I was the one that voted for math subject acceleration as you said you weren't as comfortable with whole grade acceleration.
"I know what you mean. There's nothing on the AOPS pre-Algebra test that DD isn't familiar with, and I suspect she'd get a passing score if I gave it to her, but that's not the same as really being ready for pre-Algebra. "
This statement has me curious. Are you sure you're not underestimating her here?
I was also wondering that, but then this kind of issue:
I worry more about conceptual gaps - like the decimal multiplication problem she solved correctly, then asked whether you counted from the right or the left when picking where to put the decimal point. (Upon discussion, it was clear she did not understand why you moved the decimal where.)
does have me worried - unless it's an isolated problem caused by a teacher explaining it wrong, but even then...
How about a combination solution: subject accelerate to 6th, *and* afterschool. Let the afterschooling focus on nonformulaic problem solving, starting easy and ramping up as she gets used to being stuck and getting herself unstuck (or not being able to get herself unstuck and needing help, and that being fine too). Aim to be ready to start AOPS prealgebra about Christmas, and do it seriously, the way they intend - start with the problems at the start of the chapter, only read on after having a good attempt at them. If that goes well, test out of prealgebra next summer.
ETA: Of course, now that Alcumus includes prealgebra, that's the obvious thing to use - why not sign up (free) and do the odd problem with DD, one or two a day? Start by doing them really together, and shift into her doing them...
I always told DD algebra was easy. So she thinks it's easy.
Yes! The "algebra is hard" mantra always perplexes me - although I think I do understand it, really. It's hard *if* the only way you solved arithmetic problems was by applying rules you'd memorised.
