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I hope you don't think this article in any way supports your belief that some people can't learn algebra/calculus due to any kind of genetic traits, because I d

I hope you don't think this article in any way supports your belief that some people can't learn algebra/calculus due to any kind of genetic traits, because I don't think the complexity of either rises to the level of "difficulty" that only gifted minds can comprehend. Very, very little in this world does. Your belief should probably be considered heretical, even among your conservative colleagues, because your colleagues should recognize how deficiencies in one area can be made up for in other areas, sometimes (but not always) at a higher efficiency cost. Where genetic gifts are lacking, determination and perseverance can almost always make up the difference, especially at a basic algebra/calculus level.

DangitBobby 5y ago
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?
        5y ago
- 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'.
syops 5y ago
My belief comes my experience teaching math the past 20 years. I think we both agree that mentally disabled people can’t learn algebra. Do you have any evidence that these are the only people incapable of learning algebra? I have lots of anecdotal evidence that the set of people who can’t learn algebra is much larger than the set of mentally disabled people.
- TameAntelope 5y ago
  Do I require evidence to not believe something you've stated? Or do you require evidence to assert something you've stated? I don't think the onus is on me to prove you wrong, so much as the onus is on you to prove that your experience is scientifically rigorous and representative of more than just your personal experience. And to be clear, I don't doubt that many people "can't" learn calculus in the same way I "can't" run a marathon; we don't have the desire, discipline, and free time necessary to do the work required. This does not speak in any way towards our capacities to do so, only our desire. So I suspect the vast majority of your students didn't have the sufficient desire to learn a lot more than they were incapable, and I think it's a critical distinction, because you can change people's motivations, but you cannot change their capacity.
  - syops 5y ago
    There’s no onus on either of us to do anything. We are just strangers posting on the internet without pay or other compensation. Your experience and knowledge about teaching help me to decide the merits of your beliefs. It appears from my perspective that you know quite little about what you are posting. I know slightly more by having a lot of anecdotal evidence but this certainly doesn’t imply that I’m more likely to be right. As stated in my original comment I’m quite liberal. In education we talk a lot about social conditions and their effects on education. It’s why teachers’ unions strongly support universal healthcare, school lunch programs, etc. After 20 years on the job I’ve come to the conclusion that some can’t learn it. This isn’t controversial in some sense since we know retarded people can’t learn algebra. So what level of capability is necessary to learn it? I don’t know but I suspect it’s well above being mentally retarded. I could be completely wrong but given your lack of experience in the topic my experience ought to at least make you pause a bit. In another comment you wrote about me: … you're more likely ignoring the real-life circumstances your students find themselves in, and your colleagues are not. Talk about making an assertion with no evidence! At least I waited 20 years before stating my absurd assertion.
taneq 5y ago
> I don't think the complexity of either rises to the level of "difficulty" that only gifted minds can comprehend This is a strawman. They never said 'gifted', they just said that some people have it and some don't. > deficiencies in one area can be made up for in other areas Not what we're talking about. GP is probably great at things that aren't chess. That doesn't mean they're good at chess. > Where genetic gifts are lacking, determination and perseverance can almost always make up the difference Determination and perseverance aren't (at least partially) genetic gifts? Honestly I think 'genetics' are a bit of a red herring here anyway because the real underlying assertion being challenged is that all humans have equal potential in all things (which anyone who has ever taught any mildly difficult topic will know is trivially disprovable). The precise mechanism whereby innate human potential differs isn't important if you can't even agree that it differs.

DangitBobby 5y ago

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?
        5y ago
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'.

syops 5y ago

My belief comes my experience teaching math the past 20 years. I think we both agree that mentally disabled people can’t learn algebra. Do you have any evidence that these are the only people incapable of learning algebra? I have lots of anecdotal evidence that the set of people who can’t learn algebra is much larger than the set of mentally disabled people.

TameAntelope 5y ago
Do I require evidence to not believe something you've stated? Or do you require evidence to assert something you've stated? I don't think the onus is on me to prove you wrong, so much as the onus is on you to prove that your experience is scientifically rigorous and representative of more than just your personal experience. And to be clear, I don't doubt that many people "can't" learn calculus in the same way I "can't" run a marathon; we don't have the desire, discipline, and free time necessary to do the work required. This does not speak in any way towards our capacities to do so, only our desire. So I suspect the vast majority of your students didn't have the sufficient desire to learn a lot more than they were incapable, and I think it's a critical distinction, because you can change people's motivations, but you cannot change their capacity.
- syops 5y ago
  There’s no onus on either of us to do anything. We are just strangers posting on the internet without pay or other compensation. Your experience and knowledge about teaching help me to decide the merits of your beliefs. It appears from my perspective that you know quite little about what you are posting. I know slightly more by having a lot of anecdotal evidence but this certainly doesn’t imply that I’m more likely to be right. As stated in my original comment I’m quite liberal. In education we talk a lot about social conditions and their effects on education. It’s why teachers’ unions strongly support universal healthcare, school lunch programs, etc. After 20 years on the job I’ve come to the conclusion that some can’t learn it. This isn’t controversial in some sense since we know retarded people can’t learn algebra. So what level of capability is necessary to learn it? I don’t know but I suspect it’s well above being mentally retarded. I could be completely wrong but given your lack of experience in the topic my experience ought to at least make you pause a bit. In another comment you wrote about me: … you're more likely ignoring the real-life circumstances your students find themselves in, and your colleagues are not. Talk about making an assertion with no evidence! At least I waited 20 years before stating my absurd assertion.

taneq 5y ago

> I don't think the complexity of either rises to the level of "difficulty" that only gifted minds can comprehend This is a strawman. They never said 'gifted', they just said that some people have it and some don't. > deficiencies in one area can be made up for in other areas Not what we're talking about. GP is probably great at things that aren't chess. That doesn't mean they're good at chess. > Where genetic gifts are lacking, determination and perseverance can almost always make up the difference Determination and perseverance aren't (at least partially) genetic gifts? Honestly I think 'genetics' are a bit of a red herring here anyway because the real underlying assertion being challenged is that all humans have equal potential in all things (which anyone who has ever taught any mildly difficult topic will know is trivially disprovable). The precise mechanism whereby innate human potential differs isn't important if you can't even agree that it differs.