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Notes -
Even outside selective schools, I think scholastic competitions are a good way to cut a precocious snot down to size (speaking as a precocious snot). I managed to pull off 1st in my (small) state in MathCounts when I was little, but then I went to nationals and didn't even make it to the Countdown round...
It might be necessary to do things like that regularly, though. I didn't join any other national competitions in grade school, and so I was still a bit blindsided when I went to a good college and wasn't ever the smartest in the room anymore and had to actually study to learn everything and barely even kept my fall freshman GPA at a B average. I'm encouraging my kids to do AMC now, in part because it would be great if they make it to the higher levels there, but in part to keep them reminded that there's a wide world out there and they're not even close to being the only precocious kids in it. They're not snots about it, but they do aspire to good colleges and I don't want it to be a surprise if they get to one and suddenly being exceptionally smart is just table stakes.
You might be right that home education makes things easier to fix. I raced ahead in math when I was little and could teach myself the basics, but eventually I got on the Algebra-I-and-onward track and it was easy to just take one-class-per-year, smugly feeling smart because I was much younger than my classmates but not actually learning any faster than them. Without that fixed class schedule I could have tried to keep going a bit faster and that might have been enough challenge to make things difficult and keep me humble.
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