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Joined: Feb 2013
Posts: 1,228
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By the way, does anyone know what it takes to get into maths at an elite institution? Is it based purely on merit? Or do you, as some have suggested on this forum, have to fluff your CV with extracurricular activities like volunteering at the homeless cat shelter and playing polo? It will surely depend on which elite institution, but I can say for sure that neither Oxford nor Cambridge could care less about anything but academic merit, because they're both on record saying this clearly. I sort of doubt that someone who had IMO medals and/or papers in reputable journals to their name, and didn't have two heads, would in practice get turned down even at US elite institutions  but it would be good to hear from someone who knows. 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=150http://www.maa.org/news/051209usamo.htmlIt'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.




Joined: Feb 2013
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Oh and the other thing to watch for since we're using that same virtual schooling model? Make sure that he can continue to work at his own pace in secondary. That's a huge catch with Connections. They can't; they MUST work synchronously and in order once they reach secondary math. Also make sure that if you're going to venture outside that system for enrichment/alternatives, that you've satisfied the requirements for graduation and have the requisite coursework listed on a high school transcript somehow. This may mean that your DS has to take "high school" geometry when he's 9 which also means that any ageappropriate flakiness has lasting consequences. If they tell you that you can use local university credits to substitute for AP Calculus get it in WRITING. We've found that national is surprisingly (or not, perhaps) stubborn about "you should take OUR class... we offer Calculus/Chemistry/Econ/Psychology" Yeah, but your version is a canned JOKE... and I want my DD's first experience with this subject to be, you know... authentic. "We offer that class." Just noting that. BTDT. My DD has had to take some really worthless electives. 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 K8 courses are much like home schooling, and you can accelerate through these courses, but in the grade 912 courses have scheduled compulsory teacherled 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 K8 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 36. (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.)




Joined: Feb 2013
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I don't have quite the same issue but I have looked ahead and made decisions based on the distant future. I have less of a problem because DS is not a math prodigy and is also equally strong verbally. We chose to wait to do Algebra next year (5th grade) even though DS appeared ready by every measure. This way he won't start PreCalcuus until 8th grade, which will leave him enough math in high school  Calculus, Differential Equations, Linear Algebra and Statistics (current offerings in our district). There is also a lot of math horizontally. DS has picked up odds and ends by reading interesting math books (not textbooks). DS has expressed some interest in business math and econometrics. My thought is to help him develop an interedisciplinary base, which is actually more beneficial in the long run. Of couse, he won't be ready for something like econometrics until he has mastered Calculus and Statistics. He will also likely do some competition math. 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.




Joined: Feb 2013
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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. http://mitadmissions.org/afford/basicshttp://web.mit.edu/sfs/financial_aid/MIT is very, very generous with financial aid. From what I've heard, they will make it work for each student they admit. 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...sthatclaimtomeetfullfinancialneedThe big thing to watch out for is when they say they're giving you $X when they're actually loaning you $X.




Joined: Feb 2010
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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. 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.




Joined: Feb 2011
Posts: 5,181
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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 57yo. 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 prealgebra 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 K5 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 prealgebra and maybe algebra I.
The other thing that I'm going to offer (both as another vschool parent and also as a STEM educator) is that this model is VERY poor in some respects, and highschool 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.
Schrödinger's cat walks into a bar. And doesn't.




Joined: May 2013
Posts: 26
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Posts: 26 
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). Funnythe 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 dicebased games.
22BFWIW 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 topnotch 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...




Joined: Sep 2008
Posts: 1,898
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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, lessmathy 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 overthinker, but I think (despite having started this thread with my overthinker 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 K12 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 3year fullyspecialised undergraduate degrees typically started at 18, Scotland has 4year 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.
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Joined: Sep 2008
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What level does Alcumus start at, and what is that like? 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 under13s, but they dealt with it very promptly.
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Joined: Sep 2008
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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. 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.)
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