As American students continue to flounder in math, Bellwether, a national nonprofit that seeks to improve opportunities and outcomes for marginalized kids, said schools seeking a turnaround must first establish a clear, shared vision of effective math instruction.

“How We Solve America’s Math Crisis: A Systemwide Approach to Evidence-Based Math Learning,” Bellwether’s done in partnership with K12 Coalition, talks about building a teacher and student “math identity” and balancing “conceptual understanding and procedural fluency while creating meaningful opportunities for real-world application.” 

The plan must also ensure that learning progresses “logically and cumulatively” to deepen students’ knowledge as they move through the perennially difficult subject over time. 

“These steps may seem familiar, and that’s because they are widely accepted best practices for developing and sustaining strong instructional design,” the report reads. “However, to be effective, they must be consistently applied over time and throughout the system.”

And that’s where schools have fallen short, Bellwether’s researchers note, despite evidence supporting the approach. 

“Data demonstrate that when high-quality materials, intentional instructional practices, and strong teacher support are combined, students’ math proficiency can improve significantly — even in schools starting with very low baseline scores.”

Anson Jackson, senior partner at Bellwether, sat down with The 74’s Jo Napolitano to describe what schools need to do to get on track. 

This conversation has been edited for length and clarity. 

What is effective math instruction? 

There’s a couple of layers to that. At the baseline, it is leaders, teachers and essential office personnel all understanding what good math instruction looks like. And they are not just focused on outcomes, but on the practices they want to see in math classrooms, the mindsets in math classrooms. There’s a shared understanding of what they believe math instruction looks like. That then determines how they build their professional development, how they build their training and how they build their assessments. It’s almost like a philosophy on math instruction. Without that philosophy, it’s like whack-a-mole. 

After they reach this consensus, what then? 

You then align on what those systems and structures look like to support that vision for mathematics. If you are focused on hands-on activities, then you want to have systems to train staff on how to develop strong activities to facilitate hands-on learning. If you believe kids need to show the work and do the math, you need to build in systems that allow kids to show the work and do the math on a regular basis. So that’s the idea: build a philosophy, build a vision, and then build a structure to support that vision throughout the district.

What if you don’t implement a shared vision? 

When you don’t have that, success is random. Teacher development is random. You’re always changing what is in front of kids or in front of teachers. When there’s no real shared vision, then the next leader who comes in changes the vision. And, without that shared vision, when you go from grade to grade, students don’t have the coherence of learning, which they need for success in math.

How can schools identify — and adopt — high-quality instructional materials, especially when time and money are tight? 

The first thing they need to do is understand the science behind mathematics and math learning. High-quality materials are backed by science and evidence of learning. Secondly, there must be coherence across grade levels — and in grade levels. The curriculum must be aligned. But before I get to the curriculum, I want to understand the key things that we know by science and evidence happen for kids to learn math at a high, high level. That could involve professional development, training, school visits, observations, doing some light research and analysis of what math looks like and coming to these conclusions as a collective — from the superintendent to chief academic officers, principals and teachers.

From there, I would then have them do a gap analysis of what they know works. They should ask, “What in our curriculum is missing or lacking from what we know should be there?” From that gap analysis, hopefully they’ll determine, “Oh, guess what? Light bulb moment: We are missing the mark on the curriculum or the materials.”

After that, they go through an adoption process where they take a look at what’s out there, and make some choices. But it needs to be a shared learning experience and not just that a team is told to adopt something because experts said it’s good. They should really understand why it’s good and what in the curriculum makes it high quality.

Is there a shortcut for cash-strapped schools with little time to do this? 

The short answer is yes: There’s lots of resources out there, including lists of high-quality instructional materials that are already vetted and backed by science. You can also use Google or ChatGPT to find them. However, this is where implementation can fail, without a deep understanding of the curriculum and why it works. A lot of folks, when things get hard, they put it away, right? 

So, I would say, yes, expert A can tell you the best resource for mathematics teaching and give you a set of resources. And that’s great. But unless they understand the true reasoning behind it and how it connects to learning, teacher practice, and systems, a lot of times it becomes another resource that’s on the shelf in two years.

How do you get teachers to support your approach? 

It’s about trying to get them engaged early on in the process, not telling them what to do, but having them learn what to do. I would not try to beat them down, but have them understand what’s working already and what’s missing. 

The second piece is that I would want to use a coaching model, side-by-side training and support for teachers — and not use it in a negative way. A lot of times we’ll shift to, “You’re not doing this, you’re a bad teacher,” when it’s actually more about a learning continuum, as in, “We’re going to focus on this in year one, year two and year three.”

What’s at stake if we don’t improve kids’ math scores?

The data shows a lot of the careers that are high paying usually have math as a core foundation. And the other piece is we know there’s an equity gap in this country when it comes to those who do math well and those who don’t — which leads to career choices, right? We want to close the gap between the haves and the have-nots.

Disclosure: Andrew Rotherham is a co-founder and senior partner at Bellwether who sits on The 74’s board of directors. He played no role in the reporting or editing of this article.

However, as the most recent eighth-grade NAEP results vividly illustrate, many young people who begin the school year behind are falling even further back: The test showed a sharp decrease in proficiency levels for those at the 25th and 10th percentiles. That’s because math is cumulative — what’s learned in one year is foundational to what’s taught in the next. Miss out on key concepts in one grade (as many did during the pandemic), and learning gaps can snowball for many more.

HQIM is not designed to address unfinished learning from prior years. As a result, math educators have the massive challenge of both teaching grade-level material and addressing students’ individual needs. To cope, they often simplify HQIM, use less rigorous materials or abandon recommended teaching methods. These approaches both dilute HQIM’s benefits and perpetuate unfinished learning.

During regular, grade-level math lessons, otherwise known as Tier 1 instruction, some schools now use software to tackle learning gaps. While this can help, significant gaps may require additional dedicated support, called Tier 2 instruction.

Tier 2 instruction aims to help struggling students catch up, but it often misses the mark. It may replicate Tier 1 lessons without addressing gaps or focus too narrowly on basic skills without connecting them to grade-level material. This disconnect makes it harder for students to bridge their knowledge gaps.

Moreover, Tier 2 teachers face diverse student needs, with gaps spanning multiple years or skills. Without proper resources, they rely on guesswork, leading to inconsistent results. That’s why a more cohesive and structured approach to Tier 2 instruction is essential.

To ensure HQIM is effective, schools need three key elements: time, actionable data and flexible instructional content.

Effective Tier 2 instruction first requires dedicated, structured time that is properly and consistently staffed. Schools might allocate part of the core math block, additional supplemental periods or even after-school sessions. It’s also crucial to establish a team of Tier 2 instructors and promote collaboration between Tier 1 and Tier 2 teachers to align their goals and efforts.

Second, both Tier 1 and Tier 2 teachers need accurate, timely information to understand students’ learning gaps. Diagnostic assessments at the start of the year or before each unit can pinpoint missing foundational skills so Tier 2 lessons can connect to the grade-level topics covered in Tier 1. Once the school year begins, the use of skill-level assessments across both Tier 1 and Tier 2 can help to ensure a real-time and shared understanding of each student’s unique learning profile. If these kinds of diagnostic and skill-level assessment tools aren’t available, teachers will need to connect the results of students’ prior assessments to the prerequisite skills required in future curriculum units — a time-consuming but invaluable process.

Lastly, Tier 2 instructors will often require instructional content that can address students’ relevant learning gaps from the current or prior school years. That may include HQIM lessons from earlier grades as well as the use of high-quality instructional software that students can use independently and that is compatible with their Tier 1 curriculum.

HQIM has raised the bar for math education, replacing inconsistent curricula with rigorous, equitable standards. For too long, students were subjected to fragmented and inconsistent curricula that did little to ensure equity or rigor. HQIM has changed that narrative, setting a higher bar for what students can achieve.

However, to fully realize the potential of HQIM, the education system must evolve further. The next step — HQIM 2.0 — requires integrating diagnostic data, flexible instructional content and robust support systems to meet the needs of all learners. This approach will allow schools to maintain high expectations while addressing individual student needs across both Tier 1 and Tier 2 instruction.

By focusing on these foundational changes, schools can create a more coherent and effective approach to math instruction.

Now, policymakers and education leaders are beginning a pivot to math, where drops in scores on both the PISA and NAEP exams have been far more acute.

What’s the plan?

One strategy states will assuredly consider is to focus on the continued adoption of High Quality Instructional Materials — curriculum aligned to college- and career-ready standards. The trend toward these materials in both reading and math accelerated when troubling that disadvantaged students were not getting equitable access to high-quality teaching. Federal recovery dollars then helped to adoption across the country.

These materials have been a major step forward for teachers who, for decades, were provided with low-quality textbooks or online resources that didn’t reflect high standards or research-based teaching practices. Introducing an objective quality rating into the textbook adoption process disrupted the K-12 publishing industry for the better and helped to ensure that all students had access to educational programs rooted in high expectations.

But before going all-in on HQIM in math, state and district leaders should consider the implications of an important nuance in how instructional materials are evaluated by EdReports and other ratings agencies: to qualify for an acceptable rating, the materials must focus on grade-level work.

In reading, most students can benefit from grade-level instruction so long as they have passed the . They become better readers when they build knowledge and vocabulary, learn to navigate more complex texts and exercise critical thinking — all of which can happen regardless of the students’ starting point. A seventh-grader at a fifth-grade reading level can grapple with seventh-grade content and become a better reader. The struggle can be productive.

But in math, specific topics that are taught during one school year are foundational for what’s taught in the next. If students fall behind, , making it harder to catch back up. A student who didn’t quite grasp enough about the concept of decimals in elementary school can struggle to understand percents in sixth grade and then to apply them in seventh. Teachers can have a hard time addressing unfinished learning when their materials are focused largely on grade-level content. Math is cumulative — a fact that doesn’t change when a student happens to move on to the next grade level.   

Each day, we see a clear relationship between foundational concepts and grade-level mastery in the data we gather within our supplemental math program, . For example, when students attempt to learn the Pythagorean Theorem having already understood concepts such as estimating square roots and classifying triangles, they have a 72% chance of achieving mastery. When they don’t know these predecessor concepts, that success rate drops to 32%. Similar rates exist for nearly all the topics in the program. 

The importance of addressing unfinished learning in math proficiency is also consistent with learning science. Among the most foundational principles of cognition is that students have , which can be overwhelmed by tasks that are too cognitively demanding. Once students memorize information and master skills, their brain is free to use their working memory on other, higher-order tasks. But if they don’t master those lower-order skills, their working memory strains and their understanding of new ideas is impeded. 

Does this mean that students should instead spend all their time addressing every learning gap from previous grades? Of course not — instructional time is too limited. If students spend an entire school year working only on unfinished learning, they finish the school year behind again, having missed out on grade-level content that’s foundational to the next year. The cycle continues, year after year, making it nearly impossible for them to ever catch back up.

But it also doesn’t mean that instruction can ignore those gaps. As Dan Weisberg and I argued in 2019, teachers need strategies to both maintain high expectations and address unfinished learning from prior years. Advances in technology, and especially in artificial intelligence, make both objectives more achievable than ever. However, a curriculum that does both would have a hard time qualifying as High Quality Instructional Materials, since it would not focus on the major work of the grade.

Teachers clearly that students are behind. So do advocates for HQIM, many of whom guide schools to access that help teachers better understand predecessor relationships. But guidance documents aren’t the same as instructional materials that could actually help teachers address foundational learning gaps. And since those materials don’t fit a grade-level-only definition, teachers often need to source their own materials to diagnose and address foundational learning gaps and then somehow integrate it into their classroom workflow. Not only is this difficult to do, but it’s what HQIM was supposed to avoid.

What can be done to ensure students have access to both grade-level content and pathways to proficiency?

Some states are broadening their definition of HQIM to allow for more than just grade-level content. Texas recently launched a in math that allows publishers to include both on- and off-grade material so long as the grade-level standards are fully covered. California seems to be on a similar path, as its new is now more focused on grade bands (i.e. grades 6-8), as opposed to individual grade levels. (Most states use grade-level bands in their science standards.)

Others who prefer to hold tight to grade-based core instruction can consider changing the definition of HQIM when it comes to evaluating supplemental resources. Rather than simply applying the same grade-level-only filter, evaluation criteria for intervention solutions can focus on the ability to accurately diagnose relevant skill gaps (no matter how far back), embed rigorous content and assessments, develop custom learning pathways, activate student engagement and integrate with core instruction.  

High-quality instructional materials help to ensure students have access to an academic trajectory that’s aligned to college and career-readiness. But access alone is not enough to unlock social mobility — mastery is what matters. For as long as the nation’s schools have taught math, they have to serve students who, for whatever reason, are not performing at grade level. That’s been true regardless of the quality of the curriculum or the training of the teacher. 

Instructional materials are the most important tool an educator can put to use in the classroom.  But as with any tool, quality should reflect both an aspirational vision for what it can do and the science to make sure it can deliver. 

The current definition of HQIM sets an appropriately high aspirational vision. But for students to meet that bar in math, their teachers need more than what HQIM — as currently defined — can offer.