This post has a lot of pictures and thus is too long for most email clients, especially gmail. Click on the title above to read it on the Substack website.
Oh, Lord.
Time to review Jo Boaler’s book.
The book by the woman who dismantled the math curriculum standards of California — the largest market for textbooks in the United States — and in so doing fucked up math education for every American.
Yes, I read it. Every single word. Most of it on my exercise bike, where the rage could at least serve a useful purpose. I got the Kindle version so I could take screenshots for this review, and even managed not to throw my iPad across the room when I really, really wanted to.
I should probably not put this one behind the paywall, as everyone needs to understand what’s happening to our educational system, but I suffered in reading this, so I’m leaving much of it behind the paywall for the satisfaction of knowing that people who’ve paid for the privilege are the ones will benefit from my suffering.
Yes, I said suffering. No, I’m not being dramatic. You try reading about what you love most in the world being disrespected, demeaned, shat upon, and belittled and tell me that the word “suffering” is too much.
My snark muscles are fully loaded, and powered by rage.
Buckle up, y’all.
(Unless otherwise noted, all pictures are screenshots from the Kindle version of the book.)
This is one of the most frustrating books I’ve ever read, because she’s not completely wrong in every aspect of her arguments.
A lot of her recommendations would be helpful in individual classrooms for some kids and some teachers in some situations.
A lot of the ideas she advocates for are ideas that I use in tutoring, in fact.
They’re not all bad ideas.
The problem is that instead of a book about how elementary, middle school, and early high school teachers can do a better job of teaching mathematics—imparting number sense, making math something that kids enjoy and aren’t terrified of, helping more kids avoid math trauma and the sense that they’re “just not a math person”—she wrote a book about how to use mathematics classrooms to “address inequity,” re-engineer human nature, and turn kids into good little collectivists.
She also undercuts her own arguments—even some of the arguments she uses to support good ideas—in a number of places, often in ways that rise to the level of “massive self-own.”
This is going to be really long, because to attack her arguments I have to go into some depth about why and how I see things differently.
And that means telling you about two things for context: growth mindset, and the math wars.
Growth Mindset
Carol Dweck’s book, Mindset, posits a dichotomy between a “fixed” mindset and a “growth” mindset. Growth mindsets see struggle, mistakes, and even failure as an opportunity to learn and grow. People, particularly children, with growth mindsets believe that if they are flexible and persistent — keep trying, and trying in different ways — they can eventually learn anything. Fixed mindsets are characteristic of those who believe that people are born with a certain level of ability that is pretty much set in stone.
For one relevant (to me) example: people who believe that they’re “just not a math person” and develop a kind of learned helplessness — the kind of people who respond to my posts and Notes with things like “LOL it’s all Greek to me, you might as well be a space alien ha ha,” and proudly refuse to ever try — have a fixed mindset.
People who read my math posts slowly, more than once, and ask questions if they need to, but trust that they can in fact get it if they try — have growth mindsets.
(Obviously, most of us have fixed mindsets in some areas of our lives; these are not categories of simple, uncomplicated purity.)
Neuroplasticity, the fact that our brains are always making new connections, especially when we’re young, suggests that the growth mindset is the more accurate framing of human potential.
Dweck’s book discusses these two mindsets in engaging and interesting ways. I love the book and have found it to be extraordinarily helpful to me.
I will write about this at length someday, but I used to have a very fixed mindset. Fixed mindsets often result from trauma, and I had one to be sure. I read the book not long after it came out, and it gave me hope that I could heal from a lot of my childhood damage, make up for what I lost when I was being “educated” in a church basement, and otherwise that I had much, much, much, much more control over my outcomes than I had previously imagined possible. That book made it possible for me to believe that an internal locus of control was something I could learn to develop. I haven’t fully succeeded at this, by any means, but I’m absolutely unrecognizable to myself, in many ways, from before I read that book.
So growth mindset is, absolutely, a powerful and important thing to try to instill in children.
But, as with most powerfully good ideas, people started trying to figure out how to make money from it.
A lot of people developed a variety of ways to try to “teach” this in schools, and many of those ways failed. Kids quickly learned the right answers to give — it’s school, of course they want you to say on the quiz that you can learn anything if you try — and the various studies showed extremely mixed results.
Note that none of this means that growth mindset isn’t a thing, or that it isn’t a powerfully empowering idea that can help individuals develop an internal locus of control. It is, and it can.
I have a degree in mathematics hanging on my wall to prove it, in my case.
But not everything is suitable for teachers to teach at scale, in a classroom.
Some things can be learned from teachers. Some things can’t. Other things can only be learned by an older child or adult, on his/her own.
The kind of self-insight it takes to recognize a fixed mindset, want to change it, and then change it is probably not something that classroom teachers are likely to inculcate outside of a few individual one-on-one relationships.
And that’s ok.
She mentions growth mindset approximately every fourth sentence, which is a problem — again, not because growth mindset isn’t real, important, vital, and empowering. It is all of those things. It’s just not something that teachers can or should be wholly or mostly responsible for. It’s something that’s largely up to parents and kids themselves. Teachers can encourage the nascent seeds to grow, but I remain unconvinced that teachers can plant it, at least in most cases.
The Math Wars
This is going to be a ridiculously short and inadequate summary, just barely enough for my purposes in reviewing her book.
The traditionalist, classic math lecture is called “I do, we do, you do.” The teacher does a problem on the board, slowly and carefully, narrating each step. Then the teacher puts another problem on the board, seeking student input at each step. Finally, the students are set a problem to do on their own.
Rote memorization and lots of drilling is part of the traditionalist approach to math teaching. It also includes ability grouping — where some kids are put on a calculus track and others aren’t, or some kids are placed into remedial math and others into advanced.
The progressive side (the “reform math” people) believes in changing everything. Students should spend a lot of time tying mathematical learning to real life, and shouldn’t be presented with new mathematical tools or ideas until they “need them”. They believe in things like having students illustrate their thought processes, endless group work and discussion taking priority over everything else, and never grouping by ability. They often carry this to ridiculous collectivist extremes. The “I” in this screenshot is Boaler, referring to her university classes:
The school she cites most positively in this book, referred to as Railside, takes communism in the classroom to a ridiculous extreme:
I cannot imagine anything worse for the kind of smart, often introverted kids — especially boys, who are frequently years behind their female peers in social skills — who excel in traditional mathematical settings than making them responsible for everyone else’s learning, lest their own grades suffer.
Boaler is the heroine of the progressive side of the math wars.
My Take on the Math Wars
My take is that the progressive side is mostly wrong, but some of their ideas are good. There’s no need to reject a good idea just because some lunatic wants to apply it too broadly. Thus, some of their good ideas can and should be incorporated into a traditionalist approach.
There absolutely are a LOT of kids who could go on to study math at a high level, and have math-based careers open to them, who wash out of math in the current set-up. Needlessly. It absolutely happens, and it wastes talent and the potential for innovation.
Adolescence is the rockiest time of life, and if every kid who hits a rough patch between sixth grade and high school graduation finds the door to a mathematical career slammed shut — which is sometimes the case, especially for poor kids — that’s a problem we should be solving. (More on this later.)
One example of a “reform math” idea that’s worth incorporating is valuing struggle. Math is hard. Often it’s the very first subject that a smart kid, especially a smart kid from a two-parent home that values education, has to struggle in. Kids who have never developed persistence or resilience in academics — because they’ve never struggled with anything academic before — often decide that they’re “not a math person,” and this is tragic. Math is the most beautiful, intriguing, amazing part of life as far as I’m concerned, but I only know that because I had persistence externally forced on me. (I had to succeed or I’d have a mountain of debt and no way to pay it off; failure was not an option.)
Substacker
wrote one of the most insightful, honest essays I’ve ever seen. When he had to struggle with something academic for the first time, he took the story that many smart kids — kids who are smart enough to fully convince themselves of bullshit — tell themselves and used it to craft a narrative of why his being “bad at math” was actually evidence of his great personal virtue. (He learned math later, when he stopped feeding himself that line of poppycock.) I will forever be grateful to him for writing that post.So yes, teaching kids that struggle is part of the process? Good idea. Important. Helpful.
Having them conceptualize struggle as a pit in which they should do interpretive dance? Not so much.
No, I’m not kidding. (Would that I were.)
Valuing struggle is important, to help students stop being afraid of it.
Making a goddamn dance party out of it is not.
Another important idea that the reformers get (mostly) right is presenting concepts with multiple approaches, which she calls “mathematical diversity”. For example, some kids will grasp that multiplication is “faster adding,” while others will have their light bulb moment with something more visual, like an area model:
When I was an undergraduate, I would go to class. Then I would often come home and watch two or three YouTube videos of professors lecturing on the same topic, downloading their powerpoint decks when available. The overlap of approaches — the same thing explained differently, often very differently — was my best tool. And it worked very well.
The most frequent thing I hear in math tutoring sessions is some version of:
“Oh. Why didn’t my teacher just say it that way? That makes sense.” This occurs when I’ve simply explained whatever it is they’re not getting, in different words than the words their teacher used.
So yes, multiple conceptual presentations is a good idea, at least in some classrooms.
The reformers despise ability grouping (the concept of remedial, regular, and advanced math classes) and on this they have one, and only one, small point. It is true that in some districts, to get on the calculus track you have to take Algebra 1 in eighth grade. And to do that, you have to take pre-algebra in seventh grade. And to do that, you have to do well on a test that you’re given in sixth grade. And ridiculously, these tracks sometimes have no additional on-ramps.
Sixth grade is the year when many kids hit puberty. So a girl who takes a test the week she gets her first period or a boy who takes the test when distracted or distressed because he’s noticing girls, or other boys, in a new way and doesn’t do herself or himself justice on a single test could, in some districts, be derailed from a math track.
That’s ridiculous. Nothing an eleven-year-old does should be that high-stakes.
Kids with involved parents will often find their way back onto the math track. Tutoring, summer school, changing schools, a summer camp, or even something as simple as having a parent request re-testing — these are all things that kids from poor or single-parent families may not have available to them.
But all this means is that the concept of “ability tracking” should be more flexible in the districts where it’s presently quite rigid. Some kids get interested in math later. Some kids have a rocky time in elementary or middle school but settle into themselves as they get older.
Some kids have a beloved grandparent die, or must deal with parental divorce, and have a bad year. Rather than being locked into a track from a very early age, multiple opportunities should be available for kids who want to take more challenging math in high school — or even potentially might want to — to get the needed prerequisites under their belts.
That’s their one legitimate point, and it doesn’t even apply in all districts. I’ve heard of kids being allowed to use a summer math camp in place of pre-algebra, to take Geometry and Algebra 2 simultaneously in tenth grade, or other such flexible approaches.
Beyond that one point, their arguments against ability grouping are horseshit.
Devil’s Advocate Hat Off
I’ve tried very hard to be fair here about what the “reformers” get right.
But instead of “reform math” types trying to improve the things that need, or at least could benefit from, some improving — they are trying to change everything for everyone.
And their efforts are driven by political bullshit, so of course they’re succeeding.
Here are Boaler’s theses as I understand them, and why they’re somewhere from partially, to mostly, to entirely, batshit.