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I disagree because math is too vast and ill defined a field for any claim that anyone can be good or bad at all of it to be taken seriously. In high school, I

I disagree because math is too vast and ill defined a field for any claim that anyone can be good or bad at all of it to be taken seriously. In high school, I was one of those people who spent tons of time and energy on it, and failed miserably, barely graduating as a result. It wasn't until I was about 25 when I picked up a basic algebra and trigonometry book on a whim and started self-teaching, that it began making sense to me. I eventually went back to school for pure math. In my case, I think what helped me as an adult was the freedom to learn on my own terms without the pressure of deadlines, and also a strong support network of friends encouraging me (compare with my teachers in high school who would actively embarrass me in front of the class or joke about their low expectations of me). And of course, some years of life experience in the real world doing things that were actually hard compared to (elementary) math as someone of limited means helped a bit too. So, all of that is to say that people who struggle in math classes struggle for different reasons. I suspect that much of the time the dominating forces are psychosocial, cultural, or plain & simple lack of interest (which itself might be driven by traumatic experiences with shitty teachers or parents with weird expectations)

username90 6y ago
So you failed, then took your time and practiced more to succeed. I don't see how that contradicts anything I said. Circumstances matters, effort matters. Talent being a huge factor doesn't contradict that.
- username91 6y ago
  Sorry for the lack of post history: I made an account to jump in. You asked.. > how do you explain the very large number of people who spends tons of time and energy trying to get good at maths but fails to even grasp simple concepts like calculus? One answer, as vector_spaces said, is that the learning environment can completely change the outcome of this effort. You agreed: > Circumstances matter It's true that talent being a factor doesn't contradict that, but given how homogenous early-life learning environments are, it's -extremely- difficult to tell whether a person "failed" because of lack of talent, vs. lack of the right environment to experiment and learn. Basically, because a "wrong environment" fail looks like a "lack of talent" fail, I believe a lot of talented people don't find out that they have the talent in the first place, as they believe that an attempt in the wrong environment is as good as any attempt, and never try again - particularly if they've been chastised and humiliated -during- that learning process, as vector_spaces was. In any case, the reason I wanted to jump in was because of your original statement: >I don't think this is because people told them anything I would just ask that you reconsider that position, based especially on your agreement that "circumstances matter." Thanks for reading. [edit: linebreaks]
  - username90 6y ago
    Learning environment matters, but I wouldn't say that it would completely change the outcome. If you are smart you don't have to work hard or have a good environment to understand high school maths. If you aren't that smart you can still pass the courses with hard work, but from my experience teaching a lot of college students in 1:1 settings people who have to work hard never really grasp the subjects. And some are so lacking that even with hard work they still can't pass. So basically, just because someone managed to improve their grades and pass classes with hard work doesn't really say anything about my points. There are still people who pass easily without any of that. In short, my view is that hard work and environment can help improve your results, but unless you are completely prohibited from attending school you wont need that if you are smart enough. For example, I skipped a lot of classes, was abused, was suicidal, never studied for any tests and didn't do any homework assignments in high school. I still got perfect math grades. Most people have better environments than that and spend more time on maths than that yet still do worse. I spent a lot of time doing 1:1 teaching in college, explaining things in intuitive ways etc helps, but ultimately I had to conclude that I can't make others understand things the way I do. They simply lacked something.
    - username91 6y ago
      Interesting. I'm still mulling over some of your points, but overall what you're saying makes sense to me. I appreciate you sharing your story - I'm sorry you had to deal with that experience.
    - antegamisou 6y ago
      The way you talk about the 'easiness' of high school math makes me think you've received education in the US, where the exams, and even some part of the curriculum, are laughably easier compared to what students from EU countries have experienced. That is not to say that some people didn't have to put as much effort as others - learned faster. But when I come across people, mostly online, brushing off math at or above high school level as easy have either received subpar/simplified math education (happens almost exclusively in the US and some shitty EU countries), or have too much confidence from their positive experience with low-difficulty exams. > I had to conclude that I can't make others understand things the way I do. If you've had this happen too often you're probably just bad at explaining things, or even worse you haven't fully understood them.
- vector_spaces 6y ago
  What do you even mean with talent? Specifically when it comes to mathematics, that is. Some astrological alignment of circumstance such that someone can realize their potential unimpeded by their economic class, physical or mental health status, abilities in the language of instruction, lack of interest in the material, or innumerable other such challenges? Or are you referring also to some eugenicist fantasy of a person whose neurochemistry/physiology happens to be optimized for that specific subset of human activities that we call mathematics? The latter assumes the former, since if such a thing exists, you can be sure that external factors would limit such a person's ability to succeed in traditional settings. In either case, I don't understand why such a notion would be useful to anyone except as a justification for gatekeeping and maintaining a culture of elitism in math, which is very much not needed. I'm genuinely curious as to why you find the concept useful
  - username90 6y ago
    If you have enough talent for maths you can get good results in every maths course up to graduate level without studying or doing practice problems outside of just listening to classes. I know I did that, so I know it is possible. I don't particularly like maths courses, I just took a lot of them since they were free credits. Is this useful information for how to treat typical students? No. However, talent having such a profound impact on peoples ability to learn, understand and apply mathematics is something most people are aware of and hence it isn't strange that people who studied maths thinks that genius requires inborn talent. The author of this piece instead takes a jab at it and tries to say that they just believe that since they got told by their parents that they were smart, I don't think that is true. Most people studying maths doesn't view themselves as good at maths, so what is more likely is that they take their own struggles despite hard work and passion as evidence that genius requires inborn talent.
    - randcraw 6y ago
      So for you, there was a royal road to math? No homework necessary? If so, you're one in a billion. It's no wonder you don't share the perspective of others who must practice in order to learn.
red75prime 6y ago
And I tried and tried, but to no avail. I can understand what formulas describe, if I take time to remember definitions. But my mind refuses to grasp the reality behind those formulas, if that reality doesn't map well to everyday things like 3D space, objects, movement and so on. It could be possible that I haven't tried long enough, but at about 35 I decided to put less effort into it and to prioritize other things. I'm not encouraging anyone to avoid trying, of course. It was a very useful experience. Knowing that seemingly different things may have unifying mathematical structure (like monad in programming) can expand your approaches even if you aren't good at recognizing and exploring those mathematical structures.

username90 6y ago

So you failed, then took your time and practiced more to succeed. I don't see how that contradicts anything I said. Circumstances matters, effort matters. Talent being a huge factor doesn't contradict that.

username91 6y ago
Sorry for the lack of post history: I made an account to jump in. You asked.. > how do you explain the very large number of people who spends tons of time and energy trying to get good at maths but fails to even grasp simple concepts like calculus? One answer, as vector_spaces said, is that the learning environment can completely change the outcome of this effort. You agreed: > Circumstances matter It's true that talent being a factor doesn't contradict that, but given how homogenous early-life learning environments are, it's -extremely- difficult to tell whether a person "failed" because of lack of talent, vs. lack of the right environment to experiment and learn. Basically, because a "wrong environment" fail looks like a "lack of talent" fail, I believe a lot of talented people don't find out that they have the talent in the first place, as they believe that an attempt in the wrong environment is as good as any attempt, and never try again - particularly if they've been chastised and humiliated -during- that learning process, as vector_spaces was. In any case, the reason I wanted to jump in was because of your original statement: >I don't think this is because people told them anything I would just ask that you reconsider that position, based especially on your agreement that "circumstances matter." Thanks for reading. [edit: linebreaks]
- username90 6y ago
  Learning environment matters, but I wouldn't say that it would completely change the outcome. If you are smart you don't have to work hard or have a good environment to understand high school maths. If you aren't that smart you can still pass the courses with hard work, but from my experience teaching a lot of college students in 1:1 settings people who have to work hard never really grasp the subjects. And some are so lacking that even with hard work they still can't pass. So basically, just because someone managed to improve their grades and pass classes with hard work doesn't really say anything about my points. There are still people who pass easily without any of that. In short, my view is that hard work and environment can help improve your results, but unless you are completely prohibited from attending school you wont need that if you are smart enough. For example, I skipped a lot of classes, was abused, was suicidal, never studied for any tests and didn't do any homework assignments in high school. I still got perfect math grades. Most people have better environments than that and spend more time on maths than that yet still do worse. I spent a lot of time doing 1:1 teaching in college, explaining things in intuitive ways etc helps, but ultimately I had to conclude that I can't make others understand things the way I do. They simply lacked something.
  - username91 6y ago
    Interesting. I'm still mulling over some of your points, but overall what you're saying makes sense to me. I appreciate you sharing your story - I'm sorry you had to deal with that experience.
  - antegamisou 6y ago
    The way you talk about the 'easiness' of high school math makes me think you've received education in the US, where the exams, and even some part of the curriculum, are laughably easier compared to what students from EU countries have experienced. That is not to say that some people didn't have to put as much effort as others - learned faster. But when I come across people, mostly online, brushing off math at or above high school level as easy have either received subpar/simplified math education (happens almost exclusively in the US and some shitty EU countries), or have too much confidence from their positive experience with low-difficulty exams. > I had to conclude that I can't make others understand things the way I do. If you've had this happen too often you're probably just bad at explaining things, or even worse you haven't fully understood them.
vector_spaces 6y ago
What do you even mean with talent? Specifically when it comes to mathematics, that is. Some astrological alignment of circumstance such that someone can realize their potential unimpeded by their economic class, physical or mental health status, abilities in the language of instruction, lack of interest in the material, or innumerable other such challenges? Or are you referring also to some eugenicist fantasy of a person whose neurochemistry/physiology happens to be optimized for that specific subset of human activities that we call mathematics? The latter assumes the former, since if such a thing exists, you can be sure that external factors would limit such a person's ability to succeed in traditional settings. In either case, I don't understand why such a notion would be useful to anyone except as a justification for gatekeeping and maintaining a culture of elitism in math, which is very much not needed. I'm genuinely curious as to why you find the concept useful
- username90 6y ago
  If you have enough talent for maths you can get good results in every maths course up to graduate level without studying or doing practice problems outside of just listening to classes. I know I did that, so I know it is possible. I don't particularly like maths courses, I just took a lot of them since they were free credits. Is this useful information for how to treat typical students? No. However, talent having such a profound impact on peoples ability to learn, understand and apply mathematics is something most people are aware of and hence it isn't strange that people who studied maths thinks that genius requires inborn talent. The author of this piece instead takes a jab at it and tries to say that they just believe that since they got told by their parents that they were smart, I don't think that is true. Most people studying maths doesn't view themselves as good at maths, so what is more likely is that they take their own struggles despite hard work and passion as evidence that genius requires inborn talent.
  - randcraw 6y ago
    So for you, there was a royal road to math? No homework necessary? If so, you're one in a billion. It's no wonder you don't share the perspective of others who must practice in order to learn.

red75prime 6y ago

And I tried and tried, but to no avail. I can understand what formulas describe, if I take time to remember definitions. But my mind refuses to grasp the reality behind those formulas, if that reality doesn't map well to everyday things like 3D space, objects, movement and so on. It could be possible that I haven't tried long enough, but at about 35 I decided to put less effort into it and to prioritize other things. I'm not encouraging anyone to avoid trying, of course. It was a very useful experience. Knowing that seemingly different things may have unifying mathematical structure (like monad in programming) can expand your approaches even if you aren't good at recognizing and exploring those mathematical structures.