if what you mean is that content knowledge isn't really the limiting factor for most people doing AOPS, yeah.
Yes, it was that exactly.
Wouldn't it be bound to end up rushing through material with no chance to actually absorb and use it? I could see this making sense if the kid knew most of it already and needed a certificate to be allowed to avoid spending a whole year on it, or maybe as a dollop of new material for a kid who won't get it otherwise
If she were breezing through 6th grade math this year, and ahead enough that a subject acceleration past pre-algebra and into Algebra I for next year was on the table, I think this course would be perfect for that. But as the first significant exposure to many of the concepts, I do worry about not having enough time to absorb things.
I'd guess there's a 75% chance that DD would be absolutely fine in the class - that she would rise to the occasion and whatever didn't sink in in the 75 classroom hours would get figured out in the 45 homework hours. (Oh, wow - that comes out to be half the instructional hours she'd get in school - and probably a whole year of homework time - and I'd have no hesitation at all over doing a school year compressed program that covered a year of material in a semester.) But if she didn't, then she'd spend the next year of school way ahead and bored.
If DD is currently keener on the history one, I think I'd go with that...
Unless the CTD Summer Programs person tells me that the history class is likely to be all younger kids with no prior exposure to the topic, I think she will do the history one.
But maybe the math one, too. The incremental cost of enrolling in both is not so large that "wasting" it by not coming back if she's miserable in the first session is unthinkable. I also ought to ask about anticipated gender balance in the math session - DD will do better if there are at least a couple of other girls who are residential (rather than day) students.
