# PROOF POINTS: How a debate over the science of math could reignite the math wars

How does a revolution start? Sometimes, it’s a simple question. For Sarah Powell, an associate professor of special education at the University of Texas at Austin, the question was this math problem: Donna and Natasha folded 96 paper cranes. Donna folded 25 paper cranes. How many did Natasha fold?

In a study, Powell posed that question to children at the end of third grade, when they should have been able to answer it easily. Instead, most couldn’t solve it. One underlined 11 words in the question but didn’t attempt any math. Another jotted down the number 96 and gave up. A few wrote down random numbers that had nothing to do with the problem. More than half the students added the numbers 96 and 25 together. Only two children out of 15 she showed me got the correct answer: 96-25=71.

“I could send you hundreds of these,” Powell said. “It’s heartbreaking. How did we let it get to this? These are kids that just get passed from one grade level to the next. You shouldn’t let a kid get to fourth grade if they can’t add 12 plus 13. I see it as a huge equity issue. It is totally unfair what we are doing to these kids.”

In early 2020, at an academic conference just before the pandemic hit, Powell commiserated with other experts in special education and students who struggle in math. They shared her frustrations about the state of math education in America. A majority of students weren’t mastering the subject, according to the National Assessment of Educational Progress (NAEP), a test that tracks academic achievement. The most recent test had shown that 60 percent of fourth graders and 67 percent of eighth graders failed to score at or above the proficient level for their grade.

The researchers begrudged the lack of attention math gets in schools compared to reading, but suddenly their rival discipline – reading – was providing a role model for action. At the time, the debate over why schools ignored the science of reading dominated education news. Parents and teachers were pressuring schools to switch to a phonics heavy curriculum in kindergarten and first grade. “We have a science of math just like there is a science of reading,” said Powell. “They are analogous. We just need to get people going.”

The special education community was also instrumental in drawing the public’s attention to the science of reading. In that case, it was parents of children with dyslexia who were clamoring for change in how schools taught reading. This time, in math, special education researchers are taking the lead.

In its most extreme version, this new math movement revives an old fight between advocates of teacher-led instruction of step-by-step procedures against those who favor student discovery and a conceptual understanding of math. It also raises new questions about what makes for good evidence in math education and pits well-designed quantitative studies of achievement gains against qualitative studies of people’s attitudes about math and why more women and people of color don’t enter STEM (science, technology, engineering and math) fields.

At the urging of her colleagues, Powell emerged as a founder of the nascent movement. In December 2020, she invited dozens of like-minded education researchers to the first science of math Zoom meeting. They believed the research showed that teaching math properly in the early grades would drastically cut the number of children struggling with the subject who might need special interventions to catch up.

The researchers continued to meet almost every month during 2021 as their campaign gained momentum. They launched a website, an advocacy group and an auxiliary group for teachers. A Science of Math Facebook group, which they started in December 2020, now has more than 21,000 members. More than 150 education professionals, ranging from teachers to education professors, have added their names to a public list of supporters. One of their leaders held a Science of Math event in Pennsylvania in 2022 and is planning another in 2023.

Their first public assault on the status quo came in August 2022, when Powell and two of her science of math collaborators – Elizabeth Hughes of Penn State and Corey Peltier at the University of Oklahoma – published a paper titled Myths that Undermine Math Teaching. They took direct aim at some of the teaching practices recommended by the influential National Council of Teachers of Mathematics (NCTM), and Jo Boaler, a controversial professor of math education at Stanford University who has a large and devoted following of math teachers.

Citing 115 research studies to back up their views, Powell and her co-authors attacked what they described as common misconceptions about teaching math. They said it’s not essential to make sure children understand mathematical concepts before they are taught calculations. They insisted that algorithms, efficient ways of solving problems quickly, such as long division, aren’t harmful. They said that inquiry-based learning, where teachers encourage students to discover answers for themselves, is often not the best way to teach while explicit, direct instruction usually is. Forcing students to struggle with problems that they not only don’t know how to solve, but also haven’t mastered the tools needed to do so, isn’t helpful. Timed tests? It’s important, the researchers said, for students to master their sums and multiplication tables in order to free up the brain’s working memory to learn more complicated concepts. Periodic timed tests help teachers measure whether students are building speed and accuracy.

Powell says she and 13 other organizers have been volunteering their time to the cause and their group hasn’t taken any money from outside organizations or foundations. Powell’s own research is primarily funded by the U.S. Department of Education and the National Science Foundation.

The group is not arguing for a return to old-fashioned rote instruction, Powell says. She’s an advocate of active hands-on learning with tactile objects, what educators call “manipulatives.” But she says that research shows that children learn best when new topics begin with direct explanations from teachers who teach procedures and formulas alongside concepts. Then students practice mastering them. She isn’t opposed to inquiry learning, but she says it’s very hard to teach this way and the appropriate time is after children have mastered multiple strategies and have the tools to think through different possibilities.

The pushback has already begun. In an interview, Stanford’s Boaler says the myths article is wrong because Powell and her colleagues “cherry picked” the research and “dangerous” because it will lead teachers in the wrong direction. And she questions why special education experts should determine what constitutes the science of math. She points out that there are no mathematics experts in Powell’s group.

In January 2023, the NCTM, the math teachers group, reiterated its opposition to the rote memorization of math facts, such as multiplication tables. But that group’s president, Kevin Dykema, said the timing was a “fluke” and not in response to the science of math movement. Still, Dykema said he was “concerned” about the group and their disregard of rival research that shows kids are turned off by math when it’s taught as a boring set of procedures.

“I worry that the science of math is so focused on rote memorization,” said Dykema, a middle school math teacher. “I know a lot of students see math as very meaningless. They think that math is a bunch of isolated skills that need to be memorized, and they don’t see any value in learning it.” A session on the science of math debate is currently being planned for the annual meeting of the NCTM in October 2023.

Behind the scenes, officials at state education agencies and education trade associations from Colorado to North Carolina are asking questions. Powell said she’s already received a positive response from the Kansas State Department of Education. Meanwhile, opponents are privately circulating drafts of rebuttals to the “myths” paper. The homepage of the North Carolina chapter of the Association of Mathematics Teacher Educators says that the organization is working to understand the research behind the science of math movement and how to respond. “More information is coming soon!” the site promises.

Jon Star, a prominent professor of math education at Harvard Graduate School of Education, says that the science of math isn’t as clear as the science of reading and that there’s much we still don’t understand the best ways to teach the subject. He also points out that we really don’t know that much about how math is taught around the country. Although Powell’s paper discusses the shortcomings of progressive ideas about emphasizing conceptual math and not drilling math facts, it’s unclear if that’s what’s actually going on in classrooms and whether those practices are to blame for poor math performance.

It seems clear that we may be heading for a new battle in the math wars, which have been raging off and on in American schools for decades. And that makes one veteran of these battles weary.

“I go into this with some ennui,” said Deborah Loewenberg Ball of the University of Michigan Ann Arbor, another prominent professor of math education. “But this is a very important conversation to me.” She said that in order to come up with the most effective approach for teaching math, we need to agree on the goals of math instruction. Do we want kids to be able to compute accurately? Yes, but not everyone agrees that this should be the main goal of mathematics education. “The public needs to understand that the goals of math education are contested,” she said. Merely invoking the word “science” doesn’t resolve that debate, Ball said.

I’m fascinated with this science of math group and what it has to say. In the coming weeks and months, I’ll be digging into the research on math instruction and what newer studies tell us about these old debates on procedures, concepts, multiplication tables, how to cultivate number sense, add fractions and solve word problems. I’m eager to see how it all adds up.

This story about the science of math was written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for Proof Points and other Hechinger newsletters.

The Hechinger Report provides in-depth, fact-based, unbiased reporting on education that is free to all readers. But that doesn’t mean it’s free to produce. Our work keeps educators and the public informed about pressing issues at schools and on campuses throughout the country. We tell the whole story, even when the details are inconvenient. Help us keep doing that.

Join us today.