Gifted Issues Discussion homepage Forums Learning Environments Finishing school maths when not ready for college

I came across the following, which makes me pessimistic. This guy was twice a USAMO winner, meaning he was in the top 12 meaning he could compete to get into the USA IMO team, but he didn't make the final 6. He was rejected from both Princeton and Harvard. (He was accepted by MIT.)
http://blog.tanyakhovanova.com/?p=150
http://www.maa.org/news/051209usamo.html
It's not clear why, but it's clear the selecting is not being done by the mathematicians, but instead by bureaucrats (admissions officers).

There's a financial issue here. Places like Princeton and Harvard (supposedly) select on merit, but charge fees based on financial means, as determined by the FAFSA formula. So a family earning say $75k/yr would pay $10k/yr instead of the sticker price of $60k/yr paid by people earning >$200k/yr. MIT (like most private and public universities) doesn't do this, so it is much more expensive.

Paradoxically the financially feasible options for us are Princeton/Harvard type places that "meet full financial need" or else the local state university (or delayed retirement). This forces us to set our sights that high, even though we really don't know that that's realistic.

I haven't checked out the situation with getting the appropriate credits for high school, but definitely will. And I am concerned that the school may be somewhat mediocre apart from the ability to accelerate.

But you have made the crucial point, that once you reach the high school courses you are locked into the standard pace. [For those who are unfamilar with Virtual Schools, the two main curriculum providers being Connections Academy and k12.com, the grade K-8 courses are much like home schooling, and you can accelerate through these courses, but in the grade 9-12 courses have scheduled compulsory teacher-led live online classes, and you must therefore move in lockstep with the rest of the class.] We were aware of this, and that is why we are having our son move quickly through the K-8 Math courses, because that's the only chance to accelerate (and they're really easy). Once he gets to the sequence Alg I, Geom, Alg II, Trig/Precalc, Calculus, he has to take the full year for each course, so he'll do them in grades 3-6. (Geometry and Algebra II can be done simultaneously, which is how these 5 courses can be done in 4 years, despite having to take the standard full year on each.)

You're lucky to have those courses in your district. Our school stops at Calculus (and it has Statistics, but not Differential Equations, Linear Algebra, or anything else). So our son was going to run out of courses no matter what, and we'd be having to find things elsewhere anyway, so there was no point holding back.

I agree with developing an interedisciplinary base, though I'm not sure how to do it.

I stand corrected. At least I hope I do because that's good news. I can't find where I thought I saw that MIT didn't meet full need. Actually the links you gave make it look like you'd pay EFC+$6k. Is that right?

I saw this, but in the past I've seen other things that I couldn't find again just now.
http://www.usnews.com/education/bes...s-that-claim-to-meet-full-financial-need
The big thing to watch out for is when they say they're giving you $X when they're actually loaning you $X.

You could have him progress through theoretical physics and learn and practice the needed math along the way. For example in electricity and magnetism taught at the level of Jackson, one learns about solving partial differential equations and special functions. Quantum mechanics uses that math and also linear algebra, and there are applications of group theory. Computational physics requires numerical analysis and programming skills.

Some philistines believe that applicability is what makes a branch of mathematics important or unimportant, so that following a math curriculum for physicists, engineers, economists etc. is a way of determining what to study.

22B, it's just me, probably...

but with a child who is just now, what-- six? seven?

I wouldn't be too concerned with choosing a college just yet. Two reasons for that.


1. You really don't know-- yet-- what that track of mathematics to calculus will look like. My DD seemed to be on that same track when she was 5-7yo. We figured that she might well be finished with calculus by 12yo. This was based on what I know now to be a pair of false assumptions on our part-- a) that pre-algebra on would involve the SAME level of cognitive demand and reviewing of material (it doesn't), and b) that she would continue to sail once she encountered genuine challenge in mathematics (she hasn't-- and the perfectionism set up in K-5 mathematics is partly WHY she hasn't, because she tends to regard being challenged as a sign that there is a problem, and that it is probably with HER). All of that to say that the child you have before you is VERY different from the one that you'll have at 14. We try to keep OPTIONS open, that's all. DD is reasonably well positioned to apply to Harvard or another Ivy, but doesn't want to.

2. You can't even BEGIN to predict what higher ed will be in ten years, what it will cost (not really, because things are probably reaching some tipping point), or for that matter what a "typical" or even "elite" path is going to look like. You also may not be able to predict what your own state will be demanding for a high school diploma, if it's anything like ours. The one thing to be cautious about is that you have enough math for FOUR YEARS of it to appear on a high school transcript somehow.
But-- as noted, I would not be concerned with this until your child is through with pre-algebra and maybe algebra I.


The other thing that I'm going to offer (both as another v-school parent and also as a STEM educator) is that this model is VERY poor in some respects, and high-school level STEM is at the very top of my list. The actual didactic instruction at the high school level is very much less than in a college setting, even-- and this is flatly not appropriate for most learners of any LOG. Basically, this means that your child may be in a position of learning calculus exclusively from whatever textbook is supplied (if there is one-- truly not kidding about that, btw), and from YouTube videos.

The biggest hurdle you may face in gaining admission to an elite (or any particular) college is in convincing the institution that the lab coursework taken in a "virtual" school is authentic enough to "count" as a prerequisite. Mostly, it's not, in my personal opinion.

But at any rate, all of that is a long way off. It's good to be thinking about things in a general way, but I've learned over the years not to plan more than a year or so into the future. I could not have really predicted my DD's current situation with math when she was 7yo.

I am new here and am thrilled to see this thread! My ds8 is exceptionally strong on the math front and we, too, have been trying to figure out what to do about math once instruction at his school runs out. Fortunately, they are keeping him moving several grades above where he formally is in school (2nd grade). Funny--the principal said to us with worry: "Eventually we will run out of instruction for him." We were just happy that they can keep things going! We told her that we understand completely that we will need to take responsibility (or a large part of it, anyway) for his math education well before the end of middle school (which is when his current school ends). So anyway, it is great to see all of these options laid out!

A couple of very informal ways that we've been "enriching" his math education so far:

1. Discussions with my business savvy brother, who helped my son "make up" a company, figure out stock prices, rates of return, etc.

2. Discussions of probability as offshoots of card and dice-based games.

22B--FWIW from my very anecdotal sense of what's happening with college admissions (based mostly on talented kids of friends): It does seem as if the top-notch universities care a great deal about well roundedness and also are attuned to "padding" with extracurricular activities rather than pursuing extracurricular activities due to true interest. As others have said, your child could change a lot in the next 10 years! Don't know if this rings true to you, but our philosophy has been to keep our DS interested and learning (and interested in learning)--and we assume that things will work out. Maybe that is delusional...

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.

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.

I got an email today saying they've revamped Alcumus, actually, and haven't looked at it - DS goes in phases with it and hasn't been doing it just lately. So this is all based on how it was a few months ago.

They have prealgebra in it now; that's a fairly recent addition. Your DS would probably enjoy it now, I guess. I recommend it. Lots of interesting and competition problems, mixes up what it offers. At your DS's age, mine needed an adult to encourage/scaffold a bit, especially because (with the default settings, anyway) it will give you some easy problems and then throw in one that's really quite challenging. You can give up, but DS was never willing to! OTOH they didn't have prealgebra then, so that should help. Give it a go. You have to fax a form for under-13s, but they dealt with it very promptly.

We are a two-Arfken household, but all the same.... argh!

(Mind you, it would be cool if someone in the household actually read all of the three volumes of Feynman's lectures on physics we have lying around, I have to say. So yes, maybe.)