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[quote=Anonymous][quote=Anonymous]
This isn’t my experience at all. For example in mathcounts there are schools in the country that have become power houses. Which is evidence that the right coaches and training make a huge difference. The math kangaroo contest and AMC have like the same types of questions on it every year. If you practice the certain types of tricks over and over you will do pretty well with an above average IQ. Go over to the AOPS forum and you can see for yourself how the kids talk about the types of problems. [/quote]

There's a huge cliff between doing pretty well and reaching elite levels, though.  It's relatively easy for an above average student to do well enough on AMC to qualify for AIME.  It's nearly impossible for an above average student to practice enough to make USAMO.  The AOPS forums are filled with kids who worked their tails off and end up disappointed that they didn't earn high enough scores to move on.   Any contest that takes only the top 250 or top 50 or some other very limited number will be filled with the kids who have both the talent and the coaching.

It's tough to truly analyze the powerhouse schools, since there's selection bias in the students who choose to attend that school.  People with kids who are talented at math seek out schools that have the best reputations and the best competition teams.  I'm sure the coaching at TJ is wonderful, but the main reason they're a powerhouse is that they're drawing all of the top mathematicians from the entire NOVA area.  [/quote]

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