We're a math-traumatized people, Jo Boaler says (although she uses the British locution “maths-traumatized”). It’s a belief she sees confirmed in everything from students crying over long division to MRIs that reveal young brains reacting to numbers as if they were snakes or spiders. And it’s something she hears just as clearly in the resignation of that common refrain: “I am not a math person.”
Boaler, a professor at the Graduate School of Education, sees math altogether differently — as a subject of beauty and creativity in which any student can thrive. Indeed, her Britishness only partly explains why she prefers “maths.” The plural, she says, is more apt for mathematics’ depth and variety. “Math” strikes her as narrow and constricted. “Maths is so much more than that,” she says.
It’s easy, though, for her to evoke math anxieties in listeners, often with little more than an elementary school worksheet. The sight of a three-minute test dense with 50 multiplication problems reliably stirs nervous memories in ways it’s hard to imagine an elementary reading assignment doing.
“I just spoke to a whole incoming group of freshmen last week at Stanford,” Boaler said in the fall. “I put this on the screen and the whole room broke out: ‘Blah, isn’t this terrible?’ ”
For Boaler, the test — with its focus on speed, volume and performance — is a big part of why math crushes spirits like no other subject. To her, it represents shallow learning with debilitating consequences. Students who work slowly are often left convinced of their own inability, although they may be the deeper kind of thinkers who make the best mathematicians. And even those who calculate speedily — not a skill Boaler thinks is particularly valuable in the digital age — may end up shrugging off math as a high-pressure hamster wheel.
As a researcher, teacher and evangelist, Boaler is a leading voice for a wholly different pedagogy where speed is out, depth is in, and the journey to an answer can be as important as the destination. It’s an approach where sense-making matters more than memorization and retaining “math facts” matters less than understanding how such facts interconnect.
Boaler is a leading voice for a wholly different pedagogy where speed is out, depth is in, and the journey to an answer can be as important as the destination.
For instance, Boaler is an advocate of “number talks,” in which students work on a problem — say, 5 x 18 — then discuss the different ways each approached it. Successful students intuitively rewrite such problems in friendlier terms, but there are more ways to do that than you might expect.
One could break the problem down to (5 x 10) + (5 x 8). Another might halve one factor and double the other to get 10 x 9 or see it as (5 x 20) – (5 x 2). The idea is that by discussing, comparing and visualizing their differing approaches, students build their own sense of context, connection and numeracy. 5 x 18 = 90 isn’t just a fact to memorize; it is a key to building a broader strategy for breaking down other problems.
The Math Wars
Battles between proponents of traditional math and progressives have flared for generations, most recently in the “math wars” of the ’90s and early ’00s. UC–Berkeley education professor Alan Schoenfeld, MS ’70, PhD ’73, likens that discourse to that of today’s cable news: “All this heat, very little light and a sensible middle ground obscured by voices on both sides.”
Since the early part of the past decade, he says, the fight has waned as research has favored progressive approaches over traditional emphasis on drills, repetition and procedure. Still, that may not mean the reality for students has changed.
“The math wars are over, but getting the right stuff into classrooms is very much an ongoing challenge,” he says. “There’s a big difference between knowing what kind of change you’d like to see and having the tools for implementation in the real world.”
Boaler’s ability to bridge that disconnect is part of her broad appeal. A charismatic speaker with thoughtful delivery, an easy smile and a habit of quick replies to emails from educators, she is a beloved figure to many teachers. “I call myself a Jo Boaler groupie,” says Christina Lincoln-Moore, an assistant principal in the Los Angeles Unified School District. “I spread the word even when it’s not wanted.”
Dan Schwartz, dean of the Graduate School of Education, calls Boaler the public face of K-12 mathematics reform. Although many colleagues across the country share similar views about what needs to be done, he says, her influence with teachers and parents is unmatched. “She is the great communicator.”
Boaler directly influences the teaching of mathematics by educating future teachers in Stanford’s STEP program, but her most far-reaching impact is probably through her Stanford-based website. Youcubed.org — which has had more than 24 million page views since it launched in 2015 — is stocked with free lesson plans and projects Boaler believes are creative, illuminating and engaging for all students. She treasures “low-floor, high-ceiling” activities that can engage anyone but challenge everyone.
As an example of how even a simple math problem can be made richer, imagine a typical early geometry question asking for the area of a 4 x 6 rectangle. The answer, of course, is 24. Boaler suggests flipping the question on its head and asking students how many rectangles they can draw with an area of 24. (There are four, with dimensions of 24 x 1, 12 x 2, 8 x 3 and 4 x 6.) One approach asks for a calculation, she says; the other makes space for thought and discussion.
Mindset Matters
Boaler’s larger goal isn’t just changing classroom tactics, but transforming the mindset that governs who we think can learn math in the first place — the stereotype that reveals itself every time someone says, “I don’t do math.”
For Boaler, there is no such thing as a math gene or a math brain. She believes virtually anyone can learn math, even at high levels, a message she reinforces by referencing everything from neuroscientific insights on brain plasticity and the benefits of making mistakes to mathematical legends who overcame early obstacles.
This year, Youcubed’s popular Week of Inspirational Math, which provides K-12 teachers with five days of lessons, activities and videos to start the school year, was dedicated to the late Stanford mathematician Maryam Mirzakhani, who died of cancer in 2017 at age 40. Mirzakhani was the first woman to win the Fields Medal, mathematics’ top award, despite having been told as a sixth-grader that she was bad at the subject and even though, or perhaps because, she worked slowly.
“So many students with amazing potential get the message that they are not good at maths, and can never be good at maths,” Boaler wrote on Youcubed in Mirzakhani’s honor. “To know of someone who received that negative message as a young girl and went on to be one of the most successful mathematicians in the world is inspiring for others.”
At root, Boaler is trying to tap the power of a growth mindset, the concept made famous by Stanford psychologist Carol Dweck, who is a Youcubed adviser and wrote the foreword to Boaler’s most recent book, Mathematical Mindsets. “Boaler is one of those rare and remarkable educators who not only know the secret of great teaching but also know how to give that gift to others,” Dweck wrote.
Dweck’s research shows that people who see intelligence as something that can be developed handle setbacks better than those who see intelligence as a fixed quality. Someone with a growth mindset is more likely to put in effort to improve because she believes it is possible, while a person with a fixed mindset more readily interprets failure as revelation of uncontestable limits. “I’m not a math person” reflects a fixed belief.
By adopting richer, more open teaching methods and encouraging kids to adopt a growth mindset, Boaler believes, educators can help students make strides. In 2015, she and her associates brought 81 middle schoolers — many of them underachievers — to campus for a four-week math camp centered on activities taken from the Week of Inspirational Math. The students began the camp convinced they were “not math people,” Boaler says. But they were soon engaged. After four weeks of morning classes and afternoon enrichment, the students had improved their scores on standardized math tests by an average of 50 percent, or 2.7 school years.
Of course, it all unfolded in a university setting, overseen by five teachers, two grad students, 12 undergrads and a staff member — a level of support a typical teacher wouldn’t dream of. But Marc Petrie, a middle school math teacher in Orange County, Calif., says Boaler and Youcubed have helped him in a setting where the challenge is undeniable.
Fifteen years ago, Petrie switched to teaching from a lucrative engineering consulting job for a variety of reasons, more time with his young son chief among them. But high among his motivations was making a difference in the lives of kids who needed it. At the school where he works today, 98 percent of students qualify for free and reduced-price lunch.
At first, Petrie was pleased with the scripted methods he’d been taught in teacher training, which he describes as, “Take notes on this, do all this work, and let’s try it again.” But he soon found himself in front of lost students. The problem crystallized one day when he looked out upon a high school class and was reminded of the final line of the Theodore Roethke poem “Dolor,” which ends with “duplicate grey standard faces.”
“When I looked out at students, I didn’t see any joy; I just saw resignation,” he says. “I just saw students falling further and further behind, which upset me.”
The moment set him looking for alternatives. He had heard about Boaler at a conference of the California Mathematics Council, picked up one of her books, and soon attended a workshop. “It really changed what I thought about.”
Today, his classes are far from the teacher-centric experiences of a decade ago. Everyone sits in groups, working together to come up with varying approaches to problems, while Petrie cruises the room as a coach, more likely to ask guiding questions than give answers. The cacophony of voices requires a careful ear to discern the schoolwork from the gossip. But he is pushing students to engage with ideas and make them their own, rather than just memorize processes.
Once a week, in addition to a normal lesson, the students watch a video designed to promote a growth mindset — a real need, he says, among the population he serves. The combined results have been dramatic rises in test scores — and teachers across his district have followed Petrie’s lead. “Jo has a system that allowed me to change in a way that had instantaneous benefits,” he says. “Our test scores have risen significantly — 60 to 90 percent. Other school districts are looking at us.”
A Reformer Is Born
The tendrils of Boaler’s reformist bent and support for the underdog go back to her beginnings. She grew up outside Birmingham, England, in the 1970s — another progressive mathematics era. Neither of her parents had gone to university. Her father was a technical drawer; her mother was a secretary.
But when Boaler was a child, her mother attended Open University, a distance-learning school, to study to become a teacher. Through her mother’s studies, Boaler was exposed to many of the cutting-edge, play-based educational ideas of the day. She spent much of her childhood, she says, holding Cuisenaire rods — multicolored sticks that allow kids to play with and manipulate numbers.
Her formal schooling, however, wasn’t particularly enlightened. It was only late in high school that she had a teacher who talked about math in a deep, conceptual way. And while she found the subject fairly easy, she could see many of her classmates languishing.
In other subjects, teachers were quick to dismiss her based on her gender. She took a physics course where the teacher declared that only the boys would take the higher of two national exams. Her mother, “a bit of a feminist,” wasn’t going to let that go unchallenged, and Boaler, alone among the girls, took the higher exam. She got an A, motivated by the fact that “he had said we couldn’t do it.”
At the University of Liverpool, she earned a degree in psychology, intending to become an educational psychologist. As part of her training, she spent two years teaching in central London. Her first assignment was a group of 13-year-olds placed in the bottom educational track. “What’s the point?” was the first thing she heard one of them say. By the end of her first year, she’d convinced the school to abandon separating students by supposed ability and to let some of the students sit for the exams that would allow them to continue their studies.
She then pursued higher education in mathematics, followed by a doctorate in math education. Her dissertation was a three-year examination of how two schools taught mathematics — one a traditional school, the other progressive. In essence, she found students from the more progressive, “chaotic” school knew less but understood more. The dissertation garnered awards and high praise, and resulted in Boaler’s getting recruited to Stanford.
Times Table Torment?
Even now, the fissure between traditionalists and progressives can erupt. Boaler has plenty of skeptics who think her ideas sacrifice rigor. In 2015, she ignited controversy in Britain by saying at a conference that she had never memorized her times tables. “It has never held me back, even though I work with maths every day,” she said. “It is not terrible to remember math facts; what is terrible is sending kids away to memorize them and giving them tests on them, which will set up this maths anxiety.”
Charlie Stripp, director of England’s National Centre for Excellence in the Teaching of Mathematics, struck back in an op-ed in the education publication Tes. “It is not the learning of times tables that is causing anxiety but rather it is lack of times table knowledge,” he wrote. “It should be an educational entitlement that all children are helped to learn their times tables.”
Like Stripp, many teachers are dubious of the change Boaler advocates. Bonnie Baggett, an assistant principal and former math specialist in Bentonville, Ark., says there are some people in her area, teachers included, who will never deviate from how they learned math. But to her, the benefits of Boaler’s ideas are evident.
Not long ago, most teachers in her area taught math classes essentially as a lecture, often following in lockstep the same PowerPoint presentation everyone else was using. “Then they’d say, ‘Go and practice 100 times’ and then, ‘Good, now you know how to divide fractions. Now we are going to do one-step equations.’”
By the time students moved on to algebra, where they were using the same concepts but with letters as well as numbers, they were flummoxed. Years of study hadn’t stuck. “To them it was just a whole new set of procedures,” Baggett says. “They were not making sense of the math; they were just following procedures to get the right answers. They were basically computers when you punch in a number sentence and an answer comes out.”
Baggett grew intrigued with Boaler after seeing her speak at a conference and reading her book. Then, on a lark, she emailed Boaler for advice on a state education matter. “I’ll be darned if she didn’t email me back within an hour,” she says. “It was amazing.”
Boaler and Youcubed executive director Cathy Williams were soon on their way to Bentonville to headline an educational conference for Northwest Arkansas, winning converts in the process.
The ensuing implementation of their methods hasn’t resulted in the dramatic test score increases that Petrie saw. In fact, scores initially dipped, which Baggett believes is a reflection of the difficulty of retraining teachers and students. For all their faults, traditional methods are effective for short-term test prep. But she’s confident the benefits will become obvious as students move to higher levels like algebra without having to start from scratch. She’s not alone, she says.
“The people in Northwest Arkansas fell in love with Jo,” she says. “I would bet 80 percent of our teachers in Northwest Arkansas are part of that math revolution because we believe in what she’s doing to try to change the pedagogy of how we teach math in the United States.”
A Wider Audience
Boaler is a subject of the forthcoming documentary The Gatekeeper, directed and produced by Vicki Abeles, who made the influential film Race to Nowhere about the pressure and stress on students caused by testing and overscheduling. Abeles says Boaler surprised her the first time they met by pointing out something that had escaped her attention: Most of the individual students’ struggles documented in Race to Nowhere began in math class. In fact, Abeles had been inspired to create the film after the suicide of a girl in her community who, her family suspected, had begun to question her intelligence and self-worth after struggling in algebra.
When Abeles learned about additional consequences of math education in America — including the fact that fewer than half of high school graduates are ready for college math — she began to envision a film. The Gatekeeper title refers to the way that sub-par math scores often restrict access to higher education and good jobs. Boaler, she says, is a major part of the movement to change that.
“You’re hard-pressed to find anybody who cares more about transforming how math is taught,” Abeles says. “For a professor at Stanford to take the time to actually bring research into practice I think is somewhat novel in this country — and sorely needed.”
Sam Scott is a senior writer at STANFORD.
