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Joined: Sep 2008
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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 standardUS 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 fulltime 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 allornothing 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 ageappropriate. Possibility of taking exams to certify the achievement. Clearly laidout 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.
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Is there such thing as dual enrollment in the UK?
After finishing the usual highschool sequence, my son took the undergraduate math courses at the university, but as a highschool student. When he matriculated and started as a freshman at his current university he started taking graduate level courses. He has never had to repeat anything. He has also self studied topics and has been allowed to skip taking the courses formally by showing mastery through discussions with the professors and, in two instances, taking the course final exams. ( didn't receive credit, just was able to waive them as prerequisites to higher level courses)
Would any of that be possible in the UK? Short version: nope. Long version: there's the Open University, but its courses are not really suitable for a very mathy person. Anything else would be a special oneoff arrangement. I know of one person, decades ago, who did have an arrangement that led to him getting a maths degree while still at school, but he had a parent available to drive him back and forth, and it was less flexible in various ways than what your DS had, I think. ETA a key element is that university here doesn't work by accumulating credits. There are courses you take in each year, and then you're done. Doing something different requires special permission and may or may not work practically. "Graduate school" is completely different from in the US; a PhD student here doesn't typically take taught courses at all, so graduate level courses don't exist in the same way, though much of the material to be found in US graduate courses is in undergraduate courses here and there are master's courses. That's interesting, thanks for that pointer. (But ouch, on top of school fees!) Edit to answer your edit: yes, there is plenty to be said for free learning. It may be that this will solve itself that way. Against it is the relatively inflexible university system he'd be going into if he read maths here later, as above. One way this could go wrong is if he'd taught himself half a maths degree, and then had to sit through all that again to get the other half. He says now that he'll probably want to read a science, in which case the issue won't arise, but he looks like such a mathematician in how he thinks that I won't be at all surprised if he changes his mind.
Last edited by ColinsMum; 05/25/13 02:15 PM.
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I will agree that Maths has a halflife.
Perhaps the online MIT courses may keep him stimulated and appropriately in condition when the time comes.
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Joined: Sep 2009
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Two things popped into my head reading your post, although I don't know how feasible or appropriate they would be:
1. Can you talk to the head of the maths department at a local university and explain your DS's position to them and see what they might suggest? Maybe they have a solution that you haven't thought of.
2. Is it possible for your DS to take a break from maths at school but instead have a private tutor working with him in more obscure maths or with math applications in other subjects such as science or technology?
She thought she could, so she did.




Joined: Aug 2010
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I can't really comment on the mechanics question  not that familiar with the details, but I'm so glad you brought up the rest of this topic. It's something we think about often.
Even without the asynchrony you mention, I think there are many reasons to try to avoid early college. Every family and situation is different and I know early college works for many, but we are also facing running out of school math and yet (at the moment) hoping for college at a fairly typical age. I agree that university math can work but can also have issues. I think my son gets access to better thinking and more love of math in the math circle than in our local colleges. If local college options were better, that might not be true.
My kid hasn't found much "school math" to be useful and has consistently been frustrated, so we've tried to go outside the standard curriculum as much as possible. AoPS is an obvious solution and taking all those courses takes time. Despite hating repetition, I don't believe DS learned everything possible about geometry at 10, so Olympiad geometry, or more contest math, or more discrete math are all possibilities. I think repetition with more depth is very different that repetition of school type math, which he would find excruciating.
Math summer programs in the US usually cover math outside the traditional curriculum (Mathpath for middle schoolers or Awesome math, or for high school, Promys, HCSSiM, etc.). These are expensive but also many are international and provide access to higher math and math growth in the summer at least.
I think it's been useful to focus on relative weaknesses in contest math, so speed and calculation have been drilled in math counts and been useful without increasing the level of math. I can see this frustrating a kid who really wanted to win, but it's been a radically different approach to math for my kid and useful, even though he likes thinking about a problem for days rather than one minute. While I think it focuses more on what I see as "tricks" than as deeper math, it's definitely been a learning experience for DS.
The wealth of online free options currently amazes me. If you aren't looking for credit but only growth, much of the math curriculum at some great universities is online. MIT OCW or coursera, udacity, etc. offer options.
We are trying to use the extra time to explore "mathy" topics more deeply that fall outside traditional math courses  physics, economics, computer science  can use math and apply it without being a typical math course.
A math circle has been huge for my son. IME, math professors running math circles are absolutely uninterested in age, or even in true readiness. I think my son entered a higher level circle before he was ready, but he was happy and engaged and so welcomed. He has grown to belong there. That exposure goes way beyond any curriculum and has fueled interest in math more than anything else. The people running it are dedicated professors who love math, love smart kids, and love feeding the fire.
We've also considered boarding school, but I'm quite ambivalent about it. Places like Exeter offer math far beyond typical high schools and I suspect such places exist in the UK??
I'm trying to focus on feeding the love of math and other subjects without worrying much about credit. DS reads a great deal rather than sitting through a formal course. He's selftaught a lot of programming in his free time. He's often frustrated with the formal course due to pace, so this has worked better for us. If you need credit, I think it gets harder.




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We have already effectively run out of English, and of social studies. Our answer has been threefold, but it DOES involve early Uni entry (then again, we're talking about a kid who is a 3+y skip across the board without any ONE area way ahead of others): a) decelerate as much as possible until things are kindof in synch (that is, drop into some kind of tolerable holding pattern with strengths until the most asynchronous areas come into focus too) b) TUTOR at the levels the student has MASTERED. There is usually room for that kind of reinforcement that forces students with material/curriculum mastery to consider things in new ways as they explain it to others, c) When the holding pattern is intolerable, or the option to revisit material via tutoring/explaining doesn't exist, independent study. (We're doing this right now with literature and social sciences.) We are trying to use the extra time to explore "mathy" topics more deeply that fall outside traditional math courses  physics, economics, computer science  can use math and apply it without being a typical math course. :nodding: Yes. Exactly. Sociology and psychology along with nontraditional literature and writing, in my DD's case. We've also had her "detour" on her math track because of how the precalc and calc courses are taught at her school (they aren't, basically... they're canned instruction and allassessments). That detour has involved tutoring lowerdivision math (prealgebra through geometry and occasionally algebra II), and taking physics, stats and econ to keep skills sharp. Finally, once we've run through those things, DD will be more than ready for college. In DD's case, she will begin college just after she turns 15, the summer after she graduates high school. I wasn't sure about the timing of it all until about a year ago, though. I was frankly kind of TERRIFIED about 2.5y back, but DD has matured a lot more over the past year than I anticipated at that point in time. We have not worried about credits here as Kaibab notes. My feeling is that if they aren't ready for a college environment, they probably aren't really ready to be racking up undergraduate credits on a transcript, either. A gap year is another idea let them run through secondary and graduate, but then use the gap year as independent study time.
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Have you read about the education of Terrance Tao? I ask because his parents found a very flexible path for him through an education system that was very (VERY) anti gifted ( elitism!!) and not flexible in this way at all.




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This is a great thread. I'm tired now. I'll write something later.




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Thanks everyone, lots of interesting thoughts there. A few responses:
 online courses: yes, it's great to be facing this now rather than a few decades ago. I'm not convinced that the Coursera etc. model is that great for maths, but at least it's an alternative to/supplement for books that gives greater choice.
 applications: yes, he's already doing some of this and will I'm sure do more.
 maths circles: yes, will watch out for such opportunities.
 talk to people at local university, check.
 boarding schools that go above and beyond; yes, there are some, and yes we're seriously considering them. The cost is a problem, and we're not sure whether sending DS away from two very mathy parents to get better maths at school makes sense; we'll see.
 credit: my only concern is, as I said, that university courses here are yearbased not creditbased. If you turned up as a first year student having already mastered half the material in the first year, but not the other half, that would be quite a hard problem for the university to deal with. There are humans in the process, though, so maybe I shouldn't worry about it too much. And of course one can skip lectures :)
 Terry Tao. Yes, I have read with great interest about his education. But do note that his mother gave up work to facilitate that solution. I can't do that and have him stay at his current school, and doing it and moving him into state education would be a backward step in all kinds of ways. Also, one article I read showed his timetable in one of those years, and he was actually getting a really weird mixture of whatever fitted  not a balanced education at all! Kudos to him, his parents and teachers for making it work for him, but it did have its downside.
Last edited by ColinsMum; 07/07/13 12:09 AM.
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I should have clarified my one point the thing that has made this work for DD is peer tutoring math(s). So I didn't mean tutoring FOR your mathy kid by BY him. This also can go a long way to improving social skills and confidence with older peers, too, which is ultimately a very good thing. DD has always had pretty darned good social skills, but they have definitely improved with tutoring. And she's found something that really lights her fire teaching.
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