You points are valid, and I don't take a hard stance on this debate, but I highly disagree with how it's called the "nature vs nuture debate," as if it's one or the other.
Learning calculus at age 10 is no small feat; it's one of many examples there are, but you are right, I can't say it can't be taught. However, research evidence will say it's very difficult.
I don't remember the name of the experiment, but this is fairly well-tested, as follows. Take n beads and lay them in a line in front of a 5-year-old. Take the same number of beads and make another line, but space them apart wider. Ask which line has more beads. Usually the kid will say the more widely-spaced line has more. This is caused by an immature perception of quantity. After a few years, this error "magically" disappears. Logically, if you don't understand descrete quantities you won't be handling high-level math.
The other example is reading. Most kids begin recalling episodic memories from age 3; reading starts later than that. Sho Yano was reading the New York Times at age 2. He played Chopin from memory at 3, with no training at all (the story goes, as his mother says, that she was in the kicthen and he just climbed up on the chair and started playing). There is simply no case to be made about it being a taught skill.
Again I'm not discounting the importance of rearing, but there are cases where innate genius is the primary factor in skill development, and again, I believe Mozart falls into the genius category. Beethoven, maybe the hard work category.
I suspect that the researchers cited in the article might point out people who demonstrated aptitude like Yano's and yet did not achieve as much as someone who had less aptitude but worked harder. There is some baseline of innate aptitude required for excellence, but among people surpassing that baseline hard work is what distinguishes them; that is the hypothesis proffered in the article.
As for Mozart, the point was that even he had to put in over 10 years of work before producing his best work. But, because he started at 3 he got there at a really early age.
That hypothesis is clear, and I agree with it. I am a fan of Ericcson's work, but I disagree with certain examples that are often cited in articles like these. There are many reasons, the first of which I mentioned above.
The rules of aptitude assessment are much different for children and adults; the returns per year is not simply accumulative. First, the curve isn't linear. Second, the curve looks different during different ages. Forgive me if this is obvious, but the reporters never seem like they know. The ten years from age 3 to 13 is a different ten years from age 23 to 33. If you learned a language in the former interval, you'd be a native speaker; in the latter, no matter how hard you work, you won't be. The "early" brain is a completely different creature from the "late" brain (which is why I think youth education is far more important than teen+ education). It is also early in life when particular natural affinities develop. If there were two TigerWoods, let one start golf at 2, trains until 18, and deprive them for 8 years. The other starts at 10, trains until 26, and bring them together to compete after a refresher for the early start, I would bet on the early starter.
Learning calculus at age 10 is no small feat; it's one of many examples there are, but you are right, I can't say it can't be taught. However, research evidence will say it's very difficult.
I don't remember the name of the experiment, but this is fairly well-tested, as follows. Take n beads and lay them in a line in front of a 5-year-old. Take the same number of beads and make another line, but space them apart wider. Ask which line has more beads. Usually the kid will say the more widely-spaced line has more. This is caused by an immature perception of quantity. After a few years, this error "magically" disappears. Logically, if you don't understand descrete quantities you won't be handling high-level math.
The other example is reading. Most kids begin recalling episodic memories from age 3; reading starts later than that. Sho Yano was reading the New York Times at age 2. He played Chopin from memory at 3, with no training at all (the story goes, as his mother says, that she was in the kicthen and he just climbed up on the chair and started playing). There is simply no case to be made about it being a taught skill.
Again I'm not discounting the importance of rearing, but there are cases where innate genius is the primary factor in skill development, and again, I believe Mozart falls into the genius category. Beethoven, maybe the hard work category.