If that's true, there ought to be some culture that doesn't have this problem. Can you name one?
I don't think the reason a kid may pick it up is so much that "he can be really good at it", but rather because he is "learning to play them for fun". I.e., he's actually interested in it and therefore puts time and effort into it.
With the calculus example, I don't think it's that he's "not naturally talented" (although he may come to believe that), but that he is discouraged/intimidated by his environment. Given enough time and effort, there's no reason he couldn't pick up calculus just as well as the drums; the class simply takes away his passion for it and/or makes it feel like a job.
but rather because he is "learning to play them for fun"
But what is fun? A person experiences fun when they have a feedback loop of effort, accomplishment, and reward. If you are good at math, you get this from doing math and you find math fun. If you are good at Halo, you get this from beating levels, and playing Halo is fun.
Also, it's not just about being above average or below average, it's also about getting that dopamine hit for performing a task successfully. An average athlete can have fun playing a game as long as he is competitive. An average math student can enjoy math as long as the material is not too difficult and not too boring.
I think kids should be made to understand that learning is very very interesting. That word understand is the most important, if they are made to feel they have to then sure they wont like it, but if they are made to understand its extremely interesting well sure they'll like it.
That's the problem, right there.
My daughter doesn't stay bored for long because she's curious about everything (essentially killing your TV helps too).
I do not really like these discussion about schooling and university though. It seems too simple to me to completely disregard the job that thousands of teachers are doing worldwide to teach these kids and consider schooling or universities a failure. Perhaps no one told them that this system has been evolving for nearly a millennia.
My daughter doesn't stay bored for long because she's curious about everything
Sure she is curious but the question is whether she and the many kids like her keep such curiosity. I remember from my early years many of my friends saying they excelled until grade four, others probably excelled until grade eight. I have said it before and I would like to repeat that schooling is such a big thing, it encompasses life itself. I do not think these kids are much different from us adults, they too would rather not do their school work but play, at other times love doing their school work, they too have their peer influence and for what an alcoholic would be alcohol for them may be going on the streets and measuring the pavements.
Schooling is there to develop these children and introduce them to life and how it works and above all lets not forget they are kids they do want some fun and they will be mischievous and not bother at times. Schooling is not to teach these kids how to live their life though. The school and life brings to these kids as much as these kids have to bring to life and school.
So how do you make this marvellous system, maybe the pinnacle of civilisation which is now perhaps universal, save the most deprive parts of this world, to become even better. I do not know but however advance our schooling system becomes it may not be immune to the criticism that it is failing many children perhaps because there is only so much that the environment may affect our biological make up. We have evolved under certain influences and sure we may be traced to one mother, but the mother after that may make as much difference down the trail of heritability. It is clear that evolution works through specialising in a certain area, i.e. faster legs, bigger jumping ability, taller neck, venom, whatever gives one an advantage and something the other doesn't have. There is no reason to not suggest that this civilisation takes this specialisation into a mental arena rather than physical. This world has so much to offer and it needs so many things to be done, it is inevitable perhaps that many children will specialise to do things outside of the schooling system while others thrive at it and as in my case like it but go on to do my own thing as well. To conclude therefore, schooling is not an end point, it is a swing board.
This drove my parents nuts, they kept telling me I was throwing my life away, blah blah.
Well, it's obvious how that all turned out.
Let kids follow their passions, and they will LOVE learning, which is the most important life skill anyone can learn.