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> if we don’t feel stupid it means we’re not really trying He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing. But one

• Gupie 2y ago
  But he is not talking about education, about doing a course, where "getting the right answer makes you file smart". He is talking about research where nobody knows the right answer.
  • dahart 2y ago
    Martin absolutely was talking about education; research is education. Granted, not early education, but I’m not making any claims about what he said, I simply used his quote as a segue to make an observation about the connections between research thinking and today’s math curriculum. Research is a continuous spectrum. We are expecting kids in elementary, secondary, and early college to have a research mentality and research level motivation in order to succeed in math classes, unlike some other subjects. (Classes which, btw, were all research topics at some point in time and took tens, hundreds, even thousands of years to develop.) The mentality and motivation are important if you want to end up doing any of the actual graduate, post-graduate, or career research where nobody knows the right answer. The kids who are pruned out by our math system never make it there, and many don’t even make it to functional math literacy, even though many/most are perfectly capable, and that’s unfortunate and doesn’t reflect well on our education system. I’m suggesting we can do better.
    • Gupie 2y ago
      I don't disagree with what you have just said except I understand education to refer to the transfer of knowledge while research is the discovery of new knowledge.
      • JoeAltmaier 2y ago
        Curiously the root of that word is 'to search again', meaning more like 'reviewing sources in the library' and less like 'doing experiments in the lab'.
        • kragen 2y ago
          re- in this case is probably an intensive prefix rather than indicating repetition. this is an uncommon re- in english, but does occur, for example in 'refried beans', a calque from spanish where intensive re- is still a productive prefix so it probably means 'search really hard' rather than 'search again'
      • dahart 2y ago
        Research is wholly about the transfer of knowledge, both before and after any associated experimentation. Sometimes there is discovery in between, but not always; survey papers and meta analyses are research, a very important part of research. Experiments that don’t research previous work and don’t communicate the results aren’t research and usually don’t result in the discovery of new knowledge. Can’t know it’s new unless you research what’s already known.
        • Gupie 2y ago
          You could argue education is wholly about the transfer of knowledge, but research isn't. The fundamental difference between research and education is the discovery of new knowledge. You can be educated without doing research, and you need an education to do research, but without this discovery of new knowledge you are not doing research. You can also do research without communicating the results, just like you can write a book without publishing it.
• derbOac 2y ago
  Reframing it as curiosity is a good point, although the essay as written resonated with me because it emphasizes the "productive ignorance" of research. One of the central problems of our time in research and academics, I think, is an incentive to focus on areas that are well-established because we know they are likely to produce results that we have confidence in (according to whatever inferential criteria we use). The idea of it being ok to not know something a priori, to have lack of confidence in it, seems sort of discouraged in the current climate, because it's too risky.
  • what-the-grump 2y ago
    Dancing around the elephant in the room, the problem is financial risk, e.g. this isn't really about research this is a business, and business must minimize risk to be profitable?
• wwarner 2y ago
  There are two authors here, since the post contains an inset about dealing with your own ignorance by another professor. They aren't saying quite the same thing. The inset is saying that every grad student will confront their "absolute ignorance" and it will be difficult, scary and possibly painful. The author of the post is saying it can be a source of joy. I suppose they can be reconciled. It could also be that so little of our behavior is based on knowledge that the only sane reaction is at least somewhat negative, whether characterized by being overwhelmed, or sad, or detached.
• taeric 2y ago
  I think the framing as "stupidity" is to highlight that you don't always chase creative questions. Quite often, you should chase the obvious or understood points. The problem, I think, comes from the weaponization of "stupid" against people. The XKCD of the lucky 1000 plays a good role here. If you are constantly deriding others for stupid takes, then anyone that derides one of your stupid takes will hit hard. And that seems to be getting worse.
• thomastjeffery 2y ago
  > He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing. I disagree. How can you be curious without something you don't understand? The point, as I see it, is that if you find yourself in a position of complete understanding, then you must also have a complete lack of curiosity. If you think you are in that position, then the way to revive your curiosity is to deconstruct your position of expertise, i.e., recognize your position of stupidity. --- Curiosity is step 2. Stupidity is step 1. Learning moves us from step 2 to step 3. The important thing to recognize is that step 3 is actually a new instance of step 1. Expertise is the base case of this recursive tree traversal: it's how you stop the learning process.
  • dahart 2y ago
    > How can you be curious without something you don't understand? Good question. You might have discovered my point: curiosity comes with stupidity, implicitly by definition, right? I think that’s what you’re saying too. Maybe you don’t disagree after all? You can’t have curiosity without stupidity, as you rightly point out. Ignorance is probably a better word than stupidity. Using “stupid” is imprecise and was used here for a bit of surprise and humor. You can have stupidity (ignorance) without curiosity. When that happens, perhaps the expected result is no progress developing new understanding nor lessening of ignorance. Given that curiosity implies ignorance, and that ignorance alone is not sufficient for learning, what justification is there for claiming curiosity and ignorance are separate steps or separate things when it comes to education or research? I’m suggesting they are two sides of the same coin, they must both exist before learning happens, and neither one can come before the other. Calling it curiosity instead of ignorance or stupidity is perhaps a kinder framing, especially for people who might not immediately get the self deprecating humor of “stupidity”.
    • thomastjeffery 2y ago
      My disagreement was semantic. Wasn't yours? My overall point is that the end of education is expertise, which itself is a form of ignorance. We generally consider stupidity and expertise to be antonyms, but they often exist as two opposing perspectives of the same experience.
• glitchc 2y ago
  Well, mathematics at a graduate level really is a subject that can only be self-taught, as are most subjects at the graduate level. Yes, some guidance can be available, but the pedagogical hand-holding that is undergrad is simply not possible. The analogy to language only really applies to mathematics that is well-understood and can be taught this way. In grad school, almost no mathematics you encounter is that well understood, so the teaching methods are absent.
  • j2kun 2y ago
    It's possible, but counter to the point of a PhD: apprenticeship for research.
  • l33t7332273 2y ago
    There are lots of areas of math grad school that are well understood. Pretty much everything up to quals (and some beyond that) is well known and teaching methods are far from absent.
    • grungegun 2y ago
      In a sense, I spend most of my time on material after quals because it's so much harder to understand.
• ColinWright 2y ago
  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 2y 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!
    • ColinWright 2y 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.
• kragen 2y ago
  kids struggle with grammar, pronunciation, pragmatics, vocabulary, etc. they do so naturally, and maybe you've forgotten your own struggles, but they're very real i think we can do better than we are doing at math education, much better, but there is no way to learn math, or anything else, without diligent effort. it won't happen by passive absorption. you can listen to people speaking spanish all day every day for years without learning more than a few words of spanish if you don't make any effort curiosity is one possible motivation for making that effort, but the immediate result of the effort is, at first, failure. that's true of language, it's true of playing the guitar, it's true of programming, it's true of throwing clay on a potter's wheel. that failure feels like being clumsy, weak, or stupid, depending on the form it takes and that's what the article is talking about. trying to do things that are beyond your mental ability makes you aware of, and frustrated with, that mental ability. that's not curiosity, it's feeling stupid. it's also how you increase your mental ability!
• bonoboTP 2y ago
  > But one of the big problems with math education is that we force students to struggle to a far greater degree than other subjects, under a belief that personal struggle, the “trying”, is the only way to truly get it. I disagree. In fact, I found that often the better and more didactically streamlined the exposition is in a book, the less deeply I end up learning the material. It is precisely the personal struggle, having to make my own sketches and derivations, starting out with a misconception because of bad phrasing in the book and having to explore that misconception until I find what I misunderstood etc. makes the knowledge stick much better because it now feels my own, like an intimate friend. Spoonfeeding may get people quicker to the point of solving the standardized quiz at the end of the chapter but that's not the same as learning and understanding. Another instance of metric-chasing in action. It's a bit like how I learned MS Office or Photoshop by trial and error as a kid, or programming by mucking around trying to make a website do what I want. And you bet it was a struggle. Struggle but with reward at the end. Compare that with a handholding tutorial where you do learn how to do whatever the tutorial makers had in mind, but it won't generalize as much. Sounds totally dry. I loved computers, but hated school lessons that tried to teach us MS Office in the handholding spoonfeeding way. It's the death of the subject. It's a safari in a safe car, looking at the animals through binoculars vs running around in the jungle in your own adventure amongst the beasts.
• spookie 2y ago
  The struggle isn't necessarily bad for learning. It really is a good way to learn. I like it. But alas, I never thought as a kid that I didn't have time for other things. I was always into something.
• seanhunter 2y ago
  As someone who is currently studing maths I strongly disagree with this > He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing. One of the most important characteristics to succeed in maths is the ability to acknowledge things you don't understand, to fail, and to persist in spite of failure. Trying really is the only way to understand some hard things, because there are some things that are conceptually extremely difficult. He's not talking about relative stupidity where there are other people you feel are smarter, he's talking about stupidity on an absolute basis. You don't know. You don't understand. But somehow you have to find a way to carry on, and then later on, looking back once you do understand, you're baffled by why you didn't know/understand or couldn't see some crucial things. You have climbed up a ladder and pulled it up behind you and it's hard now to imagine what it is like to be on the ground. It's not about curiousity. Of course you have that - if you didn't you wouldn't be there in the first place.
• Arisaka1 2y ago
  Curiosity is when you're reaching out to find out about a thing (let's call it X) which you want to learn more about. Feeling stupid is when you're confronted with an external you cannot understand why it works. Curiosity can help push through feeling stupid, but you can be curious about something you won't struggle understanding it at all.