related education session.

Jinghong Cai, Ph.D., is the senior research analyst at NSBA’s Center for Public Education.