You’ve read the research. You know the frameworks. You’ve sat through the PD sessions, shared the NCTM talking points with your team, and genuinely believe that if teachers just did more of this — more productive struggle, more discourse, more number sense routines — student achievement would follow. So why isn’t it following?

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This is the question haunting almost every math coordinator, coach, and district leader we talk to. And here’s the uncomfortable truth: it’s not because your teachers aren’t trying. It’s not because the research is wrong. And it’s definitely not because you lack good ideas.

Your system is perfectly designed to get exactly the results you’re currently getting.

Read that again. Your system — the structures, the PD calendar, the coaching model, the measurement approach — is doing exactly what it was built to do. And if you don’t like the results, the problem isn’t effort. The problem is design.

After working with hundreds of math leaders across North America, we’ve identified three specific barriers that show up again and again — blocking traction, burning out teachers, and preventing the kind of lasting instructional shift that actually moves the needle on student achievement. Let’s break them down.

Barrier #1

Your Math Program Has Puzzle Pieces, But No Shared Picture (The Coherence Problem)

Picture this. It’s September. You’ve got a new fluency resource your team is excited about. There’s a teacher down the hallway doing incredible things with number talks. Your curriculum has been aligned. You’ve got coaching structures in place. You’ve invested real time and real money into professional learning.

And yet — walk into ten different classrooms and you’ll see ten different things. Some teachers think fluency means timed tests. Others think it means flexibility and efficiency. Some coaches are pushing productive struggle. Some principals are still rewarding quiet, compliant classrooms.

Everyone is working. Nobody is lost. But nobody is building the same puzzle.

This is what we call a coherence problem. And it’s far more common than anyone wants to admit.

When we talk to math leaders about their biggest challenges, the word that comes up most often is “buy-in.” Teachers aren’t engaging. Practices aren’t sticking. The new initiative is getting lip service but not landing. It feels like resistance.

But here’s what’s really happening: it’s not resistance. It’s confusion. Teachers don’t have a lack of effort — they have a lack of a shared picture to work toward.

Think about what happens when you say “fluency” to a room full of educators. One teacher is picturing a timed drill. The principal is thinking of a number talk. The coach means something else entirely. Same word. Three different classrooms. That’s not a training problem. That’s a coherence problem.

The research backs this up. NCTM’s Principles to Actions — published in 2014 and still the most comprehensive framework for effective math teaching in North America — outlines eight research-based teaching practices that, when implemented consistently, develop the mathematical proficiencies we all want for students. The challenge isn’t awareness of these practices. It’s that most systems have never created the shared mental model that makes them land the same way at every level.

What to do about it: Your first job — before curriculum adoption, before coaching cycles, before any new initiative — is to design the puzzle. What does effective math instruction actually look like in your context? Not in theory. Not in a book. In your classrooms.

What does fluency look like? What does productive struggle sound like? What should a visitor notice when they walk into a strong math lesson? These aren’t rhetorical questions. They need shared, specific, written answers that every teacher, coach, and administrator can point to. You need a math vision — and it needs to travel coherently from the district office to the classroom.When Betty, a curriculum director in a PreK–8 district, came to us, she described the feeling perfectly: “It felt like spaghetti at the wall.” Goals weren’t consistent across schools. Words meant different things depending on who you asked. Once her team built a shared instructional vision and made it coherent across roles, the puzzle pieces finally had a picture to snap into. Tools like the Math Coherence Compass exist precisely to help leadership teams make decisions that reinforce one another — so that improvement doesn’t depend on who happens to be in the room.

Barrier #2

You’re Measuring Math Improvement With the Wrong Ruler (The Indicator Problem)

Here’s a question every math leader should ask themselves in June: Did the work I did this year actually cause the shifts I was hoping for?

If your honest answer is “I think so… maybe?” — you’ve got a measurement problem.

Most improvement plans are built around a familiar logic: we want to raise student achievement, so we’ll measure it via state or provincial assessments, and if scores go up, the work worked. It seems reasonable. It’s also, unfortunately, almost completely useless as a feedback mechanism.

Think about what you’re actually doing when you use year-end test data to evaluate your instructional improvement efforts. You’re looking at a lagging indicator — gathered months after the instruction happened, shaped by dozens of variables outside your control, and delivered too late to course-correct anything. It’s like trying to improve your diet by stepping on a scale once a year. The signal is too slow, too noisy, and too removed from the actual behavior you’re trying to change.

Here’s the consequence: because you can’t confidently trace test score movement back to any specific instructional shift, you don’t know what’s working. So you keep adding. New resources. New routines. New initiatives. Teacher plates get fuller. Nothing gets taken off, because you’re afraid to remove something that might secretly be working. And teachers — rightly — start to feel like every year brings something new without ever removing anything old. This is how math improvement plans create exhaustion instead of momentum.

The fix is simpler than you’d think. Measure the thing you’re trying to change, not the downstream outcome you’re hoping for.

If you want teachers to use more student discourse in the classroom — measure that. Create a walkthrough tool. Do a baseline observation in September. Come back in January. Come back in May. You’ll know, with real confidence, whether that shift happened. If you want teachers to grow their mathematical flexibility — assess that directly. You’ll have data you can actually use. This is what it looks like to know whether your math initiative is actually working.

There’s also a focus dimension here that leaders consistently underestimate. 

A landmark review by Yoon et al. (2007), published by the U.S. Department of Education’s Institute of Education Sciences, found that teachers who received substantial professional development — averaging 49 hours — boosted student achievement by approximately 21 percentile points. Meanwhile, PD lasting 14 hours or fewer showed no statistically significant effect on student learning at all. 

One practice. Forty-nine hours.

Let that sink in for a moment.

If you’re running PD on fluency strategies in October, mathematical discourse in November, problem-based learning in January, and formative assessment in March — you’re not making progress on any of them. You’re making noise. And you’re building the very overwhelm you’re trying to solve.The answer isn’t more PD hours. The answer is focus. Pick fewer things. Go deeper. Measure them accurately. And trust that depth creates the momentum that breadth never can.

Barrier #3

Your Math Teacher PD Is Built Backwards (The Proficiency Problem)

This one is going to sting a little. But it matters too much to leave on the table.

The dominant model for math professional development — the one most districts and schools are still using — goes something like this: identify the mathematical practices students should develop, figure out what instructional shifts teachers need to make to support those practices, and then build PD around those pedagogical moves.

It sounds logical. And to be fair, it’s not wrong. It’s just incomplete in a way that quietly undermines everything.

Here’s what that model misses: most of our teachers learned math the same way their students are currently being taught. Procedurally. Step by step. Here’s the algorithm, now practice it. They were told what to do, not why it works. They were evaluated on speed and accuracy, not flexibility and reasoning. And so, without ever meaning to, they tend to teach the way they were taught.

Now ask yourself: can a teacher facilitate genuine mathematical discourse if they only know one way to solve the problem? Can they respond flexibly to a student’s unexpected strategy if they’ve never seen that strategy before? Can they make productive use of conceptual models — area models for multiplication, tape diagrams for ratios, visual representations of the Pythagorean theorem — if they were never taught to think that way themselves?

The answer is mostly no. And pedagogy-first PD can’t fix it, because pedagogy assumes the mathematical understanding is already there. When it isn’t, you get teachers who know what they’re supposed to do in the classroom but don’t have the mathematical depth to actually do it. They know the moves. They don’t know the math.

We call this the backwards support problem. And it shows up in a very specific, frustrating way: teachers who go through effective teaching practice training and still don’t change how they teach. Not because they don’t want to. Because they don’t yet have the mathematical foundation that would make those practices natural.

Think about what it actually takes to orchestrate a productive math discussion. A teacher needs to anticipate multiple solution strategies before the lesson even begins. They need to look at a student’s work and recognize whether it reflects a partial understanding or a deep one. They need to sequence student presentations in a way that builds conceptual understanding — which means they need to have that understanding themselves.

That flexibility doesn’t come from a pedagogy workshop. It comes from a math epiphany.

What’s a math epiphany? It’s the moment a teacher realizes — often for the first time — that the Pythagorean theorem isn’t really about squares. It’s about area. Any regular shape on each side of a right triangle will work. The reason we use squares is because they’re easy to calculate — but the relationship holds regardless. Most teachers have never seen this. And when they do, something shifts. They don’t just know a new fact. They see the concept differently. And that changes how they teach it.

Or consider division. Most teachers know one kind: sharing equally. Twelve divided by three means splitting twelve things into three equal groups. But there’s a second kind — measurement division — where you’re asking “how many groups of three fit into twelve?” Same equation. Completely different meaning. Different contexts. Different models. Different language. When a teacher has that math epiphany, their next question — almost without exception — is “how do I bring this into my classroom?”

That’s the order it has to happen in. Math understanding first. Pedagogy second.When teachers deeply understand the mathematics they’re teaching — conceptually, flexibly, with multiple representations and connections — the pedagogical moves follow naturally. They become curious about what their students are thinking. They start to anticipate strategies. They stop being afraid of the wrong answer because they can see why a student arrived there. The five mathematical proficiencies from Adding It Up — conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition — aren’t just goals for students. They’re goals for teachers too. When was the last time your PD calendar was explicitly designed to strengthen all five in your educators? That’s a question worth sitting with.

The Math Improvement Flywheel: What Happens When You Remove the Barriers

Here’s the thing about all three of these barriers: they’re not unsolvable. They’re design problems. And design problems have design solutions.

When you build a shared, coherent math vision — one that travels from the district office to the classroom and means the same thing at every level — teachers stop guessing and start moving. When you measure the inputs you control instead of the outputs you’re hoping for, you get real feedback you can actually act on. When you invest in your teachers’ mathematical understanding — creating the conditions for math epiphanies — you unlock the pedagogical flexibility that all the workshop training in the world can’t manufacture on its own.

This is what a math improvement flywheel looks like. It doesn’t spin easily at first. The early stages require the most effort — the learning, the designing, the building of shared language and shared vision. But when it’s designed well, it gains momentum. Year after year, the structures compound. Teachers go deeper. Coaches get better. Leaders stay aligned. And eventually, you’re not pushing the wheel. It’s pulling you.

Your system is perfectly designed to get the results you’re currently getting. The question is: are you ready to redesign it?

The Make Math Moments team works with school districts, states, and countries to design mathematics improvement plans that actually move the needle. Take our free 12-minute assessment atmakemathmoments.com/growto get a customized improvement plan for your math program — and find out exactly which of these three barriers is limiting your system most.