Re: relationship between SAT scores and intelligence?
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The content of many courses in the U.S., especially science and math courses, is pretty uniform. Often the very same texts are used. You can't take calculus at the University of Louisville and only be taught half as much as someone taking the equivalent course at an Ivy League school.
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In my experience teaching at elite schools and discussing teaching with mathematicians, scientists, and engineers elsewhere, this is dead wrong.
You can find many exceptions, but in general, mediocre schools do not have anywhere close to the same depth of curriculum as schools like Harvard, Princeton, MIT, etc. Almost all (over 95%) of the students taking freshman mathematics (Math 1) at Caltech have passed AP BC calculus or the equivalent in high school. The content of the course is not set by keeping pace with the other calculus classes in schools with students with weaker backgrounds.
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These are obviously not equivalent classes then, and I would not expect them to be evaluated for content as equivalent.
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