I had a quick look at that 157 page PDF document. Obviously your son should just do the whole lot if possible. From your comments in various threads I wasn't quite sure how he's covering this material, since he's just going to his regular grade in a B&M school. How is he doing it?
Ah, this is not so easy to explain. (And yeah, sorry about the length of that document! It was just that I wanted to give just one link, and that was the closest to comprehensive I could find.)
First thing to say is that we're very, very lucky with DS's school, I think (well, we chose it very carefully and we're paying for it, so that part's not luck, but we're lucky it's there to be chosen and that we have the means). They have people willing and able to do the right thing, and the resources to make it happen. So he's "going to his regular grade" but that doesn't mean he's doing the same maths they're doing; he hasn't done that since he was 5. His current maths teacher has a maths degree and has taught 18yos, and is rather ably giving DS his own work each lesson. Currently that's mostly problem solving - problems from the UKMT challenges and the like - but also, we keep in touch by email and sometimes I mention that DS could do with some exercises on [whatever] and his teacher will find some for him. A couple of years ago (when he had a different, less-mathy teacher before he got to the stage of the school where they have specialist teachers) he was working through a textbook that we provided in school, because that worked better in that context. It's very much play it by ear, without, actually, much of a plan at all - yet somehow, he learns, and always faster than I expect. < spooky music >
Well, except that partly I know how it happens - to feed DS's desire (which he does have) to have "new stuff" we also have books at home, of course, and we have an ALEKS subscription most of the time; he gets fed up with it sometimes and then we let it lapse, but he's wanted to go back to it repeatedly. Typically he'll do a few topics at the weekend, and more during the holidays. For example, he started ALEKS precalculus at the start of the Christmas holidays and finished it (bar the final assessment) in the Easter holidays. Yes, the ALEKS questions are mundane and I wouldn't approve if they were all someone was doing, but given that he's spending most of his school time (and of course some leisure time too) on problem solving, this works for us; he learns definitions and techniques in ALEKS (and I like that he's learning them by needing them in problems immediately, even if the problems are mundane; it's interesting to see how seldom he needs any explanation of how to do a "new" topic). So far, his getting to being able to apply them in harder problems seems to just happen.
I tend to be an over-thinker, but I think (despite having started this thread with my over-thinker hat on!) the thing we're doing right here is actually not to plan too much. If it turns out he didn't really get something in an ALEKS course and we didn't find out because he only got to use it on easy problems, well, no matter; he has time, he can learn it again when he's ready. So far, this doesn't happen much; in fact, the reverse happens - something that's happened more than once is that I watch him, make a list of things I think he could do with reinforcement of, and send them to his maths teacher, only to find that by the time his teacher gives him the reinforcement, he's mulled it over somehow and no longer has the weakness I'd identified.
The UK K-12 syllabus certainly covers more than in the USA. I assume that's due to earlier specialization, and due to not lowering the level so that more people can reach it. It's true that one can do 100% maths in a UK undergraduate degree, right?
Absolutely one can, in fact single subject degrees are the norm in England. (Actually, Scotland has a different tradition; where England has 3-year fully-specialised undergraduate degrees typically started at 18, Scotland has 4-year degrees typically started at 17 in which the first two years have some scope for taking courses outside your specialism. But there is never any
requirement to take anything outside your specialism, as I understand is common in the US.)
Yes, in both systems, the last two years of school involve specialising, and the highest level maths qualifications are not designed to be accessible to everyone. Nevertheless, we still have "dumbing down" pressures and controversy about it and about what to do about it. Which I could write screeds on, but it's probably not of much interest, so I won't! I think the single best thing about the UK system is that school achievement is measured by externally set and marked exams, not by teacher opinion, fwiw.
