The growing and complex debate over math reforms — as well as different approaches to teaching and curricula — demands attention from stakeholders who will be setting policy and supporting instruction in the subject, according to a report released Tuesday from the Center on Reinventing Public Education.
CRPE refers to the report as a guide for these stakeholders, who include policymakers, educators and parents. The nonpartisan research and policy analysis center says the aim is to build knowledge of the issue's nuances so they can evaluate competing claims and determine which approaches fit best in their schools.
Recent “science of math” conversations follow on the heels of intense attention toward science of reading approaches for literacy instruction. The science of reading approach explicitly teaches students the connections between letters and sounds through decoding and phonetic memorization. In contrast, the three-cueing approach in reading instruction encourages students to use meaning, structure and visual cues to identify unfamiliar words.
Math and reading reforms have taken center stage in education as student performance has dipped or stagnated in recent years. On the 2024 National Assessment of Educational Progress, 4th and 8th grade math performance was below pre-COVID-19 results from 2019.
But, unlike the general consensus reached on science of reading approaches, the science of math movement is far from settled, the 60-page report said.
"There is a debate around conceptual understanding versus procedural fluency, so we pit one thing against the other, but the reality is a lot more complicated," said Alexander Kurz, co-author of the report and senior fellow at CRPE.
Understanding the intricacies of the math of science debate will "sharpen the discussion and crystallize some of the next steps" for educators, policymakers and other stakeholders, Kurz said.
Here are a few highlights of what the report says needs to be understood about the science of math.
What is the “science of math”?
The science of math is a research-driven movement, and supporters say math instruction should be guided by empirical research and cognitive science — a goal shared by researchers, advocacy organizations and educators.
In the classroom, science of math approaches include explicit instruction with structured, teacher-led lessons, guided practice on math problems, and corrective feedback to students. But it is not a call for rote memorization of math formulas or that students spend 100% of class time listening to teacher lectures.
The movement also emphasizes that there's not a one-size-fits-all, evidence-based practice for all students. Proponents say these approaches are especially relevant for students with disabilities and struggling learners.
The movement has drawn criticism from prominent math organizations that argue the approach "misapplies research and promotes too narrow a vision of what teaching could be," according to CRPE's report. There is also unresolved consensus about what is considered strong scientific evidence and whose professional expertise should guide math instruction decisions.
What are the "math wars"?
The science of math is part of the ongoing "math wars" in education over what students should learn and how math should be taught. The issue dates back to the early 1900s with the debate about whether foundational education should prioritize the knowledge and experience of the teacher and a formal curriculum, or whether students' needs, interests and abilities should be at the starting point.
The two factions within the math wars are known as traditionalists and reformers. The traditionalists, for example, favor procedural fluency over conceptual understanding and prefer explicit instruction over discovery learning. The reformers prioritize conceptual understanding over procedural drills and favor inquiry-based learning over direct instruction.
But what Kurz found was that in the present day math wars debate, the research shows competing recommendations into what approaches are effective. And, he said, it's not fair to ask teachers to reconcile those differences.
"Who gets to decide on the evidence is now a new question," Kurz said.
There are also areas of agreement between the traditionalists and reformers. For instance, both sides agree students need fluency and understanding, that learners' needs vary, and that teachers need dedicated preparation and support.
What approaches are schools taking?
An FAQ produced by CRPE to accompany the report said that asking more specific questions is the most productive response to conflicts in math instruction guidance. Among the possible questions:
- What exactly is the claim?
- Which students does the evidence apply to?
- What kind of research supports it, and what does it leave out?
Nationally, states are honing their math instructional approaches with a focus on more structured and intervention-focused approaches, but the states differ substantially in scope, intensity and emphasis, the report said.
CRPE's research found that as of late 2025, 18 states and the District of Columbia enacted math policies since 2022. States like Alabama, Maryland, Iowa, Kentucky, Mississippi and Oklahoma have approved broad, multi-component packages that reflect several science of math themes, the report said.
States are also making more targeted reforms. Florida and Kentucky, for instance, prioritize the identification and support for students with math difficulties, including dyscalculia. Texas and New Mexico's policies seek to expand access to advanced courses.
California, on the other hand, updated its math framework in ways that seem more reform-oriented by placing emphasis on discovery learning, group work and sociocultural responsiveness while putting less priority on memorization and direct instruction, CRPE's report said.
As the math wars and, specifically, the science of math debates continue to ramp up, Kurz cautions about a "forever math war" if there is continued polarization of math instruction. More quantitative and qualitative research into math instructional approaches are needed, as is a better understanding of the middle ground, he said.
"If you want to issue broad guidance about how to teach math to an entire state or entire nation, you better have more than just anecdotes," Kurz said.
"It is not sufficient to say, ‘Well, both sides matter.’ This doesn't tell teachers what exactly to do Monday morning," he said. "That's where we need to take a stance.”
