Math Wars Continue

 From the Chronicle of Higher Education (you can get a free account to read), The Divider; Jo Boaler of Stanford is leading the math-instruction revolution. Critics say that her claims don't always add up. 

This is a very lengthy, meaty article about the different forces trying to gain ground for their view.  The central figure appears to be Jo Boaler, a British researcher who is a Stanford professor and an expert on math instruction.

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.

About Boaler and her new math teaching:

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 six 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.

There is a study that Boaler did that seems to have touched off the suspicion around her research:

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

The article goes into great detail about the great outcomes from the Railside study but also troubling issues.  It seems to devolve somewhat into charges of sexism from her critics. 

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.

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.”

Boaler went out there, full speed ahead:

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. 

I have always embraced that idea of a "mindset" about learning but that last sentence? You'd have to define "right conditions" because students come from many home environments that may or may not have the "right conditions," schools that may or may not have the "right conditions" and students who are able to work "hard."

Per usual, in comes this idea of "tracking:"

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.” 

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.

That sentence I put in bold? Big red flag to me.

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.

Those include using studies in neuroscience to support her work. When it is pointed out that those studies aren't saying what she says they are saying, she calls it "nitpicking."

“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.”

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 was asked to and did join a group of academics in rewriting California's K-12 math framework. 

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.

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. 

But her fiery personality led her to attack the questioning of a Black Berkeley professor, Jelani Nelson, and her seemingly to have threatened to call the police on him in a tweet. This led her on a chain of actions, none of which seemed to help her.

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 reform.

And where does this leave students and parents? I cannot say.