Last December, several members of a national organization for math education leaders came together to issue a warning.
A growing movement in the field, they claimed, was calling on schools to adopt an “impoverished” approach to math teaching that would strip students of their autonomy and relegate them to “mimicking their teacher.” Proponents of the movement were misapplying educational research, they said.
In the field of math education, long plagued by heated pedagogical debates, the position paper from the National Council of Supervisors of Mathematics has kicked off another round of conversations about what practices work best in the classroom—and what the subject’s ultimate goals even are.
And it serves as evidence that conversations about how schools should consider and apply research, a question at the core of the ongoing “science of reading” movement, are now spreading across the math field, too.
Debate over best practices in math education is far from new, said Jon Star, a professor of educational psychology at Harvard University who studies how children learn math. “This has been debated for over 100 years in math education in the U.S. It seems to flare up every once in a while, and we seem to be in one of those flare-ups.”
The stakes are particularly high now, though, as nationwide math scores have flatlined after large post-pandemic drops, following more than decade of declines. In response, more states are mandating “evidence-based” methods to teaching the subject. And that means that what the field views as research-backed, something that’s currently in contention, could have far-reaching consequences.
Rachel Lambert, an associate professor in special education and mathematics education at the University of California Santa Barbara, and one of the writers of the NCSM position paper, said the goal of the document isn’t to restart the math wars. It’s a framing she says is “counterproductive.”
Still, the statement calls on math teacher leaders to “take a stand” against what it describes as the “misapplication of research.”
“It doesn’t feel like there’s an effort to try to identify places for common ground in the work,” said Julie Cohen, an associate professor in the University of Virginia’s School of Education and Human Development, who has studied ideological divides in math education.
“It troubles me, in part because I think it’s reinforcing this idea of camps instead of providing shared understandings in service of supporting kids.”
What is the ‘Science of Math’ movement?
The target of the NCSM statement is the “Science of Math” movement, originated in the early 2020s by a group of mostly special education researchers and school psychologists in the wake of the “science of reading” movement.
The Science of Math’s aim, as outlined on the group’s website, is to use “objective evidence about how students learn math to make educational decisions and to inform policy and practice.” An affiliated Facebook group numbers more than 35,000 members.
Among other practices, the Science of Math website promotes explicit instruction, a method in which teachers explain and model new concepts and procedures step-by-step and then ask students to practice them. It’s a myth, they say, that inquiry-based approaches boost outcomes for all kids.
Explicit instruction lays a crucial foundation, especially for students who struggle, and can equip students with the skills they need to tackle more complex problem-solving, said Sarah Powell, a professor of special education at the University of Texas at Austin, and one of the founders of the Science of Math movement.
“It’s really, really difficult to actively engage in problem-solving when you still struggle with, what does it mean to add, how to compare fractions, how do I deal with a system of equations?” Powell said.
The NCSM paper argues that explicit instruction has some value in math teaching, but that it should be minimized. (It is not a new criticism: the Science of Math’s embrace of explicit instruction has previously placed the group into the math establishment’s crosshairs. A separate statement earlier in 2025, from a collection of math education organizations including the National Council of Teachers of Mathematics, criticized what it called an overemphasis on the method.)
Instead, the predominant approach, NCSM says, should be “guided inquiry, in which teachers provide structure and support in well-designed inquiry-oriented activities.”
The statement calls explicit instruction a “pedagogy of poverty,” arguing that it is more commonly used in schools in low-income areas, systematically denying these children opportunities for discussion and collaborative problem-solving.
Math has “long been taught in a way that turns people off,” said Lambert.
An over-reliance on explicit instruction could reinforce that problem, she said. If it’s the only approach that students experience, she added, “then they’re not allowed to think.”
In practice, researchers on both sides of this divide acknowledged, the distinction is rarely so clear cut in the classroom: Guided inquiry should include moments of explicit instruction. Good explicit instruction should incorporate time for meaning-making and student reflection.
But debates continue over how to prioritize and sequence these two types of teaching, and over the conceptual underpinnings of each approach: Are there foundational processes, like adding multi-digit numbers, teachers must explain directly before students can move on to more complex problem-solving? Or does doing so inherently short-circuit the development of problem-solving skills?
The argument isn’t just ideological, though. The NCSM paper and the Science of Math group dispute how to interpret the studies the latter group has highlighted and how to translate them into daily instruction.
What does the research say about explicit instruction and inquiry-based learning?
There’s a lot of evidence to suggest that good math instruction includes some explicit instruction and some more student-led problem-solving. Practice guides from the U.S. Department of Education’s Institute of Education Sciences offer a clear example of this.
The guides, which summarize research on different instructional topics, promote a mix of strategies for supporting students who are struggling in math.
A guide for improving mathematical problem-solving in grades 4-8, for example, suggests explicitly teaching students how to use different visual representations of quantities in different kinds of word problems and walking them through the process step-by-step. But it also directs teachers to use a combination of problem types that students have seen before and “non-routine” problems that aren’t as predictable.
Still, recommendations in the guides usually assume some explicit instruction comes first, and then students problem-solve after.
Many of the studies that support these recommendations are experimental or quasi-experimental, meaning that researchers can draw causal claims about quantitative outcomes—using these practices helps students do better on standardized tests.
But the NCSM statement argues that the research base in math is broader than just studies of interventions that lead to quantitative results. “Such a narrow definition of ‘evidence’ distorts what is viewed as ‘scientific’ and ignores most of the research on the learning, teaching, and experiencing of mathematics,” it reads.
Understanding how to solve problems on a test is only “one sliver” of the goals of math education, said Charles Munter, an associate professor of learning, teaching, and curriculum at the University of Missouri, and an author of the NCSM statement. A primary focus on test scores, he said, “is only further contributing to and reinforcing a way of doing education right now in this country and many countries that is largely a bad idea.”
This perspective frustrates Powell, though, who says it ignores the realities in which states, districts, and educators exist.
“It seems a little nonsensical to say we’re not concerned with raising scores,” she said, “when that’s how kids are judged in the United States, whether we like it or not.”
How teachers find a balance
In the classroom, things are often less ideological.
“There needs to be a balance of both,” Ashley Davis, a 4th grade math teacher at Central Intermediate School in Central, La., said of explicit instruction and inquiry. “I don’t think one is right and one is wrong. When both are used properly, they’re both super effective—regardless of the students.”
Over the past 30 years, leading organizations in the field have promoted a more inquiry-forward approach to math. Popular curricula tend to emphasize problem-solving and discussion of mathematical ideas.
Davis thinks these are good goals. She wants her students to be able to use math flexibly in their everyday lives. But she wants her students to do well on standardized assessments, too. “In a school setting, there’s really only so many ways you can prove that they know it,” she said. “And it’s through unit tests and state tests.”
There are times when she introduces a new concept through discovery, Davis said, like when she started a lesson about equivalent fractions. She gave students pieces of paper and asked them to fold them in half, and then in half again and again, and asked them what they noticed. Her students—an inclusion classroom with a mix of general and special education students—figured out that 1/2 was equivalent to 2/4, which was equivalent to 4/8.
When she introduced the mathematical notation to represent these concepts, students picked it up right away, because they had already grasped the conceptual underpinnings, Davis said.
“There are other instances where I can think of, where you have to explicitly teach something, so they can then use inquiry later on,” she said—how to use an area model for multiplication of multi-digit whole numbers, for instance.
More broadly, some high-profile education leaders have made clear that their vision for math teaching necessarily includes explicit instruction—even if the materials teachers are using lean more toward problem-solving and discovery.
Kamar Samuels, the new schools chancellor in New York City, said earlier in January that schools would be making “tweaks” to existing middle and high school math curricula that emphasize inquiry-based learning and discussion, so as to ensure that all students have mastered basic arithmetic. “You want automaticity, you want to be able to do that fast, or else you’re going to struggle,” he said during a visit to a New York City high school, Gothamist reported.
Still, there’s often little guidance about how to negotiate and sequence these two priorities to lead to the best outcomes.
Some work has tried to fill that gap. Last year, for example, a group of researchers in cognitive psychology and special education published research-based recommendations to get students fluent with math facts, integrating both explicit instruction and what they describe as “cognitive reflection.”
“Too often,” they write, “recommendations for a ‘balanced’ approach lack the depth and specificity needed to effectively guide educators or inform public understanding.”
Getting this balance right is hard, and there’s not always a roadmap, said Star, the Harvard professor: “We as a field could be better at guiding teachers toward what that mix looks like.”
