cites content, competencies, ways of thinking, and motivators as the cornerstones to numeracy. The findings build upon hundreds of earlier studies and will help kids enter middle school with a strong math foundation, CEO Arun Ramanathan said. 

And there is considerable consensus to the approach, he said.  

“The framework offers long-needed alignment: not how to teach, but what must be developed and how the pieces fit,” Ramanathan said in an email. 

According to its report, released Feb. 4, content is centered on the core mathematical ideas all future learning is based on while competencies refers to the skills students need to use math meaningfully. 

Ways of thinking encompasses the cognitive processes that support reasoning and problem-solving while motivators signal the beliefs and mindsets that foster engagement and persistence.

“If you asked teachers what they think numeracy is, you will get a lot of different answers,” said Gloria Lee, lead author of the report. “There is not a clear framework or scaffolding for people to communicate all of these parts. So, we are trying to fill that void.” 

The organization acknowledges the ongoing math wars, which pit explicit instruction, procedural fluency, guided practice and repetition against inquiry-based learning and conceptual understanding. It calls the dispute an unnecessary distraction. 

PowerMyLearning, which hopes their paper becomes a guide for educators and policymakers, said each of these pillars breaks down into four different categories. 

The four areas of content, for example, are integers, fractions, shapes and data while the four competencies are conceptual understanding, fact fluency, procedural fluency and application. The four ways of thinking are symbolic understanding, pattern recognition, explaining and sense-making while the motivators include math identity and persistence.

“Teachers, administrators and families must make intentional efforts to communicate that math is for everyone and everyone belongs in math,” the paper notes. “This requires explicitly promoting inclusive messages and countering negative ones, creating inclusive classroom environments, and establishing policies for support and acceleration rather than exclusivity.”

Jo Boaler, a mathematics education professor at Stanford University who co-authored California’s new math framework, reviewed PowerMyLearning’s paper and provided research for it. 

“I appreciate that the report gives a balanced perspective on number sense, highlighting the importance of reasoning, problem solving and mindset, as well as procedures,” she said. “Hopefully it helps to bridge the divides in mathematics education.”

was established in 1999 under another name and focused on technology in the classroom, including giving free hardware and software to schools in need. It later shifted to the “triangle of learning relationships” among students, teachers and families before zeroing in on early math. Though the organization aims to improve education for all, it has a focus on multilingual learners and children from historically underserved communities.

CEO Ramanathan told �鶹��Ʒ in an interview last week that despite ongoing disputes about how math should be taught, there is actually an enormous amount of agreement around what students need to succeed. 

“When you look at the areas folks are disagreeing about — conceptual understanding, fact fluency and procedural fluency — we put them all in one area, as competencies,” he said. 

Students, he said, can’t spend all of their time repeating certain skills. 

“They also have to be able to dig deeply into the reasons why certain elements of mathematics result in a correct answer,” he said. “For folks to be focusing on one element of that versus all of them together, when you see them all in one place, you don’t see them as (being) in conflict but in alignment.” 

There is no need to favor one element of learning over another, the report notes.

“In fact, the evidence is clear that fluency with facts and procedures helps students with conceptual understanding and vice versa. Numeracy requires fluency with facts and procedures as well as conceptual understanding and the ability to apply these mathematical capabilities to situations in the real world.”

The group says its findings further the and integrate more than 200 studies across math learning science, developmental psychology, and mathematics education.

Disclosure: The Gates Foundation and the Joseph Drown Foundation provide financial support to PowerMyLearning and �鶹��Ʒ.

Bill McCallum, a lead writer for the Common Core math standards, and Kristin Umland, then a faculty member at the University of New Mexico, led the effort, which was supposed to last a year or two. 

At first, Umland said, the organization was focused on helping other groups, including the and testing companies, improve their products to meet the more rigorous standards. 

Eventually, she said, the group shifted to creating the curriculum — including lesson plans — that it felt best served students as they strove to achieve both a conceptual understanding of math, the why of how math works, alongside procedural fluency, the ability to solve problems. 

Illustrative Mathematics now encompasses 90 employees — all are remote workers — with no central location. For those states that still use it, the curriculum is aligned to Common Core standards — and there are also state-specific versions for those states that don’t.

“Our goal is to change outcomes for students, regardless of the standards they are using,” Umland said. “Math is math, and all states agree that kids should learn math.”

Select schools within the New York City system have been using Illustrative Mathematics for half a decade. A recent, massive rollout across hundreds of campuses has been met with sharp criticism from many teachers and  

Some said the curriculum and for students to practice what they’ve learned. One educator acknowledged these initial growing pains but said , one that helped students more easily understand abstract concepts.  

Umland has heard all of the complaints. While she acknowledges these early days struggles,  it doesn’t mean the move is a failure. Only that it needs more time, she said. 

“There’s no magic bullet,” she said. “If there was, somebody would have figured it out by now.”

Los Angeles, which adopted the curriculum in its middle and high schools in 2023, meanwhile, .

�鶹��Ʒ talked with Umland recently about the math wars, how her organization’s approach stands out from the rest and about Illustrative Mathematics’s bumpy New York City rollout.

The interview has been edited for length and clarity.

Where does Illustrative Mathematics fit into the math wars? And by math wars, I mean that push and pull between teacher- and child-centered learning? 

We always see ourselves as a third way. There’s no-one-size-fits-all for all students in all contexts. There are times when students need to understand and hear a direct explanation. And there are other times they should be given a chance to think about it for themselves, make sense of it, grapple with it and discuss it. So, it’s not either or. It’s what’s appropriate for what you’re trying to help students learn in the particular moment.

What type of lesson would require a direct explanation? 

So, a perfect example is when kids are learning to count. There’s no way they can figure that out on their own. Numbers are different in different languages. That’s a completely cultural thing. That’s something you have to learn by hearing other people say the number to you. 

But when you’re starting to do addition, once they understand what three is and what two is, you can say, “If I have three marbles and two marbles, how many marbles do I have altogether?” 

The things that are cultural have to be taught directly. But once you understand what the meaning is, you can figure it out. 

How does Illustrative Mathematics’s approach to teaching and learning compare to most other curriculum methods?

A lot of folks learn mathematics from an “I do, we do, you do model,” where the teacher does an example question, then they work together with the students, and then the students go practice.

Our method sort of flips that model on its head, allowing students to think about a problem so they can get oriented to it. And then there’s discussion where they make sense of it. 

And, finally, the teacher brings it all together. It gives students a chance to think for themselves before being shown something. 

I can show you how to do two plus three by counting it all myself, or I can say, “Here’s a picture that shows two marbles and three marbles. How many marbles do you see altogether?”

Some kids will know how to count it and will do it. And some kids won’t. They’ll talk about it, share their strategies, and then the teacher can make sure that the student who does it correctly shows their solution. Or if none of the students do it, they can show them how.

Illustrative Mathematics had a rough rollout in New York City. What went wrong for some teachers/schools? 

A lot of the complaints weren’t necessarily about the curriculum itself, but about the rollout or the implementation. 

Teachers need to have professional development where they get oriented to the design structure and they get a chance to experience what a lesson feels like. They need a chance to practice.

Ideally, they have opportunities to collaborate with their colleagues on planning and they have coaching support as they go. It’s just sometimes hard to coordinate all of those pieces.

A lot of teachers, in the first couple of months, are still trying to understand how it works. But once they get to the second or third month, then they start to see how it works. When something is new, it’s harder. It doesn’t necessarily make sense. And it takes time for people to get oriented to it. 

We’re seeing the best success in the places where they’ve been doing it longer. They’ve put in a lot of time to support it and when they get to that phase, then they’re really seeing the outcomes for students.

What do you want to fix about mathematics education in this country?  

A lot of school districts have come to realize that they need high-quality instructional materials. They’ve made that commitment. Then they start to ask themselves, “OK, so what do we do for (struggling students)?”

In a multi-tiered system of support, tier one instruction is the core instruction that all students receive. Students identified as needing additional support will receive tier two instruction. Often, this means they will be pulled for small group instruction or additional instruction.

One of the problems is that for many of these students, it’s like they’re on a highway and then they get pulled off onto the frontage road — only they never find a way back. They end up on a parallel track. What we want is to figure out how to support these students.

How might you help kids stay on track? 

Right now, we’re really focusing on early math. We are currently developing a pre-K math curriculum. It will be available next school year. If you can get to students early, it has an exponential impact on them before they head on to later grades. If we can do a better job with the youngest math learners, they won’t have the problems that we see at the secondary level in the future. 

The Center on Reinventing Public Education’s latest notes the number of teacher preparation program graduates ready to teach math fell by 36% from 2012 to 2020, dovetailing with a decline in student achievement. While the study released today did not prove causality, the link, researchers say, seems clear. 

“High-quality teachers matter,” CRPE director Robin Lake said. “It’s the most powerful in-school factor in kids’ learning experience and it’s something people are not talking about enough.” 

At the same time, a topic that has been widely discussed — the debate over whether explicit direct instruction trumps a more student-centered learning approach — has left some educators unsure of how to teach the subject, researchers found.

“The math wars are as old as education itself,” said CRPE senior fellow Alexander Kurz. “That debate is alive and well through the science of math. As an educator, you are caught in the crossfire.” 

The result: Nearly 4 in 10 eighth graders failed to achieve even the most basic level of math proficiency on the National Assessment of Educational Progress, such as calculating the area of a circle or multiplying fractions, the study notes. The most recent NAEP scores, released just last week, showed the nation’s 12th graders doing worse in math than any senior class of the past generation.

While those scores were the first to come out for seniors since COVID, the study’s authors say the problem long predates the pandemic. They note that math performance in U.S. public schools has been declining for more than a decade and achievement gaps are at historic highs.

Girls, low-income kids, Black and Hispanic students, children with disabilities and multilingual learners are struggling most, CRPE reports. Citing NAEP data, the report notes that since 1990, the gap between the highest- and lowest-scoring students has grown 18% wider among eighth graders and more than 8.5% wider among fourth graders.

In addition to the teacher shortage and instructional quagmire, CRPE cites a number of other factors it believes contribute to abysmal student performance pre- and post- pandemic, including that many states’ test scores are inflated, obscuring results, “especially for different student groups.”

The report, the fourth of its kind, found that in , for example, students’ average math grade point average jumped 0.34 points from 2019 to 2021, triple the increase of the prior eight years. 

In , the report notes, math proficiency dropped 11 points on state exams while A and B grades on local courses declined by only 3 points. 

“A national study from 2021 to 2023 found that 57% of grades didn’t align with student knowledge as measured by tests, and two-thirds of those misaligned grades were inflated, most often for underserved groups,” the CRPE report reads. “ACT data show rising GPAs, especially in math, despite falling test scores. By 2021, even students scoring in the 25th percentile were graduating with B averages or better.”

The study found, too, schools are overly rigid, tracking students and hindering their success in the subject.

“Middle school math-tracking acts as math predestination, putting some students on a track to take Algebra I in eighth grade or earlier,” the report reads. “Less-advantaged students are less likely to be placed in advanced math courses, even when they demonstrate readiness.”

Joel Rose, co-founder and chief executive officer of New Classrooms, a nonprofit that focuses on student-centered learning, called the report spot on, adding schools don’t account for children learning at different speeds. 

“There is really only one track, the grade-level track,” he said. “If you stay on it and never fall behind, you do fine. The problem is most kids fall behind for one reason or another and there are not any viable paths for them to catch back up.”

It’s because of this, he said, that math education is turning into “our nation’s social sorting machine.” Students who don’t catch on to the subject will find a whole series of career pathways closed off to them, he said. 

But all of these problems are solvable, CRPE contends, noting that states like and school districts like New Jersey’s and , have made replicable gains. 

Alabama is the only state where fourth graders scored higher in the subject than they did in 2019, prior to the pandemic. 

Karen Anderson, director of the state education department’s Office of Mathematics Improvement, said Alabama has worked hard to align classroom lessons with state standards and to use evidence-based practices and high-quality instructional materials to help all students — no matter their zip code or performance level.

“We want to make sure we are using instructional strategies that actually provide results,” Anderson said. “We also want to make sure we know what students know — and what they don’t know. And, when we see students who need help, we provide assistance immediately.”

CRPE recommends schools stop poo-pooing direct instruction — in which teachers demonstrate or explain procedures and concepts. Likewise, it concluded teachers need clear guidance on how to balance conceptual understanding with procedural fluency — in addition to real-time data to identify gaps and better structure their lessons.

Melodie Baker, founder and executive director of , which aims to use research to empower communities of color, has worked in mathematics for decades. She said robust teacher preparation at the elementary school level is critical for student success.

“The lack of emphasis on math in elementary is a big issue,” she said. “For example, teacher prep programs spend far more time on early literacy than math.”

But they are of equal importance, Baker said.  

CRPE concluded states should consider better pay, team-teaching models and math specialists as a means to address the math teacher shortage. 

In terms of improving the student experience, it advises schools to adopt “flexible pathways with multiple on-ramps, automatic acceleration, and no lower-track dead ends.”

Based on their conversations with students, CRPE concluded that schools need to better serve children who require more time to understand math concepts.

“One thing I don’t like is when I ask a teacher a question because I don’t understand it, and then they make me feel like I’m a bother and I really shouldn’t ask more questions,” an 11th grader from Connecticut told CRPE researchers in 2022. “And that prevents me from learning. And I hated that because I actually want to know.” 

The student’s claims correspond with what CRPE found: Schools are regularly missing opportunities to address academic problems head-on. 

And while the federal Every Student Succeeds Act explicitly requires states to develop a concise and easily understandable online report card, most don’t meet the standard. CRPE found just 18 break down math achievement and growth data by student subgroups “in a way that we thought was clear and understandable.”

Only Illinois, the report notes, earned the highest rating in this category by providing comprehensive math performance and opportunity data that CRPE thought most parents would be able to use and understand.