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 sciencequietly 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.


peonypower said…
this makes me think of the movement to drop phonics from reading instruction for "whole reading" methods that have left a generation of students struggling to read. the story on NPR's Reveal dissected that story of a charismatic educator promoting a method that was then embraced almost like a cult. This seems to be some similar it is worrisome. While learning data science is a great goal and should be taught in high school leaving behind algebra 2 seems like a mistake.
Anonymous said…
Jo Boaler and Lucy Calkins and Irene Fountas & Pinnell are are snake oil salesmen. Their schemes are not reproduceable or evidence based. They are essentially squatters in academia: Jo at Stanford, Lucy at Columbia, Irene at Lesley University, and Gay emerita from Ohio State. They are rolling in personal profits and wealth at the expense of struggling students and struggling school districts.

Gay Su Pinnell bought herself a Maserati (

Irene Fountas paid $3.1 million in 2006 for the house she lives in and records show that she appears to own or co-own at least seven other properties (ibid)

Lucy Calkins has an LLC that was worth nearly $23 million in 2021 (ibid)

Jo Boaler charged Oxnard School District in CA $40,000 ($5,000 per hour) for professional development training for math teachers. ( By the way, Oxnard school district is 72% FRL and 50% ELL.

Our colleges of education are full of shams. Kids pay the price.

For Shame
Anonymous said…
Do you think the nations of China or South Korea or Singapore are figuring out ways to deny their kids algebra?

Are they busy actively trying to sabotage their public school’s academic opportunities or academic excellence for their kids in their nations’ public school systems?

Are they actively trying to limit the number of children who can take calculus before matriculating onto college, technical school, or university? ( California had a referendum about calculus in their public school systems.)

Flat earth - the book…
Glass palace is incapable of looking up from navel-gazing to figure out we’re not alone, and our past performance as a nation is no guarantee of future results. We have led the world in innovation but that doesn’t mean we’re always going to be the leader, it does mean that other nations have seen economic prosperity innovation brings, and have recast their policies accordingly to build to that, and certainly front and center is public mass education.

School is school. Math is math. Calculus was invented in 1675, it has not changed since. Developed? Yes, but fundamentally has not changed. What has changed? It’s applicability, that has mushroomed up exponentially to deny our Seattle kids. The opportunity to thrive in multivariable calculus in the first year of university is to deny them a high-pitched STEM career.


The denial goes deep with these folks. The common sense completely absent

Calculus isn’t for everybody, just like engineering degrees aren’t the be-all end-all, but I sure would like kids who are interested to have a shot at it.


PS - AI (artificial intelligence) is pure math. Can’t participate in any of that computer science if you’re not profoundly sophisticated is mathematical operations and thinking.
Michael Rice said…
This is nothing new. This is what the Math Ed. schools have been pushing for years. It does not work. The motivated kids, who are concerned about their grades and want to learn, do all the work and the unmotivated students just copy the answers while they get better at World of Warcraft.

The way you get better at something is practice the basics and the fundamentals until you have mastered them. That is true in any pursuit in life. Only after you have mastered the basics can you move on to the more complex and complicated. In math that means knowing your math facts, knowing your times tables, knowing how to add, subtract, multiply and divide whole numbers, fractions, decimals and percents. To do anything else is to sentence a student to struggle in mathematics.

I am in my 18th year teaching math in Seattle. I have seen the fruits of the failed polices to not require mastery of the basics before moving on to more advanced topics.

I will slightly disagree with peonypower on one thing. I strongly believe that an on-level statistics class should be offered as an alternate path for the third year of math. I am in no way saying get rid of Algebra 2. Algebra 2 is an very important class that I have taught many times. An on-level statistics class should be offered because most people will spend their lives reading about, using and analyzing data. Being data-literate is an important 21st century skill that should be taught to all students, not just in AP Statistics. That being said, I am NOT advocating for the elimination of Algebra 2.

Anonymous said…
In our SPS experience (three kids, with two still in high school), the math *and* science curriculums no longer work. Our kids are floating through without attaining mastery or deep knowledge about these subjects. I don't at all blame the teaching - it is more the manner in which these subjects are taught now. No physical text books or print-outs; everything is online, and for the life of me, it is always difficult to find the pages that actually describe a subject vs. the "discovery" stuff that our kids are supposed to use to understand something. It is a common occurrence at our dining room table for me to ask my kid "where are the materials you used to learn this?" and for my kid to say "we didn't learn it - we only have this worksheet". I think there is an over-reliance on what happens in the classroom, and little or no material that students can refer to when they get home and try to apply what they've learned (homework). It is hugely frustrating.

Last night trying to help our 9th grader prepare for a chemistry exam, she couldn't point me to any concise resources describing what she was learning - only worksheets that seem to hint around at the answer a lot without actually providing solid information. We have resorted to buying "Chemistry for Dummies" (no kidding) to help our kid understand what they're supposed to be learning. PDFs and online worksheets and ethereal online "discovery" forms...a huge barrier to learning.

Lost Generation
Downward SpiralContinues said…
Franklin HS plans on killing AP Chemistry and AP Physics.

Anonymous said…
The old math/science sequence was often more or less like this for all students:

7th grade - algebra 1 - review of elementary science
8th grade - geometry - chemistry (with math)
9th grade - algebra 2 - biology (with math)
10th grade - trigonometry (= precalc) - physics (with math)
11th grade - calculus - AP or honors chemistry, physics, or biology
12th grade - stats or linear algebra - Advanced science elective
College: Ready to start most STEM majors on admission, graduate on time, possibly saved a lot of money for credit awarded for AP test results

The new Boalerized sequence most kids are getting locally now is:

7th grade - previously 6th grade math and science
8th grade - review elementary math and science
9th grade - algebra 1 - chemistry A (no math) + physics A (no math)
10th grade - geometry - biology (with some math)
11th grade - algebra 2 - chemistry B (mostly review chem A, then some new content with math) + physics B (mostly review physics B, then some new content with math)
12th grade - precalc (or a non-college-prep data science course or sociology of math course) - no science at all, an AP/honors class, or astronomy, geology, marine etc.
College: No savings on credits awarded via AP test, probably can't get into first-choice school and maybe not even into UW, spend 2-4 semesters taking high school math and science in college, ready to start in STEM major only by junior year, graduation likely delayed by 2-4 semesters (also higher risk of dropping out)

The splitting of the required chemistry and physics courses with a one-year gap between them is an unmitigated disaster, and the nearly math-free chem A/phys A courses should be an embarrassment to all of us.

In Seattle, we do have an opt-in compacting option for students in most but not all middle schools:

7th grade: 7th/8th grade math compacted
8th grade: algebra 1

This allows high school students to take (AP, honors, or regular) calculus, at least. Jo Boaler doesn't like 8th grade algebra one bit, but Seattle does still allow it.

We don't have any science compacting.

Running Start offers a free way to compact any subject sequence starting in 11th grade (where 1 year of high school = 1 semester of community college).

SFUSD lied about its results using Boalerized math, which showed essentially no effect on equity but with substantive harm to college admissibility, and we are not seeing promised equity gains in Seattle with our math and science sequencing, either.

Math Girl
Stuart J said…
I've been following the math wars for many years. The bottom line is parents need to be really watchful, and likely hire private help if they can't help their student themselves.

Some comments.

1. Jo Boaler has a daughter in college. I spotted her bio on a sports web site, which listed the daughter's high school. It is Notre Dame of San Jose, which is all girls, California's oldest high school, and has a curriculum that puts it a step above Holy Names, Lakeside, Seattle Prep, University Prep and every other private school in Seattle. The course cat does list a Youcubed class.
They have Honors and regular version of Geometry, Algebra 2, Trig/Pre Calc, Statistics ... and then regular Calc, AB Calc and BC Calc. I've never seen a school with so many different honors and regular options.

So if de tracking is so wonderful, why did Boaler send her daughter to the ultimate tracking school? She could easily have sent her out of district to San Francisco.

2. Boaler wrote an article in the Stanford alumni mag, which a friend gave me. The article had an interview with a person from northwest Arkansas at the end .. but no data of outcomes, just anecdotes about how test scores dipped and are likely to go up. The article was written in 2018. What has happened since? It is hard to know. But at this point, Boaler's methods have been tried in a lot of places and there never seem to be data points of increased numbers of kids going to college, majoring in math etc

3. San Francisco .... ugh. Low numbers of kids in general, high percentage in private schools, lots and lots of private tutoring companies ... and when SFUSD keeps kids in Alg 1 in 9th, they do provide some work arounds ... the students can take a year of Geometry in a summer school, so that way they can take Alg 2, Pre calc and then Calc. But .... the summer school classes were not offered at every school. From what I could tell, they were much more likely to be offered in the affluent neighborhoods, and the district did not provide busing. So is that equity?

4. Data Science requirements. Students without Calc will have limited options. Here are two colleges as examples.


required for the major: Math 280. Required pre req: Calc 152.

Data Analytics at WSU requires 10 credits of Calc and Linear Algebra

5. Irony: she says no need for Alg 2 / Trig ... but has a problem she loves that involves trig!

Anonymous said…
Great, so Boaler tries to destroy earlier/harder math for every public school student in California while sending her own daughter to a school with earlier/harder math.

This reminds me of former San Francisco school board commissioner Alison Collins, who stopped S.F.'s Lowell High School from using a merit-based admission policy (because she says those are racist) but happily sent her own daughter to San Francisco's only remaining merit-based high school, the Ruth Asawa School of the Arts.

There seems to be a lot of this kind of thing going around.

House Glasses
Outsider said…
In any successful ideological scheme or scam, there will be elements of truth. So it is with Boaler. It's true that:

1) Some students really do learn math better with manipulatives, group work, and other non-traditional approaches. How many of these students will ever attempt a university STEM major is less certain, but perhaps it's not zero.

2) For students not on a STEM track, and perhaps not even on a four-year college track, "data science lite" would usually be a more engaging and valuable course than Algebra II or trigonometry / pre-calculus.

3) For students "far from educational justice" (i.e. have affirmative action leg-up and can get into a university STEM program even without high school calculus), a genuine applied statistics + math review + calculus warm-up course in high school might be better than trying to take calculus in high school. These students can take calculus in college.

When these truths are combined with a militant one-size-fits-all philosophy, however, the nature of the project is revealed. It's not about helping any students with math. It's a social engineering project, designed to limit the math education of students who previously did fine with traditional approaches; and undermine their college and career prospects; and redistribute college and career opportunity toward categories of student who haven't done well in the past with traditional math instruction. If you understand that part, nothing Boaler et al. say is a mystery, and none of it is incorrect relative to their true goals.
Anonymous said…
@lost generation, I believe the no-homework, no textbook is intentional. I believe I read that SPS considers homework inequitable because not everyone has help at home. They intend for all learning to be done in the classroom only. As you’ve discovered, this doesn’t work. Downward achievement will be blamed on COVID for a good bit so who knows when this will come to a head.

Anonymous said…
4 Sets of Problems:
I.) An education policy cla$$, as well as too many teachers, who completely disparage the grunt work of practicing basics to mastery.
Mastery of basics frequently has boring repitive work so that the basics can be mastered. Grow Up, Tough Shtuff (GUTS).

II.) An education policy cla$$ who will NOT fund, at family wage pay, the SYSTEMIC supports needed by our pre-k and k-5 kids who are struggling. [counselors and nurses and music teachers and social workers and and and ...]

III.) An education policy cla$$ incapable of creating and sustaining SYSTEMIC supports because they disparage the grunt work of making Shtuff work.
IV.) An education policy cla$$ with an ethos of proudly having their privileged head$ up in their privileged cloud$.

A.) To many of these people are proudly unaware of the FACTS that
-- there are appx. 131 million households in the USA,
- to be in the top 20% of households, appx 26 million, you need a household income over
appx. $150,000 a year.
- what life is REALLY like for that bottom 60 and 80%,

-- there are appx. 175 million Americans with money income,
- to be in the top 20%, appx. 36 million Americans, you have to have an income over
$92,000 a year
- what life is REALLY like for that appx 140 million in the bottom 80%.

B.) Bureau of Labor Statistics, employment by occupation and industry.
-- there are appx. 155 million people working in the USA,
- we can NOT all be high level policy peep$, searching our privileged cloud$ to author
the study of the study contemplating the thought of actin ...
[See COVID lockdown and essential employees! ]
- there are tens of millions of lowly working stiffs with hard skills who make life work,
and those skills took years of actual work to acquire.

V.A.) Mix in the Seattle implementation of Identity Politic$, a special cancer where massive efforts are burned up in New Jargon vocab acquisition, and, in persecuting Non Compliant New Jargon Resistors, resistors who won't be vulnerable cuz they won't learn cuz they're protecting superiority ...
Consequently, year after year, you can guareentee that about all that will trauma-fej-mtss change is the tunes of the merry go round. Year after year, the powerful will be at the front of the trough, the rest of us will be fighting each other over scraps as we gut each other over vocabulary interpretations.

B.1.) We-The-Peee-0n$ are afflicted by the powerful righ pig$ through the clauses of the laws, rules, and regulations created by the toadies of the rich pig$.
2.) Since the first web browser, for the FIRST TIME IN HUMAN HISTORY, we little know nobodies could actually know the ins and the outs of the clauses of those afflictions.
WHO wrote and WHO enforces the clause?
WHERE does the writer and the enforcer work?
WHAT is the job title of the writer and the enforcer?
HOW do the writer and the enforcer get their work done?
where do they live ... ooops!
WHEN ...
3.) Nevermind.
Go To V.A.), and, make sure the kids growing up in this mess don't have much in the way of arithmetic or number or per cent of decimal or algebra or finance or computing or economics or business or science ... skills.

Linh-Co said…
The Math Wars is very similar to the Reading Wars. The Sold a Story Podcast is a good start to understanding how these education fads harmed our schools.
So many of the districts bought into Lucy Calkins Readers and Writers Workshop with no efficacy results or research supporting them (including Seattle School District). For over a decade, the ineffective and costly programs have harmed many students especially the disadvantaged student population. Discovery math programs are no different. Thank goodness, most states are now distancing themselves from "balanced" literacy programs.

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