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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

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.
  - username90 6y ago
    I took the most rigorous college degree in Sweden and did pure maths up to masters level. High school maths included calculus, although not as rigorous as you learn at college. > 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. I understood the subjects well enough too solve problems on exams I hadn't seen before. That was the main way I managed to get good grades without doing practice problems or studying. I didn't manage to get others to understand things that well. I don't think that failing to get people to that level means I am bad at explaining as there is nobody in the entire world who can get average college students to that level. For my masters thesis I solved a problem that had stumped one of the more renowned mathematicians in Sweden for decades. I'm not sure if that was hard or not, but to me it didn't seem hard. I didn't continue doing maths as I didn't really have enough passion for the subject to continue doing research, it is pretty boring. After that I realized I needed to earn money, so I learned programming, started getting top 100 spots and sometimes top 10 spots in world wide programming competitions and joined Google. That didn't seem particularly hard to me either, as it took about half a year just doing things on my own. Why aren't I famous etc? Because I just don't care that much about things. I get bored and stop doing them long before I have worked enough hours on things to get any notable results. I aren't bragging here, I know my value to society thus isn't that high, I am just giving my perspective on things. There are tons of people online arguing that I can't exist, I don't like that.

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.
- username90 6y ago
  I took the most rigorous college degree in Sweden and did pure maths up to masters level. High school maths included calculus, although not as rigorous as you learn at college. > 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. I understood the subjects well enough too solve problems on exams I hadn't seen before. That was the main way I managed to get good grades without doing practice problems or studying. I didn't manage to get others to understand things that well. I don't think that failing to get people to that level means I am bad at explaining as there is nobody in the entire world who can get average college students to that level. For my masters thesis I solved a problem that had stumped one of the more renowned mathematicians in Sweden for decades. I'm not sure if that was hard or not, but to me it didn't seem hard. I didn't continue doing maths as I didn't really have enough passion for the subject to continue doing research, it is pretty boring. After that I realized I needed to earn money, so I learned programming, started getting top 100 spots and sometimes top 10 spots in world wide programming competitions and joined Google. That didn't seem particularly hard to me either, as it took about half a year just doing things on my own. Why aren't I famous etc? Because I just don't care that much about things. I get bored and stop doing them long before I have worked enough hours on things to get any notable results. I aren't bragging here, I know my value to society thus isn't that high, I am just giving my perspective on things. There are tons of people online arguing that I can't exist, I don't like that.