Does anyone have kids at both? I'm really curious how the pedagogy/class size/social-emotional learning/extracurriculars differs between the two. All I know about HCES is that the kids are super smart, but wanting to know more about the school than that!
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Worry about this when your child gets into HCES.
No. When your kid gets in you have one week to decide, which is very little time to do research. OP is right to worry about this now.
Have many friends who turned down HCES for private due to class size, facilities, and less emphasis on SEL than what one finds in private. The differences on those factors are real. But it's such a personal and individual thing that it's worth getting in and touring / talking to people and then deciding for yourself. Every family is different in the value it places on such things.
Agree. Some more points:
At HCES the teachers are unionized, and don't seem particularly answerable to the administration. At privates (save perhaps EC/F?) the administration has more control. You can decide which is better. It's not clear to me that the teachers are necessarily better at one than the other.
In the lower grades the academics at K-12 privates move at a snail's pace. (I think K-8s are more driven.) Make sure you're comfortable with that if you choose private.
Regarding HCES, in short there is nothing special about it other than (a) the kids are very smart (or at least test well, if you want to quibble), and (b) it guarantees admission to HCHS (de facto, if not de jure). Of course (a) leads naturally to somewhat fast-paced academics, though keep in mind that by the time they get to HCHS the HCES kids are arguably weaker on average than the incoming kids. My guess is that HCES is probably better than most privates at addressing the academic needs of very smart kids, but even they aren't great at dealing with super-geniuses (e.g. 5th graders taking calculus).
Some parents feel that being around other very smart kids trumps all. Others don't. I don't think there's a right or wrong answer.
@Anonymous: these are excellent points and all true, esp on the academic front. One other thing is the peer group. You are likely to be in a MUCH wealthier peer group overall at a TT private than at HCCS. As OR said, leave to you to decide whether that is good or bad. It's likely a combination of both. This is not say there are not fabulously wealthy people at HCCS. There are. Plenty of them. Just saying that overall there is more wealth in the TT privates.
@Anonymous I don't agree that there are "plenty" of fabulously wealthy people at HCCS. More like a few per grade. Which is not a lot.
Honestly, if you have the money, I would hands down choose TT private.