Yesterday we wrote about Jo Boaler, her latest own goal and some of her checkered history. But her defenders are coming out as well to, well, defend her. Fair enough. Except, that their defense is dishonest and farcical. As it must be.

Yesterday, Keith Devlin took time off from trying to start World War III to retweet support for Boaler:

Devlin also tweeted his support for the Boaler-inspired California Mathematics Framework (CMF):

OK, Professor Smarts, let’s just slow down a minute.

There are three obvious and important questions we might ask of Jo Boaler:

**1. Is Jo Boaler’s research work open to serious criticism?**

**2. Is Jo Boaler’s personal conduct open to serious criticism?**

**3. Is Jo Boaler’s work on CMF open to serious criticism?**

The answers, of course, are “Hell Yes“, “Hell Yes” and “Hell Yes“.

Now, it is importantly true that one “Hell Yes” does not logically imply another, a truth that almost everybody is happy to ignore. Both Boaler’s attackers and defenders are very willing to bait and switch. In particular, and as we wrote yesterday, the current vicious attacks on Boaler are framed around 2 but are very clearly motivated by 3. But, to begin, Devlin’s defense of 2 is dishonest and absurd.

Devlin wrote,

*Leaving aside the original Boaler-Nelson exchange for the two of them to resolve …*

Why? Why should anybody leave it aside? Jelani Nelson had every right to make public Boaler’s nasty email to him. And, people have every right to be appalled by Boaler’s nastiness, even if she didn’t have form. Which she most definitely does. But as well, while suggesting others “leave aside” Boaler’s conduct, Devlin does not:

*The letter S.L. refers to is powerful.*

It is typically gutless, and typically weird, for Boaler to set up a new website for the sole purpose of posting someone else’s defense of her conduct. Is she somehow gagged and unable to defend herself? In any case, Devlin is wrong: the letter defending Boaler is not “powerful”; it is absurd.

But, Devlin wants to talk about 3. Fair enough, although we shall not. We have our own village of idiots to try to manage, and we simply don’t have the time to give proper consideration of the CMF. We have read enough to be convinced that it is awful, and we have read nothing to suggest otherwise. We’ll just make three quick points about Devlin and his defense of CMF.

Firstly, we simply don’t trust Devlin. He is clearly very smart, but he also seems to us to be manipulative and a pompous ass.

Secondly, Devlin notes of the creation of CMF,

*The new CMF is the result of a multi-year, open, consultative process …*

Yeah, right. Although, as we have written, California’s process is clearly way better than ACARA’s Orwellian lunacy, it’s a pretty safe bet that the process was “consultative” in name only.

And, lastly a point on the nature of Devlin’s defense of CMF:

*The new CMF is … in fact closely aligned with the OECD’s new PISA 2022 Framework*

Oh, really? This PISA? Or this PISA? Or this PISA? Well, sign us up!

OK, 2 and 3 are done, and we are left with 1. How, then, do Boaler’s cult-fans, or Boaler herself, defend her against the very serious criticism of her research work?

They don’t. Ever.

**UPDATE (13/04/22)**

Foolish Greg Ashman was foolish enough to criticise Lord Devlin on Twitter, to which the Lord responded in a lordly manner. Ashman has subsequently written, very well, on Lord Devlin’s lordliness and the Lord’s defense of the CMF (partly paywalled). We hope to write something soon.

Professor Devil-n sinks even lower. Anyone with degrees in math familiar with Boaler should know that any of her “works” are a load of bullshit. I’m seriously baffled how people with more experience in math – you know, people with Ph.D.’s in mathematics – can look at what she’s doing and think she’s doing any better than admittedly already brain dead K-12 math. I don’t get it. Like, I just don’t see it. I don’t see it.

It almost strikes to me as a bias on the level of climatologists denying man-made climate change or an evolutionary biologist denying theory of evolution.

I agree. There’s something wilfully ignorant about Devlin. I think part of it is he likes seeing himself as the maverick compared to other mathematicians. He wears the contempt of other mathematicians as a badge of honour.

Yeah.

The thing that puzzles me the most, is that there’s an essay by a math teacher Paul Lockhart called “Mathematician’s Lament,” which Keith Devlin said he completely agrees with (I don’t btw). And in the essay, Lockhart dedicated an entire long paragraph on how we have this problem of teachers not knowing math and how absurd that is.

Well, it should become clear that Jo Boaler doesn’t know math, certainly not enough to promote the kind of mathematical creativity that she so claims to espouse. So, how does a mathematician, who knows enough math, and who believes knowing math is important, believe Jo Boaler is somehow the savior of the math?

“Willfully ignorant” sums it up nicely what Devil-n is all about. Or better put, willfully dense. He was like that in his multiplication =/= repeated addition articles, and he’s like that in the WW3 tweet, and he’s like that in his support for Boaler.

And Devlin keeps getting dickier. He just blocked Ashman on Twitter for “gaslighting” and “trolling”. I’ll try to write and link things later today. So much crap …

“He just blocked Ashman on Twitter.”

Why am I not surprised?

To be fair, it must be annoying for Devlin to have criticism interfere with the applause of his adoring fans.

Johnald,

I looked up this article by Lockhart – I vaguely recall having read it a long time ago. I tend to agree with the thrust of what he is saying.

Let me quibble with one statement. “Math is not about following directions, it’s about making new directions.” At all stages of one’s learning, it’s a mixture. In the early stages, following directions is more important; in the later stages, making new directions is more important. This applies to most (perhaps all) endeavours.

Lockhart is very much a double-edged sword. He says some very good things, and idiots also read into him license for their idiocy. (Hi, Anthony.)

I’ve long intended to write about Lockhart’s article (and book), but just haven’t found the time.

It seems to me that many commentators who write about how mathematics should be taught ignore the fact that some students in the class don’t want to be there in the first place. And it takes only a few to disrupt the learning of the others.

Even if true, what do you conclude? What does this have to do with what’s being discussed?

Only some?

There, whether by accident or not, you have hit upon perhaps the most central issue of education: lots of people (of voting age) keep talking about how X, Y and Z should be taught in schools but if those who need to learn about X, Y and Z are not really “there” (physically, emotionally, mentally due to lack of sleep or lack of attention-span) then the rest of the debate is pretty much moot.

Unfortunately, there doesn’t seem to be an easy solution to this. Hence the gap grows.

And to answer Marty’s question – it may not be 100% relevant to the original post, but then again, if students are not engaging in the classroom, does a new curriculum really matter?

A new primary curriculum could matter. If there were some understanding that young children need to be taught to sit still and to attend, then maybe we could get somewhere. But that would necessitate an understanding that schooling is about, well, schooling, not entertainment.

Change “schooling” to “parenting” and you will simultaneously be applauded by some and abused by others.

Lockdown taught me a lot (as a teacher, not a parent) about what really matters in education. Unfortunately, the lessons were either not learned by curriculum leaders and principals or were quickly forgotten.

Indeed. I’m not blaming school solely, or primarily, for this failure.

My opinion, as a mathematics Ph. D. who now mostly teaches future secondary school mathematics teachers, is that Lockhart’s diagnosis is sound, but his remedy might not entirely be. Lockhart’s recognition that there are many students who enjoyed mathematics in school, but then realise after they’ve decided to study it at the postsecondary level that they actually don’t like it and aren’t good at it, while there are on the other hand students who would have enjoyed mathematics if they’d thought they could have liked it and had pursued it, rings true to me. Lockhart also rails against what Ashman calls “mundanisation“, which seems to have been invented by educationists who hate mathematics and cannot imagine anyone could possibly want to do it unless it has direct relevance to their day-to-day life. And when I look at what passes for “problems” in mathematics education, I definitely agree with the criticism.

On the other hand, Lockhart seems to think it might be good to replace mathematics education as it currently is with completely open-ended mathematical exploration. Now I understand why it’s tempting, as professional mathematicians looking at the state of mathematics education, to wish students could do “real” mathematics instead of what they’re presently doing, but it’s probably also not the best way to teach the subject in order to optimise retention. Lockhart does seem to recognise this, and says that since students aren’t learning any mathematics now, what he proposes couldn’t be worse. Maybe he’s right, but there might be better proposals than either the status quo or Lockhart’s ideas.

I’ve only recently started following debates in mathematics education, and I’m still not really up to speed on the whole thing, but I’ve noticed that there seems to be a split among mathematics education researchers (or didacticians, as we call them here) between those who think links between mathematics and other disciplines, in science for example, should be emphasised (we could call that the mundanising tendency), and those who think students need to be introduced to genuine mathematical thought (a more Lockhartian tendency). But none of them seem to necessarily care very much about procedural fluency. While researchers such as Ashman have convinced me that it is necessary to develop a mastery of the procedures in order to even be able to do genuine mathematics.

Do my views on Lockhart sort of mirror yours, Marty? Is there something I’m missing? And do you have resources that you could recommend to a (still relatively) young mathematician who’s now responsible for the mathematics education of future secondary school teachers?

I’m afraid you’re both doomed to disappointment. I’ll try, but I don’t think I have much to offer. I’ll ponder and reply tomorrow.

Hi, Marc. Thanks very much for your long pondering on Lockhart.

In a nutshell, i *think* my feelings about Lockhart are very similar to yours. But, truth be told, I haven’t thought specifically about his article (and the book that followed) for a long time. It does feel to me as if, as with all these smell-the-roses guys, that there’s no proper appreciation of educational structure and, as you put it, procedural fluency. It’d be worthwhile thinking carefully about Lockhart’s book

Measurement, to think to what extent such a style of program could genuinely be taught. Little, I suspect.I *will* try to get to Lockhart at some point. He is worth pondering, if only to reject.

As for who a teacher of maths teachers should read, God only knows. I’m only in the business of pointing out what is wrong. (Of course if someone paid me to teach teachers or to edit books then I’d work hard at determining what is right. But, that ain’t gonna happen.) The only tentative suggestions I have are:

*) Tony Gardiner

*) Hung-Hsi Wu

Is there anybody else?

Thanks Marty. Although in fairness I’m not sure we should “reject” Lockhart, I think there’s something quite interesting in what he writes, and I’ve shown his essay to some of my students. Lockhart’s ideas can be revelatory to some of them, but they need to be balanced with, as you say, concerns for educational structure. (Although as I understand it Lockhart did teach secondary school mathematics, so he’s aware of these constraints.)

Thanks, Marc. I don’t really think the conclusion would be to reject Lockhart. But i do get a bit tired of the “Can’t it all be beautiful?” speeches from mathematicians, who seem to believe, or are at least happy for others to believe, that students don’t need to do the hard yards. Australia has a bunch of these mathematician con men, and they’re starting to get up my nose.

I don’t think Lockhart is in the same class as the Australian clowns, but there appears to be a shared element.

Please do! I’d be very much happy to hear your thoughts.

Lockhart has a great diagnoses of the problems with math education in the US, but he seems to be someone who never actually taught in a rigorous class filled with those who love math (i.e. honors or gifted classes) and what that’s like.

Hi Terry Mills,

I definitely was not saying I disagree most of what Lockhart was saying, and in fact, I agree with at least one of the premises – that math should be taught by those who know a lot of math. I hope that was already clear.

The parts where I disagree with him are where 1) he over eschews the “formalism” (he rails against teaching calculus as limits, etc.), 2) (and as others pointed out below) he calls for more open ended approach at high and middle school level, and 3) he rails against fluency (compares third graders learning addition and multiplication processes with a nightmare where music is only taught in this bullshit memorization).

As for you comments, yeah, I’d agree with you in spirit. I was bringing up Lockhart to illustrate how there’s literally an entire paragraph that should make Devil-n not support Slow Boaler, and he’s missing that almost willfully.

I attended a large keynote speech by S. L. I got annoyed when he challenged anyone to give an example of when a student would need to divide 2.72 by 32. So I took the bait and aggressively said, “A teenager ate a whole bag of fun size Snickers that had cost $2.72 and then went to sleep without brushing his teeth. During the night, all of his teeth rotted. How much did it cost him to rot his teeth — per tooth!!!?

Result: raucous laughter. All S. L. said was, “That guy is obviously a delinquent!”

That is funny.

I don’t know S. L. from a bar of soap, although I did notice that he titles himself “Math Education Change Agent“. Which probably tells you everything you need to know.

Devlin comes across as woefully naive, politically inept, and an egocentric narcissist. I like some of his books, mind you, but that doesn’t mean I have any respect for his opinions outside the rigorous confines of proper mathematics. (I make the distinction between mathematics as I think we understand it here, and the curiously empty material beloved of the Boalerites. And of ACARA.)

I think the tweet you quoted in a previous post sums it up; that “Stanford assholes” should: “Sit the fuck down and shut the fuck up.” Quite.

I don’t think Devlin is inept or naive, but “egocentric narcissist” seems close to the mark.

Also, to be fair, the guy who suggested that Devlin should “shut the fuck up” did it in the context of Devlin campaigning for WWIII. It’s perfectly reasonable for Devlin to comment maths ed. It’s just not reasonable for him, while commenting, to be a manipulative twat.