Keith Devlin and His Struggle with Maths Non-Experts

Is it significant that Keith Devlin’s twitter handle has “prof” in it, and that the name of Devlin’s website has “prof” in it? Maybe not, but at the moment it feels significant. Greg “Non-Prof” Ashman could reasonably regard it as significant.

Last week we wrote a bit about Slow Jo Boaler, her threat to call the cops on a critic of her California Curriculum work, and Keith Devlin’s slippery and silly defense of Boaler and her work. Greg Ashman had also been commenting on this, including a snide but pretty innocuous response to a tweet of Devlin’s. This inspired Professor Smarts to block Ashman and to dismiss Ashman with a wave of his lordly professorial hand:

What a dick.

First, to take care of Devlin’s flippant slander, his suggestion that Ashman had previously “trolled” him, or anyone, is thoroughly implausible. It’s just not what Ashman does; Greg is simply too busy pissing people off with, like, facts and things to be bothered trolling. But of course it’s much easier to yell “troll” or “gaslighting” than it is to engage with a critic or their criticisms.

But, now, to Devlin’s substantive charge, that Ashman has “little to offer”. Really? It’s an interesting question, of which Devlin is in no position to judge and in any case has no mind to do so in a fair or thoughtful manner.

Greg has written an excellent (semi-paywalled) post on Professor Smart’s lordly dismissal of him, and some serious questions raised by the ridiculous little spat. Titled The Experts We Need, Greg takes a look at Devlin’s defense of Boaler’s CMF work and offers very strong and ostensibly substantiated criticisms. We haven’t looked enough to offer an informed opinion, but we’ll bet plenty that Greg’s criticisms are accurate and important. Our interest in Greg’s post is different, and partly personal.

As regular readers will know all too well, we have spent the last year hammering ACARA and their appalling draft mathematics curriculum, now a real albeit Top Secret curriculum. In particular we have been hammering the insane decision to exclude mathematicians from any meaningful role in the development or review of the draft. As part of that, we have hammered a progression of stenographic education journalists for their inability to determine the meaning or the importance of the phrase “maths experts”, and their consequent idiocies. And, as a small part of that, Greg Ashman has occasionally received some friendly fire grief. Although Greg bats hard and very well for The Good Team, we have been frustrated by journalists’ focussing on Greg’s important concerns, and on Greg, to the exclusion of equal or greater concerns, and to the exclusion of mathematicians.  Now, quite rightly, Greg has returned with some friendly fire grief of his own.

In his post, Greg notes our hammering of education journalists and notes that he himself is not a “maths expert”:

I am not a mathematician, I have never conducted maths research and so I cannot reasonably be described as a maths expert.

However, after hammering what he perceives as Devlin’s blatant errors in educational psychology, Greg notes,

And yet, unlike me and by any reasonable definition, Devlin is a genuine maths expert.

What does this mean for the nature of expertise?

A very good question. After a brief description of his PhD research, Greg continues:

Which kind of expert do you need to write a maths curriculum? In theory, it should not involve me much at all. A curriculum is supposed to be a list of mathematical content that implies no teaching methods. I may have some views on the best sequencing, but that should be about it.

It should be the domain of maths experts to select the content. But imagine if we left this task to maths experts such as Devlin? Before we knew it, we would have lists of vaguely defined thinking skills, dispositions or whatever. And as we have seen in the case of the draft Australian maths curriculum, such a document is likely to wander way off its terms of reference and push flawed teaching approaches.

Indeed.

As it happens, ACARA contrived to stuff up the draft curriculum without the involvement of mathematicians. Well, not counting whatever “subject matter experts” ACARA employed who, evidently, were either incompetent or ignored, or both. Which is possibly making Greg’s point; it is quite possible ACARA had a compliant team of too-clever Devlins assisting them to produce their crap. It doesn’t matter. Either way, Greg’s critical point stands: the involvement of competent mathematicians, while necessary for the production of a coherent and good mathematics curriculum, is by no means sufficient.

But what about Greg? Did/Does Greg have “anything to offer” in the production/repair of  Australia’s draft/new curriculum. The answer is an undeniable “Yes”, for three distinct and important reasons.

First of all, it is a contingent fact that ACARA were, and undoubtedly still are, hell-bent on promoting inquiry and exploration and aimless game-playing as part and parcel of the Australian curriculum. Given this contingency, given that ACARA is wedded to such pedagogical and psychological lunacy, it is critical to have this countered by pedagogical and psychological anti-lunatics, such as Greg Ashman. This is Greg’s point:

So I guess I’m the kind of expert you need when things go wrong — the plumber who unblocks the toilet or something.

True. But we also think Greg is inappropriately narrowing the point and thus underselling himself, which brings us to the second reason.

While it is a contingent fact that ACARA’s cesspool of inquiry learning guaranteed the awfulness of the draft curriculum, it is also a necessary fact that any curriculum will reflect, and largely demand, specific pedagogical approaches. It is simply inconceivable, for example, that the Singapore primary curriculum could possibly have been produced with or be delivered with the “Let’s all explore” inquiry mindset of Australian maths ed. Now, one can argue chickens and eggs and things, the origins of Singaporean sanity (and of Australian insanity). But, as either impetus or consequence, the direct delivery of skills and knowledge is foundational to the Singaporean curriculum. Which implies, if only for supplying critically clarifying comment, and probably much more, guys like Greg Ashman are fundamental to the discussion of such a curriculum.

Indeed, Greg knows this well, better than his humble sentences above indicate. Greg was friendishly hammering the point to us from day one, since we began collaborating on the open letter. It is fair to say that that Greg came to the discussions with a part-healthy distrust of “subject matter experts”. He argued correctly if, as it happens in regard to ACARA, irrelevantly, that being a subject matter expert doesn’t automatically make one a curriculum expert. Greg’s hammering included throwing at us an excellent paper by Paul Kirschner, one of his gurus.

And the third reason that Greg has something to offer? Because he is a human and because everyone has something to offer.

There is nothing quite as revolting as an official expert employing their formal expertise to shut someone up. Sure, we’re the first to say that most people are ignorant and stupid, and so what they have to offer on pretty much any topic will be ignorant and stupid. Most people on most issues will have nothing worthwhile to say and will say it on the basis of imagined facts or thin air. But you still let them say it. You don’t stifle people with qualifications and purported expertise. Unless you’re a dick.

Expertise has its critical place, and the devaluing of genuine expertise has been a constant theme of this blog. But the other, greater theme of this blog has been the incompetence of unquestionable authority. Devlin could have been an example of one but is, instead, an example of the other. He is a dick.

13 Replies to “Keith Devlin and His Struggle with Maths Non-Experts”

    1. Good question. I don’t think it’s really relevant to the post, but a good question.

      I think a convenient shorthand is “person with a mathematics PhD”. But, I’ve met *plenty* of Maths PhDs who couldn’t reasonably be regarded as maths experts, and I’ve met a few non-PhDs who I would regard as maths experts.

  1. Keith Devlin as author:
    Set Theory and Proof Theory – awesome
    Recreational mathematics- really good
    Maths Education stuff-mediocre, confused and counterproductive
    Social commentary on academia and education- puerile and petty

    And all of these things are in chronological order of his career. Nuff said

    1. Thanks, Simon. I read a set theory book by Devlin when I was an undergrad, and I remember it as being uninventive but good and solid. I also *really* liked his book on Fibonacci. But, yes, there’s at least one other Devlin we’d be better off without.

      1. Love this stuff about Devlin..
        I recall him making (crass unsubstantiated) remarks about Multiplication not being the same as repeated addition…
        Though it’s an easy thing to show, he has never offered any proof type or explanation, relying totally on his reputation to influence others…
        Am more than slightly “off piste” regards your posting, but empathise by being generally “piste off” with the so called experts in the Mathematics community, particularly when they have a go at someone they perceive to be a “non expert”…
        Keep chuntering on – do love your blog – refreshingly emotive…
        Would really love to have someone like you read the news on our “National treasure” BBC T.V., expletives and all, lol…
        Just hate the shallow, solemn non emotive delivery on the likes of “War in Ukraine” followed by a jovial piece on football or the like, with barely a change in tone..
        Go get him Marty…

        1. Thanks, Ewen. I honestly don’t love this stuff. Devlin mostly just bores me, and I’d prefer to not think about him or write about him at all. But the business with Greg Ashman really got up my nose.

          If someone gets pissed off with me and/or my blog, I understand it. Their reasons may be nonsense, they may be do-nothing pompous snot-noses, but I have given them the opportunity to dismiss me cheaply and so I understand if they do so. But Greg is different.

          Greg has strong opinions and tends to express them strongly. But, by the standards of the media he employs, Greg is professional and polite. He simply does not deserve the kind of garbage that Devlin, and plenty others, throw at him. I hope to write about another, worse, episode involving Greg in the next day or so. (Greg has not asked me to write such posts defending him, and it’s not even clear to me that he approves of them. But I loathe bullies, and I really loathe bullying in the name of some fantasy moral high ground.)

          On Devlin’s “repeated multiplication” shtick, I think you’re being a bit unfair, but only a bit. There’s some discussion of that in the comments on this post.

          As for the language and demeanour of this blog, believe it or not I’m trying to tone it down. But it’s difficult, largely for the reasons to which you allude. Everything everywhere else is so precious and so faux-polite, so fake. If others yelled more, or at all, I’d yell a hell of a lot less.

      2. The problem is that some people with proficiency in field A start believing that this automatically gives them proficiency in field B. And then you get other people (eg. Govt Ministers) who, impressed and blinded by said proficiency in field A, are sucked into thinking that this gives proficiency in field B.

        Examples are everywhere, not just in education curricula. Look at all the self-styled mathematical ‘gurus’ who jumped on the CAS train, and the suckers who believe that this gives those ‘gurus’ mathematical credibility.

        Devlin (and many others) should stick to what he’s good at (or was good at). And stay the apt away from matters he has no expertise in. Of course, this won’t happen – see my opening sentence.

        1. Thanks, John. I suspect in Devlin’s case the motivation is more psychological than you suggest. I think he enjoys being the independent, maverick mathematician who gets along with Boaler and her ilk. He wears the disapproval of (much more visible) people like me as a badge of honour.

  2. Here’s something that mildly ticked me off while reading Greg’s post on this. (Disclaimer: I fully agree that Devlin’s tweet/stance is cruel and unfair.)

    It seemed to me to be converging on a viewpoint that mathematics experts are not useful in writing the curriculum/discussing the teaching of mathematics. I thought this was unfortunate. In my view the fact that mathematicians are not involved in the construction and maintenance of a curriculum, nor consulted in its delivery/teaching, is bad.

    Greg’s value is beyond him being a math expert or not. His value (apart from being another human, important to note) is very high due to his actual expertise. I think he might not have felt comfortable claiming this, which I understand.

    1. Thanks, Glen. I think Greg indeed has mixed feelings about “subject matter experts” being involved in curricula. I would agree with Greg that experts who have not thought properly about school mathematics and curricula can do more hard than good. The Kirschner paper is relevant to this.

      1. Oh I know, there are plenty of examples… so I can understand the point of view. I still think it is wrong though.

        I’m not saying *all* mathematicians should be involved in the math curriculum, but *some* should be. Now if we get crap ones, then that’s something we can complain about. But they should be there. That’s the first step I think. (I think school teachers should also have input.)

        1. Of course. We agree. But who gets more attention and applause: the industrious mathematician working to understand the curriculum, or the “feel the beauty” showboater?

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