Comment by ColinWright

Comment by ColinWright 3 days ago

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I don't know your background, but speaking as someone who has done a PhD in Pure Math, and working with a lot of people who have done PhDs in Pure Math, I disagree with you. It's very much a case of feeling stupid, and being able to embrace that and live with it.

The "being curious" thing is independent of the "feeling stupid" thing. It definitely exists, but it's absolutely not the same thing.

Looking at the rest of your comment, maybe we have a lot in common, but I definitely disagree with a lot of what you've written here, so no doubt our experiences are wildly different. Perhaps over a coffee[0] we could talk constructively about education, math, struggles to understand, and work ethics, but suffice to say here that even if we do have substantial common ground, I think we might have very different points of view.

[0] Other beverages are available.

dahart 3 days ago

Of course you disagree with me ;) You’re talking about the minority of people who’ve had incredible amounts of math success (yes despite sometimes legitimately feeling very stupid). I’m not talking about my own experience, FWIW, I’m talking about the majority of people who never get anywhere close to a PhD in math, because they were left behind by our math education system. Obviously I don’t know exactly what you disagree with since you didn’t elaborate, but we have bumped into each other in mathy threads fairly often, right? If we get the chance some time, it would be super fun to discuss math & education over coffee!

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  • btilly 3 days ago

    Your starting "of course" presumes that you are right. I'm disagreeing because I truly and honestly think that you're wrong.

    People who are struggling with math, even in elementary school, will often say things like, "That's so simple, why couldn't I get it? I must be stupid!" I've heard this over and over again in a wide variety of contexts. Including from my own children. We honestly believe that if it is simple, it should be easy to understand. And so the experience of having struggled with something simple, leaves us feeling stupid.

    Even people with an incredible amount of math success, wind up feeling this. And pretty much universally have also developed coping mechanisms for it. But the experience itself is pretty much universal. My son felt it in middle school when he was struggling with long-division.

    Now does a poor education system make this experience more likely? Does it serve us poorly? Absolutely! I consider it a crime that Singapore has developed a better way of teaching elementary math, and we have not adopted it. Singapore is now moving to #1 across different subjects according to PISA, and Western education systems aren't even curious about how.

    However that is orthogonal to the key point here. Which is that math tends to be simple in a way that our brains aren't built for. And when we're confronted with how hard it is for us to learn something simple, it is easy for us to feel stupid. This can be very demoralizing. And it is very helpful for us to learn to accept and deal with that feeling.

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    • dahart 3 days ago

      My ‘of course’ to @ColinWright was intended to be tongue in cheek playful, and not presume anything. But I accept it might come off a different way than I intended.

      I think (like with others in this subthread) that I have mislead you or am being misunderstood or both. I’m familiar with the feeling of stupidity in math, and I’d agree that it’s useful when/if harnessed. I’m calling the process of accepting it and dealing with it “curiosity”, partly since if curiosity is missing then people tend to feel shame and anxiety with their stupidity and tend to avoid math and give up on learning it.

      I don’t believe there is such a thing as right and wrong here. I’m making a point of view framing distinction, not disagreeing with the article or the quote in the article. I think that “stupidity” isn’t the best word choice in general, even though it might work for math researchers in this case. That word comes with many overloaded and negative meanings that aren’t accurate to what the article is really trying to say.

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      • btilly 2 days ago

        I think that stupidity is the perfect word. It is how people actually feel, and the word that they are overwhelmingly likely to use. Therefore using language that connects with the experience means that you're saying something which is accessible in the difficult moments that need to be dealt with.

        Curiosity is a tool for dealing with it. But it's but one tool. And we need a whole toolkit.

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  • ColinWright 3 days ago

    I suspect part of the friction here is the difference between teaching math to people who will not go on to study it at an advanced level, versus teaching it to people who will.

    In that case, what is being taught is actually different, it's the similar in some senses to the difference between teaching someone to operate a machine, versus teaching them how to maintain, fix, and possibly improve said machine.

    I've said for a long time that if only we could identify early the students who will not go on to study mathematics at an advanced level then we could better benefit them by having a substantially different curriculum taught in a completely different style.

    But even then, the willingness to be confused by something, and resilience in the face of being made to feel stupid not by the teacher[0] but by the current (temporary!) lack of understanding, is really, really powerful.

    [0] Teachers who unnecessarily make students feel stupid should be prevented from ever, ever going near students again. Ever.

    > If we get the chance some time, it would be super fun to discuss math & education over coffee!

    Where are you based? I travel a lot ... my email is in my profile, and you could always register with my "Meet With Me" system to get a heads-up if I'm going to be in the area.

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    • dahart 3 days ago

      > if only we could identify early the students who will not go on to study mathematics at an advanced level then we could better benefit them by having a substantially different curriculum taught in a completely different style.

      Yeah I'd very much agree with this. Actually strong agree with all your points there, it’s well aligned with what I think I was trying to say.

      I’m US based, currently mostly Utah, sometimes California.

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      • ColinWright 3 days ago

        I was in CA for three weeks earlier this year, including getting to spend half a day with Cliff Stoll (Hi Cliff!).

        But I'm unlikely to be in the US now for a bit, but if you ping me an email then I can tell you how (if you choose) you can register with my "Meet With Me" system.

        Or not ...

        Regardless, yes, I think we do (or would) agree on most of these issues.

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bbor 3 days ago

As a self-proclaimed cognitive engineer (it’s really easy to proclaim stuff these days!), I absolutely agree with you, for two basic reasons:

1. I don’t think the author was just saying that math is hard or “a struggle”, I think they were specifically pointing out the unusual nature of math(s) as a collection of meaningfully novel cognitive tools rather than facts or recombinations of existing tools. AKA “feel stupid” means “feel embarrassed you don’t understand earlier because now it’s obvious”, not “take a long time to understand” or other synonyms for struggle. We all agree on the vague shape of the proposed improvements to pre-graduate math education, I would guess!

2. That’s not how first language acquisition works, at all: the rules of grammar—not to mention etiquette-are far more complex than most laymen imagine, and intentional parental involvement via correction or the occasional picture book is absolutely the exception, not the rule. This is the core insight driving Noam Chomsky’s lifetime of scholarship, and I think he would agree that childhood linguistic development is more similar to mathematics education than practically any other activity, if we’re talking about “feeling stupid” like the author is.

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