I've re-read through ColinsMum's thread "AoPS Intro to Geometry course review"
http://giftedissues.davidsongifted....7284/AoPS_Intro_to_Geometry_course_.html
My DS8 just took an AMC 8 Basics AoPS course that he found somewhat challenging, so on that basis, it wouldn't make sense to think he'd be ready for AoPS Intro to Geometry course yet (although one could be ready for the book sooner than for a course, since you can slow down, take a break, come back to it later etc.)

[BTW the AMC 8 Basics AoPS course, was a good one for him to take. Often he'd be newly learning about a topic, rather than applying an already learned topic to problem solving, but he got exposure to a lot of topics that he can follow up on later.]

[Also, after thinking about "AoPS: Book vs Course"
http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/197574/AoPS_Book_vs_Course.html
we've decided to generally cover material via the books not the courses, so we're not tied to a schedule. DS8 doesn't need the courses for motivation. (He'll still probably take the contest courses, and maybe some others.)]

DS8 seems happy to just work through Intros to Alg, C&P, NT, and to wait for later for Intro Geom. He should have no problem with the level of these 1st 3 books, though I'm sure there'll be plenty of challenging problems. It gives him more variety, as I think he was getting a bit sick of doing just algebra. (C&P and NT seem like more "fun".)

But he was right to question my earlier decision that he shouldn't start C&P and NT, so I really need to figure out the optimal time to start the Intro Geom book, because I'm not sure. I'm not so much concerned about the suggested prerequisites, he's close enough on those, and I could catch him up as needed. And he'd be able to learn the basic geometry material itself (e.g. from a typical lighter course). But it may be that the problems are too complex/difficult. Now if I did let him start on the book, and he realized it was too difficult, and he couldn't do the problems, and decided to set the book aside until later, then that outcome would be fine.

But here's the potential problem. With the Intro Alg book he works on every single exercise and problem (which is good) but he almost always does so without writing anything down, just doing it in his head. That's good brain exercise, but he's not developing the math writing/reasoning/communication skills that he should be at this curricular stage. (For example he'll try to solve 3 linear equations in 3 variables, he might make a mistake, which he'll discover when he checks if his solutions satisfies the equations, but he's persistent and will try again until he get's the right solution. But he's not writing it down. He's doing it in his head. I try telling him he needs to write it down, for several reasons, but he won't.) I'd really like him to develop these math writing/reasoning/communication skills, before starting Geometry for real.

So what I'm concerned about is that if he starts Geometry too soon, before reaching a certain level of "mathematical maturity" then he might start "solving" problems in a superficial way, in his head, not writing it down with proper reasoning (and possibly convincing himself he's solved a problem when he really hasn't). In these circumstances, he might proceed through the book, not getting as much out of it (and maybe not realzing this), when waiting until later would have yielded better results.

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Originally Posted by ColinsMum
Concretely, I do remember an AoPS geometry question assuming children could easily factor a quadratic.
Coincidentally, I walked in the door yestarday, and DS8 said he wanted to solve x^2+x+1=0. This led to discussion of several interesting topics. Then he said he wanted to know how to solve ax^2+bx+c=0 in general, so I guided him to derive the formula for the solutions. (This was all done mentally/verbally with no writing down, but this time I allowed that on purpose to give his brain a workout.) There's a lot more he can learn on this topic, and he'll learn it with the Intro Alg book, but he's fine with material at this level and can learn it quickly.

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I guess I'm trying to navigate an optimal learning trajectory, not superficially rushing through material, but not overcautiously holding back either. I want DS8 to wait for a time to do the Geometry when he'll get the most out of it. On the other hand I don't want to be saying, no you're not allowed to read that book yet (or to give reasons for waiting when my reasons are wrong).