NCTM position paper ignores reality of math teaching challenges

Suggestions on how to ‘change the culture of math teaching’ aren’t supported by evidence

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Using evidence to improve the ‘culture of math teaching’

In my two-year investigation into why so many students aren’t proficient in math, I have focused a lot on math teaching—it’s not the only driver of lagging achievement, but a significant one. My reporting has shown that, in many ways, early math teachers have been failed by their prep programs similar to what we’ve seen with early reading teachers. Often they’ve been given ineffective tools for teaching math. Making things worse, many elementary school teachers have low confidence in their own math ability, causing them to spend less time on it in class compared to reading.

A recent survey of teacher prep programs from the National Council on Teacher Quality (NCTQ) revealed that many undergraduate teaching programs don’t teach nearly enough math content to future teachers; graduate-level programs cover hardly any math content at all. In addition, few teachers in training are taught how the human brain learns. Simple lack of knowledge might be a core driver of many elementary teachers’ own math anxiety.

Once teachers are in classrooms, they often don’t know how to help students who struggle with math, for a variety of reasons—understanding and recognition of math disabilities is less well-known than reading disabilities, along with perhaps a combination of lackluster preparation and a majority of states that don’t require schools to provide support for struggling math students.

This long wind-up is a way of saying that there are several significant issues with math teaching, and they’re likely affecting how well students are performing in math. Which is what makes a new position paper from the National Council of the Teachers of Mathematics (NCTM), “Changing the Professional Culture of Teaching Mathematics,” come off as defiantly tone-deaf, as it concerns itself very little with neither teaching nor math.

The advocacy group, which boasts some 70,000 educator members, wrote to them in June:

“For too long, the culture of teaching mathematics has narrowly defined mathematical competence. This limited view often ignores the diverse ways different cultures learn and express understanding, such as through storytelling, collaborative problem solving, and practical applications. Without exposure to these varied approaches, educators may overlook students whose mathematical abilities shine in non-traditional ways, ultimately leaving many capable learners unrecognized and unsupported. The culture of teaching mathematics must shift from coursework being the gatekeeper to advanced mathematics and career aspirations to all educators valuing the community and integrating that knowledge into mathematics teaching and learning. If educators collaborate and investigate their personal beliefs and teaching practices, they can improve classroom experiences where mathematics is more relevant to students’ lives and, as a result, students will see themselves and their peers as powerful mathematical thinkers and doers.”

The professional culture of math teaching, the group goes on to say, needs reform—but many of their prescriptions aren’t based on the available evidence of what produces more competent math students. Instead, what’s found in this position paper are suggestions that rely heavily on belief and emotion instead of evidence. I’m having a really hard time trying to figure out how ideas like teachers “investigating their personal beliefs” is going to meaningfully change math learning for students. It’s not that that’s not possible, it’s that the call to action is so vague and means so many different things to so many people, how could it meaningfully change classroom practice at scale? How could it reform the entire culture of math teaching?

Other suggestions in the paper on how to change teaching’s culture—like improving teachers’ math knowledge, and drawing on what students already understand about math—are good, and on the margins, based in evidence. But that crucial evidence for improving math knowledge, or activating students’ background knowledge, aren’t mentioned, or connected to why they’re important to do.

From the first paragraph, NCTM’s position makes it clear that a positive development for the ‘culture of math teaching’ would be for math teachers to become much less concerned with whether students can do actual math. How else to interpret the idea that students will be doing some other kind of math that allows them to shine in ways current methods aren’t? If a student uses storytelling to solve a math problem—something I’d argue that math teachers are working on with students every day in the form of story problems, one of the most difficult pieces of math learning—are those students doing a different kind of math, one that is more aligned with their culture? One that a teacher must train themselves to recognize? Or are they just doing story problems, which schools already recognize as a valuable thing for students to learn?

Students’ dismal math performance can’t be blamed solely on math teaching, of course—but considering how few students come out of k-12 schooling proficient in math, it’s worth asking why more hard evidence on what works isn’t included here.

I’ve been ruminating on the NCTM position statement this week in light of an essay by two University of Toronto professors, Nidhi Sachdeva and Jim Hewitt, earlier this week on how teaching is not yet a science-based profession. That truth is on full display in this position paper—unlike medicine and engineering, teachers are rarely presented with the existing evidence to help shape what they do in classrooms.

Sachdeva and Hewitt wrote:

“In medicine, new treatments are developed through a disciplined process of research, controlled testing, evaluation, and refinement. The benefits of this approach have been obvious. Life expectancy has increased dramatically. Deadly diseases have been eradicated or brought under control. We now have minimally invasive surgeries, advanced diagnostics, and targeted therapies that would have been unimaginable just a few generations ago.

“Education, on the other hand, lacks this cycle of progressive improvement. In spite of decades of reform and billions spent on improvement initiatives, it’s not clear that teachers are any more effective today than they were fifty years ago. While the curriculum has evolved over that period, it would be difficult to claim that the quality of education has significantly improved or that the gap in student outcomes has narrowed substantially.”

Below I’ve taken a few of the paper’s statements and looked at how they might look different if the evidence was included. I think in math we’ve got a long way to go when it comes to letting go of ideas that are akin to educational blood-letting, and making education an evidence-based profession.

* NCTM’s claim that teachers should see all students as competent in mathematics is a good one, and it’s important to believe in students’ ability to improve. But that belief does no good without teacher math knowledge.

“Teachers continually strengthen and deepen their mathematical content knowledge and mathematical knowledge, so that students’ thinking can be productively expanded. Collaborative efforts among educators can significantly enhance their understanding of mathematical concepts and mathematical knowledge for teaching (MKT).”

To their credit, NCTM’s focus on teachers improving their math content knowledge is based in evidence. My reporting has shown that elementary teachers are often weaker in their math knowledge compared to reading, and that both undergraduate and graduate teacher prep programs don’t cover math content knowledge thoroughly, especially in the very basic “numbers and operations” category.

Many math teachers I’ve interviewed support this claim—in recent interviews, math teachers say that much of their graduate school preparation was focused largely on theories of education and philosophy, not evidence and concrete practices on math content and how to teach math.

Once in the classroom, the focus on increasing teacher math knowledge doesn’t get better. Teachers said in a recent RAND survey that they spend very little time increasing their math learning—half of all teachers say they spend less than two hours a month on professional learning in math content.

“There is definitely math anxiety and avoidance going on with elementary school teachers,” University of Southern California associate professor of education Yasemin Copur-Gencturk recently told EdSurge. Teacher math knowledge seems to be a high priority to help improve student math learning, and NCTM should take a look at what all the evidence suggests are strong ways to do that.

* Vague teacher tactics like “valuing the community,” aren’t supported by any current research on how students learn math—and are impossible to measure. Teachers might be better off learning how the brain learns and about evidence-based teaching methods.

“When the culture of the mathematics teaching profession shifts to value continuous improvement and students'/families' mathematical ways of knowing, each and every student will be able to see themselves as brilliant doers of mathematics.”

There’s certainly value in educataors appreciating the communities where they teach. But when it comes to helping students improve their actual math skill, it is likely more valuable for teachers to have a basic understanding of how the brain learns, and how those general tenets apply to student learning. All students, no matter which community or culture they hail from, learn math in similar ways.

Understanding the concept of biologically primary and secondary knowledge, the role of working memory and long-term memory in learning, how background knowledge informs learning new material, and how practice leads to mastery have strong evidence behind them. But helping teachers learn how the brain learns is nowhere to be found in a paper calling for a culture change in math teaching.

It’s misleading to suggest to teachers that students have multiple ways of knowing or understanding math, when research suggests that our ways of knowing are likely more alike than different.

* Coursework isn’t a gatekeeper keeping students out of higher math—like playing football or becoming an electrician, mastery of key skills is the key to success.

“The culture of teaching mathematics must shift from coursework being the gatekeeper to advanced mathematics and career aspirations to all educators valuing the community and integrating that knowledge into mathematics teaching and learning.”

As I’ve written about again and again, it sounds stupidly obvious but teaching the material really matters in how much students are able to learn. And it’s getting frustrating that in 2025, with all the evidence available, it's still being suggested that teaching math material is what’s holding students back from being brilliant mathematicians. Imagine thinking that it’s the coursework on heart surgery that’s holding a cardiologist back from being brilliant? When students don’t perform well, can we honestly look educators in the face and tell them it was because they didn’t “value the community” enough?

Math mastery is the key to success in math, in advanced math and future lucrative STEM careers. But in my experience talking with dozens of educators, few have foundational knowledge in the research on how best to help students achieve mastery.

Practices like using the instructional hierarchy to adjust instruction and committing math facts to memory have proven track records of success with all students, even ones who really struggle with math. But that evidence isn’t found in this paper.

It’s borderline unjust to tell professional educators that these vague bromides and positive thinking will improve math learning.

One of the most important things NCTM could do to change the culture of math teaching is to begin incorporating the gold standard evidence on teaching and learning in their communications to educators, and help teachers understand how it applies to their classroom practice.