I didn't mean to propose an exact multiplicative relationship. I merely used it to illustrate how the two claims
a) innate talent exists and is important
b) practice is also important
are not incompatible.
As for correlation between IQ and various professions, not to mention wages, there is plenty of statistically significant data on this. See for example [1], which shows excellent correlations between AFQT (the US Army's IQ-like test) scores and post-military wage (not to mention many specific objectively graded tasks within the armed forces).
(Note that IQ test-retest scores tend to be highly correlated - it's rare that a child scoring 1 stdev below the mean will later score 1 stdev above the mean.)
In the particular case of math proofs (which I think you're referring to) you have the additional issue that (I think - I'm not a mathematician) proofs often require intuitive leaps...Teaching intuition/pattern-matching is of course really hard.
True. But nevertheless, some students pick it up immediately while others never do. The question arises, why?
Also, as for what is "well accepted", there are lots of things in the field of education that are well accepted but false. For example, people widely believe that test prep significantly improves SAT scores [2]. They also believe school quality (rather than % of Asian students) explains many of the differences in test outcomes between US schools and Asian schools [3]. See also Bryan Caplan's book [4] which shows lots of evidence that most of what is done to children before age 18 has little effect on adult outcomes.
So if you have evidence that public schools and private schools significantly affect outcomes, go ahead and post it. But most of the evidence I've seen suggests school quality is dwarfed by non-school factors. People just ignore the evidence because they don't like the conclusion.
[1] Handbook of the economics of education, by Hanushek and Welch
While I accept that IQ has some statistically significant correlations with interesting things, and is stable within individuals, I don't think there is consensus as to what that actually means. But I might just need to read more. Actually, I always need to read more.
That aside, I think the core disagreement here is that (I think) we have both taken the same data (a lot of stuff surrounding 'hard work' and education is clearly utter rubbish) and taken it in two different directions: you've gone in a more innate-ability, behavioural-genetics direction (I think), while I'm more interested in things like the effect of practice. The nature-vs-nurture debate will probably outlive both of us, and there is evidence for both arguments.
Ultimately, I don't find innate stuff that interesting, because there is nothing I can do about it. I would rather focus on a minor factor that I can change than a major factor that I can't, and the research suggests that practice et al are far more than minor factors. So I focus on those. And until the debate is resolved, I will continue to espouse education policies which reflect that attitude.
Thanks for the references; a couple there that I hadn't seen before, and it's always worth reading stuff that disagrees with you.
a) innate talent exists and is important
b) practice is also important
are not incompatible.
As for correlation between IQ and various professions, not to mention wages, there is plenty of statistically significant data on this. See for example [1], which shows excellent correlations between AFQT (the US Army's IQ-like test) scores and post-military wage (not to mention many specific objectively graded tasks within the armed forces).
(Note that IQ test-retest scores tend to be highly correlated - it's rare that a child scoring 1 stdev below the mean will later score 1 stdev above the mean.)
In the particular case of math proofs (which I think you're referring to) you have the additional issue that (I think - I'm not a mathematician) proofs often require intuitive leaps...Teaching intuition/pattern-matching is of course really hard.
True. But nevertheless, some students pick it up immediately while others never do. The question arises, why?
Also, as for what is "well accepted", there are lots of things in the field of education that are well accepted but false. For example, people widely believe that test prep significantly improves SAT scores [2]. They also believe school quality (rather than % of Asian students) explains many of the differences in test outcomes between US schools and Asian schools [3]. See also Bryan Caplan's book [4] which shows lots of evidence that most of what is done to children before age 18 has little effect on adult outcomes.
So if you have evidence that public schools and private schools significantly affect outcomes, go ahead and post it. But most of the evidence I've seen suggests school quality is dwarfed by non-school factors. People just ignore the evidence because they don't like the conclusion.
[1] Handbook of the economics of education, by Hanushek and Welch
[2] Studies funded by parties other than Kaplan tend to disagree. http://online.wsj.com/article/SB124278685697537839.html
[3] http://en.wikipedia.org/wiki/Trends_in_International_Mathema...
[4] http://www.amazon.com/Selfish-Reasons-Have-More-Kids/dp/0465...