Tag: Stanford University

Last April, Jelani Nelson woke up to a jarring email from Jo Boaler, a Stanford University professor and the nation’s most prominent expert on math education. The two had never met. “As you know,” she began, “I am one of the authors of the proposed mathematics framework and I know you are working to oppose it.”

That “framework” is a policy document that will shape how math is taught in California and beyond, and Nelson, a computer-science professor at the University of California at Berkeley, had major problems with it — and with Boaler, too. He’d seen a series of tweets critical of her, and reposted one of them with his own scathing commentary. Now, Boaler was confronting him.

“I wanted to let you know,” she wrote, “that the sharing of private details about me on social media yesterday is now being taken up by police and lawyers.”

Later, Boaler apologized on Twitter for “leaving the impression” that she’d called the cops on Nelson, saying she was upset because her address had been posted elsewhere in the same Twitter thread. She’d just wanted to talk, she told me, “which is why I wrote him an email.” Nelson, who is Black, wasn’t buying it: “She wanted me to be scared. She wanted to intimidate me.”

Welcome to America’s knock-down, drag-out math wars. Boaler is fighting for what she calls a more inclusive way of teaching, armed with influential research. To the K-12 teachers who agree that math isn’t just for “math people,” that memorizing times tables should be replaced with real-world problem-solving, the Stanford professor is a “beacon of hope,” as one educator put it. But Boaler is a divisive figure. She has at times misinterpreted studies and made bold assertions with scant evidence, experts say, empowering skeptics who fear that her proposals would water down math and actually undermine her goal of a more equitable education system.

In pursuit of that goal, Boaler is helping draft California’s latest math framework, a nonbinding guide for how public schools in the most populous state should teach math. It is expected to shape instruction not only in the Golden State — which flounders in math, despite being home to Silicon Valley — but also the rest of the country, which struggles with it, too. Some of the document’s key ideas are already reshaping math class, as well as admissions, at some of the nation’s most selective colleges, much to Boaler’s delight. “Viva la Maths Revolution!” she often declares.

But Boaler can’t shake her critics, whom she sees as elite gatekeepers standing in the way of better lives for young people. Their resistance is merely an invitation to keep marching. “When doing the work of the warrior, it is important to remember this: You should expect and even welcome pushback,” she has written. “If you are not getting pushback, you are probably not being disruptive enough.”

Boaler was always a good math student, but she didn’t always like math class. She went to school and grew up outside of Birmingham, England, where she was raised by her mother, a secretary, and her father, a technical drawer. Math was rote and procedural until Boaler had a different kind of teacher, one who wore dangly earrings against school rules and encouraged her teenagers to discuss problems in groups. “Suddenly, the subject was really different,” Boaler recalled. “It was more interesting than I thought.”

Not all teachers were as nurturing. In preparation for a national physics test, a male instructor told her that she and the other girls should practice on a lower-level version, which would cap how high they could score. Her mother intervened, arguing for her to take the higher-level exam, and Boaler ended up with the highest grade in the class, she said. She still remembers her teacher apologizing in front of her friends for underestimating her.

A few years later, Boaler saw firsthand that telling students they were incapable was a self-fulfilling prophecy. Fresh off earning a bachelor’s degree in psychology at Liverpool University and thinking she would end up an educational psychologist, she taught math in central London. Her class of 13-year-olds, who had been assigned to take the lower-level exam, felt defeated from the outset. “This girl says to me, ‘Why should we bother?’ And I didn’t really know how to answer that,” Boaler said. “In those moments, I decided I would just teach the higher-level maths.” She talked the administration into letting her students take the harder test, she said, and they passed.

Boaler would never forget the girl who wanted to give up. “Both she and I had been told we were not good enough for the quantitative subjects we were studying — and it was not true for either of us,” she would later write. Convinced that math class was in need of a transformation, she pursued a master’s, then a Ph.D., in mathematics education at King’s College London.

It was the early ’90s, and the math wars were alive and well on both sides of the Atlantic.

Math education in America today follows a sequence that has been in place since roughly the Cold War: arithmetic, algebra, geometry, a second year of algebra and trigonometry, then pre-calculus. (Calculus, which a few decades ago was virtually never offered in high school, is now widely perceived as necessary for admission to elite colleges.) In 1957, the Soviet Union’s launch of the satellite Sputnik prompted the U.S. to infuse its math instruction with an emphasis on conceptual understanding. But parents and teachers balked at this “New Math,” leading to a return to, more or less, a pre-Sputnik curriculum. This tug of war — between traditionalists and reformists, between calculations and big-picture thinking — would repeat itself many times, as Alan H. Schoenfeld, a Berkeley professor of education and mathematics, has written in his history of the math wars.

By the 1980s, Japan’s soaring tech sector was churning out video recorders and semiconductors, and America’s math students were still not doing well at either problem-solving or the “basics.” In a 1983 report titled “A Nation at Risk,” a U.S. panel of education experts warned: “Our once unchallenged preeminence in commerce, industry, science, and technological innovation is being overtaken by competitors throughout the world.” Students were dropping out of the math pipeline at staggering rates each year after ninth grade, Hispanic and Black students most of all.

In 1989, the National Council of Teachers of Mathematics attempted to breathe some life back into the reformist approach. It published standards that called for mixing in practice in math methods with projects, group and individual assignments, and discussions. The standards de-emphasized some traditional methods: long division, rote memorization of rules, complex calculations by hand. The National Science Foundation commissioned 13 sets of textbooks based on these standards.

Did they work? The closest thing to definitive evidence, according to Schoenfeld, came in the early 2000s. Studies showed that students using the new textbooks generally performed as well on skills-based tests as students using traditional ones, and even outperformed them on tests of conceptual understanding and problem-solving.

But in the decade in between, traditionalists grew alarmed. California, early to embrace the “new new math,” was a breeding ground of dissent. When Palo Alto’s school district planned to align its program with the 1992 state framework, angry parents organized on the nascent internet under the name Honest Open Logical Debate. Other anti-reform groups followed, like Mathematically Correct and Q.E.D., and their opposition blossomed into a statewide movement backed by irate mathematicians and Republican lawmakers.

They got their way. In 1997, California’s State Board of Education rejected a set of reform-minded math standards and commissioned four Stanford math professors to help overhaul them. One was R. James Milgram, whose expertise was a branch of abstract math called algebraic and geometric topology. He was then enlisted to help shape how those standards would be taught, resulting in a curriculum that was praised by mathematicians and reviled by math teachers.

By the time Boaler was in graduate school, the U.K. was in a similar whiplash. It had adopted a national reform-oriented math curriculum, and upset Conservatives were pushing back. For her dissertation, Boaler compared two schools, one in each camp, and found that students using reform methods were better at thinking critically about math skills and applying them to unfamiliar problems. Stanford soon came calling.

Boaler quickly realized that her new, sunny campus was ground zero for a conflict that was going national. In 1999, Milgram invited her to his office — not to welcome her, but, as Boaler told me, to warn her: She should avoid discussing her research in America, where teachers were “too weak” to use the methods she was studying. (Milgram has denied saying this.)

But as far as she could tell, the teachers weren’t the problem. At an eye-opening high-school meeting she attended, parents protested its new curriculum, which stressed integrated math and mathematical reasoning. Guided by “extreme traditionalists,” a group of mothers “bombarded the gathered parents with data that had been fed to them, telling them that if their children continued with the new math program, then they would not be eligible to go to college and that test scores would fall,” Boaler writes in her book What’s Math Got to Do With It?. Parents even allegedly pestered students to sign petitions. The district ended up reverting to traditional textbooks and methods, leaving teachers “demoralized and defeated.”

Not Boaler. If anything, she was even more determined to build on her research from across the pond.

In Boaler’s ideal math class, the kids do most of the talking. Rather than listen to a long lecture and silently plug through worksheets, students discuss open-ended problems in small groups and help teach each other. Teachers prompt them to explain their answers to the class, and provide explanations and guidance along the way. Students of different abilities are mixed together, similar to classrooms in Japan, where students are among the best in the world at math.

Real-world problems blending different skills are Boaler’s favorite types to assign. (If a skateboarder jumps off a merry-go-round with a radius of 7 feet that rotates every 6 seconds, how long before they hit the wall 30 feet away? Finding the answer involves both geometry and trigonometry.) Demonstrating how math concepts relate to each other, and to life, is key to keeping all students engaged, Boaler believes, particularly girls. She favors visual aids — puzzles, patterns, shapes, toy blocks, bowls of beans — to deepen understanding. And she says it is much more important for students to be able to flexibly break down and recompose numbers, a skill known as number sense, than to memorize procedures without understanding them. Boaler points out that she never memorized the times tables, but that has never held her back.

Boaler’s approach is informed by a body of education scholarship, including her own seminal piece of research: the Railside study.

In 2000, the National Science Foundation awarded her a grant to conduct a longitudinal study of 700 students across three high schools in California. “Greendale” and “Hilltop,” as they were called in the study, each had a traditional math curriculum and allowed students to start algebra in middle school (known as tracking), while “Railside” had a reform curriculum and started all students in ninth-grade algebra (detracking).

On math tests designed by Boaler’s team, Railside students scored lower than the others at the beginning of ninth grade. But they caught up by the end of the year, and by the end of year two, they were outperforming the others. Even more promising, Railside was a working-class, diverse, urban school with many non-native-English speakers, compared to the two more suburban, less diverse schools, and many of the achievement gaps between ethnic groups at Railside were eliminated.

These findings, released in preliminary form in 2005 and published in 2008, became a rallying cry in the battle to overhaul math education, and they cemented Boaler’s status as an evidence-backed champion for equity. Complex instruction, a method for effective, equitable group learning, was a nice idea in theory for math class. “Railside was important for showing that could be possible,” said Nicole Louie, an assistant professor of education at the University of Wisconsin at Madison.

Carlos Cabana, a former math teacher at Railside, said he saw these methods work up close. “You’d see kids talking and working together or up at the front presenting in every single math classroom,” he said. “Kids came to us often from middle-school experiences that had left them fearful that they were somehow not good enough intellectually, and then they came into our classes and found a very different culture and set of expectations. So many of them, I could tell, breathed a sigh of relief that they might suddenly be mathematically capable again.”

But to Milgram, the Railside study seemed too good to be true.

It all began when his neighbors in the Santa Cruz area told him that a Stanford professor wanted to study their children’s schools, he recalled. Later, when the Railside findings came out, an acquaintance in the Bush administration’s Department of Education emailed him to express interest. “I felt that I really had no choice in the matter, that I had to check this out,” Milgram said.

Cross-referencing test scores listed in the early version of the paper with state data, Milgram — along with Wayne Bishop, then a math professor at California State University at Los Angeles, and a third collaborator — identified and took a hard look at the schools. (They didn’t name them, but the scores indicate that Railside is San Lorenzo High School in San Lorenzo, Greendale is San Lorenzo Valley High School in Felton, and Hilltop is Aptos High School in Aptos.)

“Boaler’s claims are grossly exaggerated and do not translate into success for her treatment [of] students,” they wrote in a 20-page analysis. (They said that their report was accepted by a peer-reviewed journal, but they didn’t go through with publication “partly to spare her and Stanford unnecessary embarrassment.”) In 2005, Milgram filed a claim of scientific misconduct with Stanford.

The university decided that the complaints weren’t severe enough to fully investigate. According to a report summary and a letter from the dean of research at the time, a two-person committee declared Milgram’s concerns about “methodological error” and “faulty interpretation of data” to be a matter of “academic debate.” That took it outside the realm of “research misconduct,” which it defined as “fabrication or falsification.” (An Inside Higher Ed story previously quoted part of these findings.)

Milgram was furious. His concerns, he felt, were misunderstood or caught in “a political game.” Later, Boaler would write that the university, having reviewed her data, found that the “allegations of scientific misconduct were unfounded and terminated the investigation.” But to Milgram, the outcome was not that cut and dried. “Stanford had not cleared her,” he said. (Bishop did not return a request for comment.)

So the debate remains unsettled. Some of Milgram’s accusations cannot be resolved without the original data. He argued that Boaler selectively compared different populations of students across schools, which Boaler said was a “false assertion.” To Milgram, it was damning that the Railside students did relatively worse on standardized tests, like SAT and AP exams. He saw Boaler’s tests as flawed assessments of California’s math standards — the ones he’d helped write. But she believed her tests were easier for all students to read and better at assessing their math understanding, and that Milgram was looking at the wrong students’ scores. She also valued metrics that Milgram’s test-centric mentality didn’t, like that more Railside students enjoyed math, took advanced math, and wanted to keep learning math when compared to students at the other two schools.

Elizabeth Tipton, a statistician at Northwestern University who specializes in education and was not involved with either the study or the rebuttal, said that the increase in Railside’s first-year test scores signals “the potential for there to be an effect” from their reform methods. Boaler’s critics didn’t address that improvement, which suggests that they didn’t fully grasp what the study was designed to isolate, Tipton said.

But they did raise the possibility that Railside’s two comparators scored unusually low due to other factors. Milgram said their math programs were experiencing “significant changes” and “faculty discontent,” which he told me he knew because he lived near the schools. That would be a concern, Tipton said: “Are we seeing Railside doing better relative to the traditional schools, but the traditional schools are doing more poorly than usual?” (Boaler said that she does not remember any such disruption.)

Either way, Tipton said that the Railside study, while “intriguing,” should not be taken as the final word on math instruction. “How do I know that this would work anywhere else?” she said. Boaler acknowledged over email that her study only involved three schools, but that it provided valuable details about how schools teach and how students learn, which is “the sort of depth and range of methods that large-scale studies cannot accommodate or provide.”

The feud symbolized the chasm between Stanford’s math-education and math faculty, who ostensibly share a goal of teaching students math.

“Was he right, was she right? I don’t think it’s my place to say. But it led to an awful lot of ugliness. The way in which this became public was very unfortunate,” said Rafe Mazzeo, a math professor and former department chair who has been at Stanford since 1986. He said that he is occasionally in contact with Boaler and respects her stature in the education world. “I believe that her intentions are good, I really do,” he said.

The episode remains an open wound for Milgram, who retired in 2010. “I’ve wished that the whole thing had never happened,” he said. “I wish that she had, as I would view it, stayed in her lane. She should not be at Stanford.” In response, Boaler said, “I do not give any credence to Dr. Milgram’s very personal and very individual assessment of what I should be doing or where I should be working.”

After Stanford let the matter go, Milgram posted his rebuttal on his faculty website anyway. “I felt that it needed to be available,” he said. Critics of Boaler’s circulated it liberally. In 2006, she was promoted to full professor, and she decided that she’d had quite enough.

She left for the University of Sussex on a prestigious fellowship, one named after Marie Curie. “I just started to think, ‘I want to be back in a more normal place where people don’t come after you for your research and make up things about you,’” she said.

Six years later, on a Friday evening in October 2012, Boaler hunkered down in front of her computer in Palo Alto, ready to take back the narrative. Stanford had spent years persuading her to return, and in the end, she was swayed by thoughts of the many teachers who appreciated her. This time, she resolved, things would be different.

As the rest of the education faculty gathered at a party, Boaler hit “publish” on a fiery essay that still lives on her faculty website.

“I have suffered serious intellectual persecution for a number of years,” she wrote, “and decided it is now time to reveal the details.” Milgram and Bishop had committed “harassment” and “academic bullying” with a litany of remarks and actions going back more than a decade, most egregiously their “baseless” “attack” on the Railside study. Their analysis’ “identification of individual students” violated federal law, she wrote. It did not identify individual students, however. Boaler told me by email she believed that it shared data about groups so small that students could be identified.

Boaler capped off her triumphant night by joining Twitter. “It feels good to be finally fighting back!” she tweeted.

Colleagues were shocked. “Milgram and Bishop simply did things that I don’t think were within bounds of appropriate academic discourse and they made life miserable for her,” said Schoenfeld, the Berkeley professor. Hundreds of sympathetic emails poured in, mostly “from other women detailing stories of bullying behavior by men in universities,” Boaler later recounted. It was “a sign that we are far from achieving gender equality in higher education.”

As Boaler often points out, math is dominated by white men. Women make up fewer than 30 percent of math and statistics Ph.D.s, and at Stanford, two women are tenured math professors compared to more than 20 men. In STEM, “I notice that women are opposed in ways that men are not,” Boaler said. “I think a man could say the exact same things I say, and they’ll get a really different response.” She added, “Women who defend themselves from attacks are often described as ‘combative,’ or worse. If ‘combative’ means, to my critics, that I will stand up for my work and for myself when it is most necessary to do so, then let them think so.”

Milgram and Bishop argued that they had been misrepresented and that if anyone had violated research rules, it was Boaler, since Stanford prioritized “openness in research.” But the more she shared her story, in books and speeches and op-eds, the bigger a hero to educators she became. “My friends often tell me that I should send flowers to Milgram,” she later wrote, “as he helped my research on equitable mathematics teaching get to many more people.”

Boaler came to view this victory as a lesson in how to deal with naysayers of all sorts: dismiss and double down. “Education is a system in which we need to challenge the status quo because it has failed so many,” she writes in her book Limitless Mind.

“Pushback is a positive sign; it means that the ideas that are ruffling people’s feathers are powerful.”

With a rapt audience, Boaler spread her message far and wide over the internet. She designed four online math courses that she says have been taken by more than 1 million people, helped create a math game called Struggly, and co-founded Youcubed, a Stanford research center with math resources for teachers and parents, which has been visited online more than 60 million times. One of Youcubed’s latest offerings is a data-science course, which mostly uses statistics to crunch data about everyday life — math skills that Boaler says every high schooler should have.

Upon returning to Palo Alto in 2010, Boaler also struck up a formative partnership with Carol Dweck, a Stanford psychologist taking education by storm. Dweck’s research showed that people with a “fixed” mindset believe that intelligence and ability are innate and unchangeable, while those with a “growth” mindset believe that success comes from learning and persistence. One landmark study reported that academically struggling seventh graders with a fixed mindset earned better grades after a growth-mindset workshop.

These findings offered a scientific basis for Boaler’s deep belief: that all students can learn math if they work hard and are taught under the right conditions. Boaler sees the eldest of her two daughters, who has learning disabilities, as proof. “All through her high-school years, she stayed up ’til two o’clock in the morning doing homework, and she ended up getting a 4.0 GPA and has a fantastic growth mindset,” she said.

Boaler is ubiquitous on the math-education circuit, from keynoting at conferences to hosting training sessions, and beloved. Cole Sampson, an administrator for Kern County schools, said that Boaler transformed the “follow the steps” mentality that he used to teach math. She is “a trailblazer pulling us all forward on her back,” he said. Jean Maddox, a fifth-grade teacher who participated in a study showing Boaler’s methods to be effective, said, “I personally will never be able to go back and teach math the way I did before reading [her] book and taking her courses.” And talking about Boaler brought tears to the eyes of Ma Bernadette Andres-Salgarino, an administrator in the Santa Clara County Office of Education. “Even with the threats she has received because of her stance to advocate for the voices of people of color,” she said, Boaler has “bravely stood her ground to fight for what’s due for our underserved, racialized, and disadvantaged students.”

Boaler’s energy impresses other education scholars. “She is really interested in having an impact on practice,” said William Penuel, a professor of learning sciences and human development at the University of Colorado at Boulder. “That is her passion — her passion for impact on practice and for equity.” She is “thoughtful and challenging, which is good for the field because it helps us to reconsider our assumptions about the ‘what, how, and why’ of children learning mathematics,” said Dan Schwartz, Boaler’s dean at the Stanford Graduate School of Education.

But parents in Boaler’s own backyard have resisted her calls to keep all students in the same math classes, rather than “track” some into gifted classes, based in part on her Railside research. Detracking is perennially controversial, and other studies are mixed on whether it can improve equity in all schools.

In 2014, San Francisco Unified School District adopted a policy of starting all ninth graders in algebra instead of allowing some students to start in middle school. Three years later, it announced that as a result, the percentage of first-year algebra repeaters had dropped from 40 percent to about 7 percent, which Boaler praised in an op-ed. But a skeptical group of residents, Families for San Francisco, reported that they could not replicate the 40-percent figure based on district-provided data. And they pointed out that the district had simultaneously stopped requiring students to test into the next math level, which alone could explain the decreased repeat rate. The math department has since seemingly admitted that the backstory was complicated: Speaker notes in a presentation described it “as a one-time major drop.” (A district spokesperson did not explain the 40-percent figure’s origin, but acknowledged that “a significant one-time drop” had occurred when the test requirement was lifted.)

“It’s still very, very concerning that they refuse to offer the calculation,” said Maya Keshavan, an electrical engineer and mother of two who requested the data from the district. What worries her and the other parents is that under the algebra policy, students have to squeeze another level of math into their four years of school to take calculus as seniors. (Nationwide, about 20 percent of high schoolers take calculus.)

Keshavan, for example, paid $700 for an outside algebra class so her daughter could bypass the policy and take geometry as a freshman. She is now a junior at a STEM college. “It’s not equitable and it’s not fair and it leaves behind the most underserved people,” Keshavan said. But she felt her hands were tied. San Francisco’s equity-minded policy does not alter the reality of hyper-competitive college admissions, especially for students trying to break into STEM. “We’re all competing for everything,” she said.

Boaler said that she had not examined the numbers — but “I do question whether people who are motivated to show something to be inaccurate are the right people to be looking at data.” This week, a group of residents alleged in a lawsuit that the district was unfairly holding back “talented” students and violating a 2015 state law that requires math policies to be objective and transparent. On the day the lawsuit was filed, the district said in a statement that it was working to identify ways to improve its math programming.

In Palo Alto, a familiar battleground in the math wars, a new generation of upset parents also sued after the school district redesigned middle-school math in 2019. The intent had been to limit how much students could skip ahead and to reduce achievement gaps, the district explained, noting that “experts in math education agree that tracking … leads to lower achievement overall.” But a judge in February found the district to be violating state law.

Plaintiff Edith Cohen, a parent and a computer scientist, blames Boaler in part. The Stanford professor met with the district when it was revamping the program, and her research was cited. (Superintendent Don Austin said that the district’s math policy differed from Boaler’s recommendations because its students progress through math faster than, for example, San Francisco’s students. Austin also said the district is exploring its legal options.)

Cohen said by email that the policy “is inequitable to an extreme, increases gaps, and makes public education inferior.” Boaler questioned the evidence for those claims. “I’m never happy to see somebody suing a school district,” she said, adding, “Of course, if you’re a very wealthy person, maybe you can do that.”

Although Boaler maintains that her views are supported by studies, experts have pointed out discrepancies with what some of the studies actually say. And while Boaler proclaims to value mistakes — one of her book chapters is titled “Why We Should Love Mistakes, Struggle and Even Failure” — she ceded little ground when asked about several apparent mistakes of hers.

Mathematical Mindsets, first published in 2015, bills itself as a neuroscience-backed guide to teaching creatively and cultivating a growth mindset in math students. The book opens with a glowing endorsement from Dweck. But in a review, Victoria Simms, a developmental psychologist who studies mathematical thinking at Ulster University in Northern Ireland, zeroed in on “numerous examples of an inappropriate use of neuroscience to back up educational claims.”

One example involved a 2011 study in which 25 college students tried to correctly respond to hundreds of rapid, repetitive prompts involving strings of letters, while researchers monitored their brain signals. The latest version of Mathematical Mindsets, in explaining why errors are integral to learning, claims that the study “shows us that we don’t even have to be aware we have made a mistake for brain sparks to occur.”

But that was not what it showed, according to Jason Moser, a psychologist at Michigan State University who was the study’s lead author. “Our study really was not about being ‘aware’ versus ‘unaware’ of your mistakes,” he said. What they did find was more nuanced and indirect: Participants identified through surveys as having growth mindsets showed higher levels of a brain signal reflecting attention to mistakes, and were likelier to perform more accurately on a prompt after messing up on the one before it.

Upon being informed of Moser’s objections, Boaler stood by her interpretation. “I am pretty confident that that study did show that there was brain activity without people’s awareness of the mistakes that they’ve gone through,” she said, adding, “Maybe he would phrase it in a way that was closer to what happened. But would it be understandable to teachers? Maybe not, I’m not sure. I don’t think it is that important.”

Boaler has also incorrectly stated, in Limitless Mind and in a TEDx Talk, that participants’ brain activity was monitored with MRI scans (a different technology, an EEG, was used). And in describing the underlying science, she writes in a Youcubed white paper that “when we make a mistake, synapses fire. A synapse is an electrical signal that moves between parts of the brain when learning occurs.” But synapses are not electrical signals; they are the small pockets of space through which neurons fire chemical messengers via electrical signals. In both instances, Boaler pledged to update her language, though she said that the latter mistake was because her paper was written around the time of Moser’s, and “science evolves.” (The science of how synapses work was established by the mid-20th century.)

But in other cases, Boaler defended her descriptions. “In the Moser study there was greater brain activity and growth when people had a growth mindset,” she states in the Youcubed paper, explaining that “growth” meant that “new pathways can form in the brain, pathways can become strengthened in the brain, pathways can connect in the brain.” Not so, Moser said: “Our study did not show that we were producing stronger connections or that we were growing connections in any way.” The same article claims that the study “tells us that having a growth mindset can cause greater brain growth when mistakes occur” — when, according to Moser, it “says nothing about causation whatsoever.” Just because two variables correlate with each other, there isn’t necessarily a cause-and-effect relationship.

Told of Moser’s comments, Boaler said that a different neuroscientist “would tell you something really different.” And overall, she said that these discrepancies amounted to “nitpicking” over “very fine details” when she is trying to bridge the gap between researchers and educators. “I’m not surprised that a scientist would say, ‘Oh, our study says this, it doesn’t talk about causation,’” she said. “That’s very typical of anybody talking about their study. That’s why, sadly, a lot of those studies never get to the public, and they never get to people who need them, because the write-up of the scientists themselves is often very, very impenetrable and also very cautious.” (After our interview, the Youcubed article was taken down.)

But in Moser’s view, the facts matter.

“It’s great when science can inform practice,” he said. “And at the same time, it’s important that when science informs practice, that it’s precise enough or it’s nuanced enough so that it actually is applicable as it can be. I think that’s just where some of these statements have missed the mark, which is it’s gone beyond where the science is.”

Another questionable claim relates to one of Boaler’s most despised class activities. “For about one third of students the onset of timed testing is the beginning of math anxiety,” she asserts in Mathematical Mindsets and a Youcubed white paper, adding that the tests are “a major cause of this debilitating, often life-long condition.”

But the basis for that causal link is a mystery, Greg Ashman, a math teacher and school administrator in Victoria, Australia, has found. Mathematical Mindsets cites the white paper, which in turn cites a 2014 opinion piece in a journal for math educators, but nowhere within it is a reference to sufficiently back up the claim. Boaler did not identify any such citation when asked, but instead provided me with a list of studies that were not in the article. She also said that “one third” was an estimate that “comes from 30 years of looking at different studies and examples.”

Ashman said he worried that Boaler was calling timed tests harmful without evidence, when research indicates that repeatedly practicing rapid calculations can help students build fluency with math and improve their math skills. Having blogged about several apparent inconsistencies in her work, Ashman, who has a Ph.D. in instructional design, told me, “She is sometimes careless with the evidence.” In return, Boaler accused him of criticizing her because he is “selling” opposing ideas, such as books about teacher-led instruction. “Of course he doesn’t like me sharing that timed tests in elementary school cause math anxiety,” she said.

In 2019, when Boaler tweeted that “timed tests are the cause of math anxiety,” Ashman responded, “I disagree — you have not demonstrated a causal link,” and pointed to the blog post he’d written. She did not respond and, later, blocked him.

She told me that she didn’t recall blocking him for that tweet alone, but that it was “probably the last straw” in a series of other critiques. “If anybody should be answering questions about things written,” she added, “why aren’t we talking to him about his defamation of me?” (Later, a spokesperson for Boaler, Ian McCaleb, said by email that she “RETRACTS any and all inference to or suggestion of defamation in regard to Dr. Ashman, or to anyone else.”)

Boaler responded similarly to criticisms of Limitless Mind, which extols the human capacity to learn all subjects, not just math. She introduces herself in the book as “a Stanford professor of education who has spent the last few years collaborating with brain scientists,” and the billionaire Laurene Powell Jobs praised her depiction of “cutting-edge brain science.” Published in September 2019, the book presents an optimistic portrayal of growth mindset’s association with academic achievement, largely citing Dweck’s work.

But developmental psychologist Daniel Ansari, who runs a cognitive-neuroscience lab about math-learning at Western University in Ontario, Canada, accused Boaler of overstating the positive effects of outdated studies. Newer, larger studies indicated “these effects are, at best, modest — and possibly, nonexistent,” he wrote in a critical review, citing two randomized controlled trials in the U.S. and the U.K. as presenting a “mixed” picture. Boaler defended her characterization in Limitless Mind by pointing to a research summary article and three studies — two of which she helped write — as well as a study released after the book.

Ansari also wrote that Boaler had misinterpreted neuroscientific concepts and made claims without evidence. For instance, she stated, with no citation, that “less than 0.001 percent” of people are “born with brains so exceptional that those brains influence what they go on to do.” Boaler did not respond to this criticism, but took issue with “the act of isolating sentences from books” because “anyone’s book can be pulled apart in this way, with the goal of finding thoughts or passages that others disagree with.”

“Ironically, despite reviews and blog posts pointing out Boaler’s clear errors of interpretation and inference in her previous writings,” Ansari concluded, “she adopts a fixed mindset when it comes to scientific evidence, continuing her past tendency to play fast and loose with these findings and to ignore those that run counter to her narrative.”

Boaler challenged Ansari on Twitter when his review came out, accusing him of misspelling her name (“so how would anyone believe anything you write?”). After Ansari explained — it had been misspelled on the publication’s website, not in the article itself — she blocked him.

“I’m quite happy to answer questions or have discussions with people,” Boaler said of the dispute, adding that she doesn’t block everyone who disagrees with her and that she is “very willing to change things” in response to feedback.

She blocked Ansari not because of his review, she said, but because he’d interacted with other men critical of her work. (She cited a tweet in which Ansari replied to one such blogger: “Excellent post.”) These men are not “offering substantive pushback,” nor have they “offered to meet,” she said by email, and she deserves to have a “social media space that is collaborative and educative, not adversarial.”

“I do not believe I have treated scientific facts haphazardly,” she added. “The small circle of people who routinely share that claim have had a clear agenda for quite some time, which is to discredit my work because they simply do not agree with it.”

When it was last updated in 2013, California’s math framework basically reiterated the then-new national Common Core math standards. It didn’t properly emphasize the importance of problem-solving, reasoning, connection-making, and communication, according to Schoenfeld, of Berkeley. California’s trillion-dollar tech sector boomed in the ensuing decade, but many of the state’s students of color were — and continue to be — left behind. On math tests, even before the pandemic, Black eighth graders on average scored 42 points below white students and 59 points below Asians.

Brian Lindaman, the state-appointed lead author of the newest framework, knew early on that he wanted Boaler on his writing team. “I was very flattered that she would even want to be involved,” said Lindaman, a professor of math education at California State University at Chico. The two of them, along with two other math-education experts and one mathematician, were supervised by a committee of 20 K-12 math educators and specialists, among them Sampson and Andres-Salgarino. (Some have criticized the dearth of math professors, but a spokesperson for the California State Board of Education said that it appointed as many members as possible after an open process and that most had to be credentialed K-12 teachers.)

When the 857-page first draft was released in February 2021, the response split as usual between enthusiastic math teachers and aghast professors. There were also right-wing commentators decrying “woke math.” Even Tucker Carlson ranted about California wanting to teach math with “a strong social-justice orientation.”

“Right, numbers are racist, kill them,” the Fox News host deadpanned, as Boaler’s smiling photo flashed in front of millions of viewers. “It’s lunacy.”

For years, right-wing media had been singling out women and minorities who study inequities in math education. After Carlson’s monologue, death and rape threats flooded Boaler’s inbox. Some messages told her to go back to her “own country,” others brought up her daughters. It was terrifying, she said, to realize “they know things about me.” Yet she couldn’t help but feel validated. “No greater indication that we all did great work than @TuckerCarlson targeting it,” she declared to a colleague.

The document carries Boaler’s unmistakable stamp. Twenty-six of her books, articles, and white papers, in addition to 18 links on Youcubed, are cited in the second draft of the framework, released in March 2022. According to Save Math, a group opposing the proposed framework, one of her two most-cited studies is Railside, which is held up as evidence for ideas like detracking, open-ended group discussions, and activities that explore math’s visual side.

The framework also contains some of the disputed claims from Boaler’s past writings — including its invocation of the Moser study as an example of how brain pathways develop, its claim that timed tests cause math anxiety, and its optimistic presentation of growth-mindset research. In another example, the document cites a 2013 study that Boaler has often discussed, twice stating that when participants “worked with numbers and also saw the numbers as visual objects, brain communication was enhanced.” But the study did no brain imaging, so “it’s simply wrong to make any neural claims from that paper,” one of the researchers, Joonkoo Park, said by email. Still, Boaler said that based on her reading, “concluding brain communication is not a stretch.”

And Boaler said that no one raised concerns about inaccurate references as the framework was being developed. “If somebody were to give feedback and say this study isn’t described in the way that somebody thinks it should be, then that’s something that would be considered and changed,” she said. “That’s the whole point of the framework, that there was a process, public comments, lots of opportunity for that. That didn’t come up as something that should be changed.”

In fact, Brian Conrad, a Stanford math professor and its director of undergraduate math studies, has compiled a 25-page summary of apparently incongruent references, including regarding the 2013 study, as part of an extensive critique of the framework. “False or misleading citation of papers,” he wrote, “cannot be used to justify public policy recommendations and guidance to districts.”

One of the framework’s most controversial proposals would allow students to swap out the second year of algebra for another course, such as data science. This option is already being codified on some campuses, to the alarm of many math professors. Under a University of California admissions-policy change in 2020, statistics-heavy data-science courses — like Boaler’s Youcubed course and Introduction to Data Science, developed at UCLA — were approved as advanced math courses. Boaler promoted it, then persuaded Stanford to add “data science” to its admissions website, she told me. She rejoiced again when Harvard followed suit. To Boaler and other data-science evangelists, like University of Chicago economist and Freakonomics co-author Steven Levitt, swaths of algebra II are as irrelevant as “sock darning and shorthand.” Many students also find the material so insurmountable that in 2018, the California State University system stopped requiring intermediate algebra for students not majoring in math or science.

But the concepts, like logarithms and trigonometric functions, remain crucial to majors like engineering, computer science, and, well, data science, according to faculty in quantitative fields. Students who skip algebra II may later be unable to, or take longer to, catch up with the advanced math they need, namely calculus, for careers in emerging technologies like artificial intelligence and machine learning. UC admissions policy still requires advanced math courses to “build upon” concepts from algebra II and be designed for juniors and seniors. But Conrad has questioned whether those rules are enforced, since Introduction to Data Science contains little algebra II and can be taken in the first half of high school. (Ryan King, a UC spokesperson, confirmed that most versions of this course and the Youcubed course meet its requirements. He also said that the data-science classes are considered to be “additional” options, not ones “replacing” algebra II.)

After faculty at Stanford and Harvard fretted that future STEM students might get the wrong idea about the math they needed before college, “data science” quietly disappeared from both admissions pages. But the California math framework’s “data science” option remains in play, and rather than “opening STEM pathways for many more students,” professors up and down the state worry it would give students “the false impression that a data literacy course will prepare them for a data science career,” as Conrad has written. Statistical data-literacy skills, like how to read a poll or analyze a study’s methodology, are important, but could be blended into the existing curriculum, he has argued.

The framework does say that STEM-focused students should stay on the traditional path to calculus, and Boaler acknowledged that some may later want to pursue STEM without having taken algebra II. But “we can’t really have a system in place that is there for half a dozen students to want to do that,” she said, “and then so many others are pushed out because of the same system.” (Data about such students is sparse. According to Boaler, out of 63 students across three schools who took Youcubed’s course in the 2021 school year, 60 percent had taken algebra II before. King, the UC spokesperson, said that “many” applicants take algebra II on top of other advanced-math courses.)

Boaler said she wasn’t surprised to see STEM professors resisting change. What she finds “very disappointing” is that Conrad is among them. “He never reached out to either one of us, which would have been a collegial thing to do,” she said, referring to herself and another collaborator at Stanford. “He just started writing things against the framework.” She felt owed a heads up because, she said, “I would just think that if you were in the same institution as somebody, it would be kind of cordial.” (Conrad pointed out by email that the document “is a matter of K-12 public policy, not an issue internal to Stanford.”)

In the math wars, little is ever cordial. And Boaler hasn’t just suffered slings and arrows; she’s hurled them.

Born in Los Angeles to an Ethiopian mother and an African American father, Jelani Nelson grew up teaching himself to code in the U.S. Virgin Islands. He earned a computer-science Ph.D. from the Massachusetts Institute of Technology, which he also attended as an undergraduate, and was on the faculty at Harvard before joining Berkeley in 2019. In his spare time, he runs coding workshops for high schoolers in Ethiopia and Jamaica.

When Nelson found out that the framework initially recommended eliminating all math tracking, he was alarmed at the thought that some children could be held back from fulfilling their potential. While that proposal has since been removed, he still thinks that much of the framework is antithetical to its goal of closing racial-achievement gaps. Watered-down “data science” instruction in public schools could drive wealthier families to pay for workarounds or switch to private schools, and leave behind lower-income students of color, Nelson fears. As other critics have noted, the affluent school districts of Beverly Hills and Cupertino declared early on that they wouldn’t follow the framework. “I don’t see it as being a ‘white male only’ kind of pushback,” said Grace O’Connell, who is half-Black, half-white and the associate dean for inclusive excellence at Berkeley’s engineering college. “I think there’s some serious concerns about the framework’s fundamentals.”

When Nelson helped author a letter criticizing the framework in late 2021, he barely knew who Boaler was. Upon Googling all the authors and oversight members, he was dismayed that none were Black. (Janet Weeks, a spokesperson for the State Board of Education, said that the framework members “were keenly focused on issues of equity in mathematics,” and that “diverse voices have contributed to deliberations at all of the public meetings in the process and in the two 60-day public comment periods.”)

One day the following spring, Nelson happened across a series of tweets from a San Francisco math teacher who was critical of the framework. She was sharing screenshots, drawn from public records, of Boaler’s contracts for consulting work with school districts. According to one of her several tweets, Boaler had charged $40,000 in Oxnard, Calif., where, as Nelson then read online, 97 percent of students are non-white and 88 percent are socioeconomically disadvantaged.

“The proposed CA Math Framework states improving math learning for black students as central motivation and has 0 black authors,” Nelson tweeted. “Instead, one author has alarmingly lucrative consulting deals with school districts with large minority populations, charging $5,000/hr.”

Boaler’s rebuke, with its reference to “police,” soon followed. “I was shocked to see that you are taking part in spreading misinformation and harassing me online,” she wrote. She implored him to delete his tweet, and “consider acting in more collegial and productive ways to help students get a better future in mathematics in California.” Boaler told me that she had been getting threats in the wake of Nelson’s tweet. “I felt that I was under threat of violence, my life, even,” she recalled of that April morning, adding, “I wish I could take back writing to him.”

Nelson was stunned to be accused of harassment, a crime, and of broadcasting “private details.” Most of all, he was shocked that she had seemingly called law enforcement on him. “I don’t know how to interpret that email other than her wanting me to believe that cops were on to me,” Nelson said. (Boaler also offered “to talk about your concerns” about the framework, but Nelson didn’t see it as genuine; Boaler insists it was.) His mind flashed back to 2017, when he was detained in the Boston area while running to dinner. After ordering him to put his hands on their car, the police officer only released him upon learning that he was at Harvard.

Reassured by attorneys that he was in the clear, Nelson decided to go public. “A @Stanford professor just threatened me with police,” he tweeted, screenshotting Boaler’s email. “Public advisory: don’t call the cops on black people for no reason. Black people disagreeing with you on Twitter is not a crime.”

“It is horrifying,” he continued, “that the CMF claiming to uplift black children was co-authored by a person who finds police intimidation against blacks acceptable.”

In a post-George Floyd world, his tweets caught fire. “How in 2022 are you not aware as a white woman that doing this to a Black man can result in DEADLY consequences?” asked one of the hundreds of people who piled on against Boaler.

With the framework in its home stretch, Boaler’s frayed relationship with the STEM community was on painfully public display. What happened next did little to repair it.

In a tweet to Nelson, the professor explained that her address had been mentioned in a different, since-deleted post in the San Francisco teacher’s original Twitter thread. It was that tweet that she had referred to Stanford’s threat-prevention office, which includes lawyers and police. Privacy was paramount, she said, having received death threats before. “I did not mention your name to any authorities or to Twitter,” Boaler wrote. “I am very sorry that my communication wasn’t clear. I understand why you might have read it in the way you did.” Two parents followed up with a defense of her advocacy for students of color.

But that wasn’t the end of it. Boaler spoke about her Oxnard contract to the San Francisco Chronicle, which reported that “the deal also means significant travel time.” That prompted Nelson to point out on Twitter that the 2020 training had been “virtual,” sparking a new wave of criticism. Boaler told me that while her consulting work usually involves travel, there wasn’t any in that case, and the reporter had likely misinterpreted her comments.

That still wasn’t the end. Months later in August, she tried to get #ProtectProfBoaler trending on Twitter, where she has more than 100,000 followers. And she called Nelson “the black male professor” who “very cleverly changed my request to meet into a claim of racism.”

That remark solidified all of Nelson’s suspicions. “She has unfortunately failed to really engage with the serious and credible arguments against many of the things she’s pushing for,” he said. “I hope she, at some point, can really self-reflect.”

Boaler said that she didn’t remember writing the tweet and “probably wouldn’t write it today.” “I was trying to defend myself,” she said, during “the worst period of my life.” She said that her earlier apology had been sincere and that she remains open to people with “genuine questions.” Yet, she added, “I prefer not to engage with the people who I believe have an agenda to suppress my research evidence and to discredit me.”

The framework was expected to be approved in July, but that deadline came and went. Janet Weeks, the state board spokesperson, said that another draft would be coming “later this spring.” While it is unclear what shape the next version will take, the original authors’ contract with the state expired last summer, and Weeks said the public would get “another opportunity to weigh in.” At which point the math wars will surely begin anew.

Not that they ever ended. In the last week, Boaler updated her website for the first time since she’d denounced Milgram and Bishop more than a decade ago. On Twitter, she shared her new essay with another hashtag: #Boaliever. This time, she informed readers that a story in The Chronicle of Higher Education was imminent. And once again, she said she was under attack, not just from the two mathematicians, but also “others — a small but loud group — who are working to stop the proposed California mathematics framework.” They would not stop her, she wrote, not when so many stand to benefit from the reforms she champions. She vowed to press on.