I was wondering whether anyone - 22B? others? - had anything to say about how to manage the situation in which a child has done all the maths - or any other subject, if similar issues arise - that's normally taught at school, but isn't ready for university yet. I'd be interested in plans, opinions, and, of course, experience.

DS9 isn't there yet, but it's foreseeable that he will be. In standard-US terms, he has most of AP Calculus and most of AP Statistics still to go. In UK terms we have a bit more flexibility, because there are more options in the final two years of school maths than any one student normally takes; if we have him do it all (and whether this is sensible is one of the questions in my mind), it'll keep him going for a few more years.

Here's one fairly typical syllabus document. *

Why not send him to university as soon as he runs out of school maths? DS is very asynchronous; it's impossible (now: could change I suppose) to imagine him being ready to enjoy life as a full-time university student a few years from now. He's anxious in new situations and fairly unskilled socially; exactly the wrong kind of person to take being a young university student in his stride. In the UK university's an all-or-nothing deal; you can't normally enroll in courses piecemeal. Some kind of special arrangement might conceivably be made with our local university, if that seemed appropriate, but (given that both parents work full time) the practical difficulty would probably make it impossible for him to actually attend.

Why not take a break from maths? Polarbear wrote:

Do you have to keep going in math continually, or can you have your ds move on to other subjects, sciences, etc, then come back to whatever math he needs when he needs it?

I think you do have to keep going in maths, just as you have to keep reading, or exercising. If he weren't doing any maths I wouldn't feel he was being properly educated. Maybe it's just me, but it's standard for universities here to insist that students do take maths right up to when they leave school, even if they have the qualifications they need before then. Cambridge even discourages prospective maths students from taking a gap year. I think the latter's a bit excessive, personally, but yeah; let's take it that he does have to keep going in maths. In any case, there's no way he'd stop - the choice is between him doing maths with some kind of guidance and some kind of plan behind it, or him doing the maths he finds in a completely unsupported way. He may be ready for the latter by the time he's a teenager - so maybe this is a problem which will solve itself - but he isn't now.

Broadly I see the three kinds of maths available to him over the next few years as:

- the remaining bits of "school maths";

- university maths

- competition maths.

The questions are around what the balance and order of these things should be. Let me try to list the pros and cons of each as I see them.

School maths. Pro: close to age-appropriate. Possibility of taking exams to certify the achievement. Clearly laid-out dependencies, so easy to make sure you don't get into pedagogically bad situations. DH and I can, with a bit of effort, teach it all ourselves (though this isn't very important; he already doesn't need much in the way of teaching for material this easy). Con: not very challenging.

University maths: Pro: challenging, varied. Con: probably no possibility of getting certification of what he's learned so, for example, if he later wanted to go to university and read maths he might then be stuck redoing a course whose contents he actually already knew. Much more effort from us required to do things in the right order and put together appropriate materials, and he might need actual teaching, some of which we wouldn't be able to provide ourselves.

Competition maths. Pro: route to meeting other very good mathematicians. Challenging. Con: there's something very artificial about hard problems which are nevertheless designed to be soluble in a certain time using certain methods. Competition as such doesn't really seem to be DS's thing, and I could see him getting frustrated in a system where he was supposed to care a lot about winning.

What am I missing? Thoughts, comments?

*Aside: when and where do US students learn the stuff that's in our Mechanics modules - kinematics, rotation of rigid bodies, simple harmonic motion, all that stuff? Physics? University? It doesn't seem to fit into any US school maths course I know about.