4 ms·

While I'm sure almost everyone can learn the basics of algebra or calculus, no amount of wishful thinking will give everyone the brain needed to master them or

While I'm sure almost everyone can learn the basics of algebra or calculus, no amount of wishful thinking will give everyone the brain needed to master them or even be proficient. I'm not sure where your belief that perseverance can overcome all even comes from. I have been trying to get better at chess lately. I grew up playing it so I'm already fairly proficient, and I've been putting a decent amount of free time into studying openings and playing puzzles. Yesterday, I played my friend who hasn't played in literally years and never really played seriously anyway, and he beat me handily 3/3 games. I know that I do not have the brain to be a chess master, no matter how much time I put in, because I don't have enough working memory to keep the board in my head.

TameAntelope 5y ago
I disagree, as it's not a sufficiently difficult topic to warrant some kind of genetic stratification. Life circumstance stratification, certainly, and you will get no disagreement from me that some people don't have the time or energy necessary to devote to something as not-immediately-useful as calculus, but from an intellect perspective, no. Everyone who is not experiencing some kind of mental illness has the intellectual capacity to learn calculus, though I will capitulate it is fortunate for me and this statement that we do classify a low enough IQ as a mental illness!
- syops 5y ago
  It’s not a sufficiently difficult topic for you. Have you ever taught algebra to a classroom of people from a wide range of intellectual capabilities and experiences? Are you even aware of some of the pain points to learning algebra?
  - TameAntelope 5y ago
    Do I need experience teaching calculus in order to suggest that it's got more to do with environment and situation than it does intellectual capability? No, I don't think that's true. Are you seriously suggesting trying to raise multiple children while simultaneously learning calculus is approximately as hard as living alone and trying to learn calculus? Honestly, I think you're trying to find a neat solution where none exists. You haven't stumbled on anything here, you're more likely ignoring the real-life circumstances your students find themselves in, and your colleagues are not.
    - DangitBobby 5y ago
      > Do I need experience teaching calculus in order to suggest that it's got more to do with environment and situation than it does intellectual capability? To suggest it? No. To be taken seriously though?
      - TameAntelope 5y ago
        What a strange world we'd live in, if only calculus teachers could talk about how people learn in ways that might also apply to calculus teaching.
        threatofrain 5y ago
        Are you seriously surprised that zero experience translates to a hit on credibility?
        TameAntelope 5y ago
        Yes, because I'd expect HN readers to understand an ad hominem when they see one. I could be living in a ditch down by the river, or I could be the leading researcher into how people learn calculus and it wouldn't make a difference with regard to my argument (though, practically speaking if I were the lead researcher on how people learn calculus, I'd be more likely to back my argument up with objective research, and that would strengthen my argument).
        threatofrain 5y ago
        Oh, well, if you're a leading researcher in math pedagogy, you should just say so and save time. Such credibility would offer serious firepower to the debate.
        TameAntelope 5y ago
        I don't think it would or at least should.
  - beej71 5y ago
    Is "and experiences" different than environment?
Mawr 5y ago
> I have been trying to get better at chess lately. I grew up playing it so I'm already fairly proficient, and I've been putting a decent amount of free time into studying openings and playing puzzles. Yesterday, I played my friend who hasn't played in literally years and never really played seriously anyway, and he beat me handily 3/3 games. I know that I do not have the brain to be a chess master, no matter how much time I put in, because I don't have enough working memory to keep the board in my head. Given the immense complexity involved with learning, there's essentially no way for you to describe the situation with enough detail for anyone to be able to make an informed judgement. It's extremely common for bad players to describe themselves as 'proficient', spending a 'decent amount of time' can mean anything, studying openings and playing puzzles is likely the wrong way to practice, the skill level of your friend is impossible to ascertain, etc. The way you actually get better at anything is by: 1. Dedicating enough time to it, consistently (~20h per week or so maybe if you want any sort of quick results). The incredibly common trap here is that people think that spending time on a game equals getting better at it. There's no way to improve without spending a certain amount of time playing, but spending time playing does not make you better on its own. 2. Doing whatever it is you want to get good at (doing anything else does not count - if you want to learn how to play regular chess, play regular chess; puzzles or anything else does not count). 3. Reviewing your games to find mistakes you've made - this part is crucial, if you can't see any mistakes you made, you cannot improve. If that's the case, get someone better than you to review your game(s). 4. Playing while trying to work on addressing one mistake at a time, until you don't make it anymore. Chess is actually really easy to improve in - fast, trivially repeatable games, chess engines, lots of learning resources, objective rating system. > I know that I do not have the brain to be a chess master I'm not sure what exactly you mean by 'chess master', but for example getting into the top 10% of players is pretty easy. You are indeed incredibly unlikely to be one of the best, because for that you will have to dedicate your entire life to playing chess. But unless you literally want to be one of the best (top 1%+ of players), genetics will not limit you. You may take more time to get to any given level than someone gifted with more working memory or whatnot, but it's still doable. > because I don't have enough working memory to keep the board in my head. Because of humans' limited memory and processing power, we play games not by exhaustively analyzing but via building simplified models and heuristics so I don't see why you'd need to 'keep the board in your head'.

TameAntelope 5y ago

I disagree, as it's not a sufficiently difficult topic to warrant some kind of genetic stratification. Life circumstance stratification, certainly, and you will get no disagreement from me that some people don't have the time or energy necessary to devote to something as not-immediately-useful as calculus, but from an intellect perspective, no. Everyone who is not experiencing some kind of mental illness has the intellectual capacity to learn calculus, though I will capitulate it is fortunate for me and this statement that we do classify a low enough IQ as a mental illness!

syops 5y ago
It’s not a sufficiently difficult topic for you. Have you ever taught algebra to a classroom of people from a wide range of intellectual capabilities and experiences? Are you even aware of some of the pain points to learning algebra?
- TameAntelope 5y ago
  Do I need experience teaching calculus in order to suggest that it's got more to do with environment and situation than it does intellectual capability? No, I don't think that's true. Are you seriously suggesting trying to raise multiple children while simultaneously learning calculus is approximately as hard as living alone and trying to learn calculus? Honestly, I think you're trying to find a neat solution where none exists. You haven't stumbled on anything here, you're more likely ignoring the real-life circumstances your students find themselves in, and your colleagues are not.
  - DangitBobby 5y ago
    > Do I need experience teaching calculus in order to suggest that it's got more to do with environment and situation than it does intellectual capability? To suggest it? No. To be taken seriously though?
    - TameAntelope 5y ago
      What a strange world we'd live in, if only calculus teachers could talk about how people learn in ways that might also apply to calculus teaching.
      - threatofrain 5y ago
        Are you seriously surprised that zero experience translates to a hit on credibility?
        TameAntelope 5y ago
        Yes, because I'd expect HN readers to understand an ad hominem when they see one. I could be living in a ditch down by the river, or I could be the leading researcher into how people learn calculus and it wouldn't make a difference with regard to my argument (though, practically speaking if I were the lead researcher on how people learn calculus, I'd be more likely to back my argument up with objective research, and that would strengthen my argument).
        threatofrain 5y ago
        Oh, well, if you're a leading researcher in math pedagogy, you should just say so and save time. Such credibility would offer serious firepower to the debate.
        TameAntelope 5y ago
        I don't think it would or at least should.
- beej71 5y ago
  Is "and experiences" different than environment?

Mawr 5y ago

> I have been trying to get better at chess lately. I grew up playing it so I'm already fairly proficient, and I've been putting a decent amount of free time into studying openings and playing puzzles. Yesterday, I played my friend who hasn't played in literally years and never really played seriously anyway, and he beat me handily 3/3 games. I know that I do not have the brain to be a chess master, no matter how much time I put in, because I don't have enough working memory to keep the board in my head. Given the immense complexity involved with learning, there's essentially no way for you to describe the situation with enough detail for anyone to be able to make an informed judgement. It's extremely common for bad players to describe themselves as 'proficient', spending a 'decent amount of time' can mean anything, studying openings and playing puzzles is likely the wrong way to practice, the skill level of your friend is impossible to ascertain, etc. The way you actually get better at anything is by: 1. Dedicating enough time to it, consistently (~20h per week or so maybe if you want any sort of quick results). The incredibly common trap here is that people think that spending time on a game equals getting better at it. There's no way to improve without spending a certain amount of time playing, but spending time playing does not make you better on its own. 2. Doing whatever it is you want to get good at (doing anything else does not count - if you want to learn how to play regular chess, play regular chess; puzzles or anything else does not count). 3. Reviewing your games to find mistakes you've made - this part is crucial, if you can't see any mistakes you made, you cannot improve. If that's the case, get someone better than you to review your game(s). 4. Playing while trying to work on addressing one mistake at a time, until you don't make it anymore. Chess is actually really easy to improve in - fast, trivially repeatable games, chess engines, lots of learning resources, objective rating system. > I know that I do not have the brain to be a chess master I'm not sure what exactly you mean by 'chess master', but for example getting into the top 10% of players is pretty easy. You are indeed incredibly unlikely to be one of the best, because for that you will have to dedicate your entire life to playing chess. But unless you literally want to be one of the best (top 1%+ of players), genetics will not limit you. You may take more time to get to any given level than someone gifted with more working memory or whatnot, but it's still doable. > because I don't have enough working memory to keep the board in my head. Because of humans' limited memory and processing power, we play games not by exhaustively analyzing but via building simplified models and heuristics so I don't see why you'd need to 'keep the board in your head'.