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<p>Well, not even Caltech is that harsh; 750+ scores are considered equivalent. 2 mistakes will get you a 750. I think once you get past that threshold, you begin to either look sloppy or that you actually can’t figure out one of the problems. </p>
<p>If people are sloppy but can do high-level math, they need to concentrate more during the test rather than trying to convince everyone that they are one of the few people who can do math that can’t break 750.</p>
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<p>What about if I send extra research papers. Plus comments made by famous mathematicians about my research? Don’t you think they will contradict the SAT scores?</p>
<p>I once got 800 on a College board’s actual practice test from 1996. Dammit, I could not do it again on the real test.
Interestingly, the hardest ones were easy for me. For example, one of the questions was asking if there is a lower limit for some particular set. Only about 5% of the students got it right, unsurprisingly the questions was pure Dedekind cut problem. Of course some one could do the computation with out knowing the history behind it.</p>
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<p>The scores have been further diluted since then, with the dropping of quantitative comparisons, shift to more knowledge-based but less cognitively taxing questions, and a rise in number of sittings per student. In MIT’s applicant pool there has also been an increased representation of groups that have explicit or de facto preparation for the SAT math exam (Asians, math competition participants, talent search and summer science camp veterans, early calculus takers). All of this means that over time, higher and higher scores, or larger amounts of further data, are needed to convey the same IQ signal. A 750 SAT by itself, if it does in fact correspond to just two errors, may be in many cases equivalent to an 800 SAT, but the latter is a progressively shortened hurdle over time and this also weakens the value of 750+. An 800 is at least a less noisy signal.</p>
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<p>That’s not quite what they said, and it’s certainly not what can be inferred about what they do. See the more detailed discussion in the other thread. </p>
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<p>Very funny. You don’t happen to know of any acausal models that qualitatively match the data — ones where admission rate has a steepening nonlinear dependence on SAT percentile, and there is no such apparent sensitivity to observables other than SAT-like test scores (SAT-2, AP, ACT, math/physics/CS olympiads, chess ratings)? For example, MIT’s data, like that of other schools, shows a weaker or even a flat dependence on class rank once in the top 5-10 percent, or GPA above a certain threshold. This is not the case for test scores. What do you propose to call it except “causal for all intents and purposes”?</p>
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<p>The question was whether MIT’s minority (benefactor, etc) applicants or admits have scores that are as high as that of MIT applicants/admits outside those categories. Other schools are irrelevant, because Ivy League has substantially lower SAT distribution than MIT, and has more SAT-lowering preference categories than MIT, such as legacies and athletes and Early Decision. You can’t really draw conclusions from the fact that minority engineering majors at MIT have higher SAT scores than Asian art majors at Cornell, white poets and jocks at Brown, minority ethnic studies concentrators, and so on.</p>
<p>If you have a reference for MIT not favoring children of benefactors, I’m sure a lot of people would like to see it. Lack of legacy preference they are clear about. Female and minority preferences are a subject of waffling.</p>
<p>There has been much chat about 700-750 indicating problems. I think this range indicates quite a low level of preparation for the SAT II math, not the SAT I. In the case of the SAT I, anything upper 600s to lower 700s is acceptable, though ideally one does better. Like collegalum suggests, it’s a matter of focus at that point.</p>
<p>But I think it’s best to look at the AP level coursework, perhaps normalized against how the school does on AP exams.</p>
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<p>I don’t have the reference you’re looking for, but I’ve seen MIT admissions people make this clear before that children of benefactors don’t get preference. I’m quite sure about it. I suspect that it also might be in Dan Golden’s “The Price of Admission” as MIT was originally the model for meritocratic admission before he found Caltech was even better. </p>
<p>Mollie seems to have references handy for stuff like this; maybe she will read this and provide one for it.</p>
<p>Griffiths and Apostol for high school students? Are you serious? I remember learning physics and calculus for the first time in high school, and if Griffiths and Apostol had been the required texts, I would have immediately lost all confidence in my abilities. </p>
<p>Griffiths requires multivariable calculus, which virtually no high schooler knows, even the most perspicacious ones. </p>
<p>Apostol throws calculus and mathematical analysis at you at once. Calculus by itself is very different from all forms of math taught before it, which makes it difficult to understand at first. Mathematical analysis is even more different still. Trying to teach both at once is just going to produce a lot of frustration. </p>
<p>Those two texts are still pretty intimidating even for advanced undergraduates. When someone suggests them for high schoolers, I have to wonder if a).they are exaggerating how good they were as high school students or b).they are the next Terence Tao.</p>
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94% of the kids who applied were in the top 5% of their class. Once you are in the top 5%, your actual class rank depends on a ton of factors, most of which are completely out of your control. I have trouble believing anyone ever plotted GPA vs admit rate, since GPA is a virtually meaningless number without context. I can’t find the data for class rank vs admit rate either, actually (beyond the rate for the top 5% as a group). Could you post a link?</p>
<p>Cavilier, admittedly I don’t know how much multivariable calculus is in Griffiths 
- if it’s too much, then it doesn’t have to be used, but otherwise, since at least solid calculus foundation is a prerequisite to AP, I see no reason why the necessary background cannot be introduced within AP Physics itself. This might in fact be one of the best ways to see the material first.</p>
<p>But take away our larger point here – AP Physics C claims to be a college equivalent, when it’s 45 minutes of multiple choice and 45 of free response per each of the topics. A huge part of college calculus is getting used to serious mathematical notation and incorporating it into arguments.</p>
<p>What I believe is that high schoolers needn’t be exposed to Purcell’s E&M book at an early age, but if they’re going to say they really got a college level exposure, they’d better really be doing it. In the basic college physics, often you’re required to either concurrently enroll multivariable or have taken it. It’s a little unrealistic to do physics without some tools at hand.</p>
<p>And using Apostol as a reference doesn’t mean expecting high schoolers to produce full theoretical proofs using advanced terminology. But making them accountable to understanding what’s going on is important, and that does have to include some theory. They definitely teach that stuff in a first year college course too. Some proofs and knowing the theory behind the classic, most important theorems is healthier than not if we’re going to teach a real class here…</p>
<p>The initial purpose of the APs was to give a true exposure to college level material, and when people passing the BC exam with a 5 can barely handle or remember any of the material past AB, there’s something seriously wrong. And I know plenty of such cases. Mark my words, these are people who just came fresh out of high school having passed BC in senior year, having not taken BC but an AB course, and still having gamed the AP exam. What a joke. And how misleading to call this a college course.</p>
<p>I’m also willing to bet quite a lot that none of us is or claims to be anywhere near Terence Tao :D, in particular, I don’t have any Fields Medal worthy ideas to publish in the next few years, sorry to disappoint…</p>
<p>To Cavalier:</p>
<p>I self-studied multivariate while doing Griffiths during summer Junior year. I have to say, it was tough at the beginning, but definitely worth it. Maybe Griffiths might be a little too mathy. But my point is AP Physics need some serious buffing up, maybe not to Griffiths/ Kleppner Level, but at least to what they claim as COLLEGE level. I know plenty of students who aced AP physics C by studying SOLELY from princeton review, and ended up screwed in college because they never really learnt the fundamentals of physics the right way.</p>
<p>I think Apostol spends a great deal of time trying to explain everything clearly. I’ve known several people who learnt calculus exclusively from Apostol or a foreign equivalent, and they all felt they have a solid understanding of the fundamentals, and are ready to tackle college level analysis (which used to be the standard 1st year math major class in other countries). Finally, people signing up for AP’s should be fairly serious about the subject. If you are serious about math, you probably can learn Calculus from Apostol if it is taught as a slow enough pace (cover vol. I in 1 yr for example).</p>
<p>Personally, I think Halliday-Resnick is a good first book for calc-based physics, and I would consider it college level.</p>
<p>I think the calc books are fine in general as well. </p>
<p>I remember the AP calc test was super easy, but it was an eternity ago for me so I don’t really remember what was on it. </p>
<p>The SATII’s were way too easy. For instance, the SATII in chem in particular should be more like the AP chem test.</p>
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<p>Quoted for emphasis. APs have become something that everyone signs up for. This is a fatal flaw – not everyone is realistically interested enough to tackle college level material in high school, they just pretend it so they can put it on their resume, and schools like MIT obviously don’t care about silly resume padding, rightfully so. </p>
<p>APs should be something the truly interested ones sign up for. Same goes for honors courses. This is the essence of what I think is an indisputable point.</p>
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<p>I think this is true, although I am a serious opponent of the crowd thinking the theorems of calculus should be presented without proof. You can do a lot with simple arguments, and I think people vastly underdo what they can without introducing undue abstraction. It’s pathetic that people exit calculus without knowing how to precisely state what the limit of a function is – when you’re pretending to learn a subject, you might as well do at least the basics right. Or not say you learned it :D</p>
<p>Further, I think the material in Halliday/Resnick requires someone to have really mastered calculus well and also a good teacher to explain the subtle vector calculus thrown in, so that people are aware. This is a good way of introducing students gently to the real stuff, but making no mistake that there’s some mathematical notation going on that they probably didn’t entirely see in their basic calculus courses.</p>
<p>The AP exam is not only super easy, it’s scored super easily. Passing AP Calculus BC with a 5 should seriously be at the level of getting an A in a final exam at a solid calculus course in college. It absolutely is not.</p>
<p>My problem with SATII’s in general is not that they are not difficult, but they are difficult for the WRONG reasons: SAT chem makes you do 85 easy questions in 1 hr. Basically, it tests your reading speed more than anything else. I would much rather have 25 more difficult questions in 1 hr. Same with PHysics. 20 questions in 1 hr is much nicer than 80 questions/hr (not sure if my memory’s right on that one).</p>
<p>AP Calc test was OK, but it tests computational skills more than actual Calculus. I would call it an “applied Calculus” test.</p>
<p>When we see an increase in AP enrollment and sign up’s, we should not attribute it totally to an improving educational system. Rather, we should question whether the tests are rigorous enough. BTW, the Old Halliday Resnick is mucho, mucho better than the new Halliday-walker-resnick. I have the impression to make things more “approachable”, the books end up having a high emphasis on applications and nice pictures as well as trivial problems with 2 gazillion sig figs answers rather than the physics itself.</p>
<p>^^ I actually think the calculus AP Exam does a bad job even at testing applied calculus. While the calculus in Halliday/Resnick and the calculus in an actual calculus textbook actually make you think and draw some diagrams to internalize what’s going on, which is good.</p>
<p>I think my qualm is less with the books and more with the way courses are run, and on a related note, where national standards are.</p>
<p>I also have the same criticism of the SAT IIs. Time pressure, and turning science multiple choice. Sad stuff.</p>
<p>I really envy you guys who have the intelligence/mental discipline to self-study Griffiths and Apostol straight up, especially Apostol. Whenever I try, I cry and scream after only a few minutes.</p>
<p>I like Physics by Halliday, Resnick, and KRANE, not Fundamentals of Physics by Halliday, Resnick and Walker. Krane’s physics I think is at an AP appropriate level. It’s accessible, but just as rigorous as a first year physics class at an average university.</p>
<p>Just a few things - </p>
<p>First, CollegeBoard does comparison testing a lot to make sure that the curves for AP tests correspond to similar level classes elsewhere. So like, they give a version of the AP test to college students who had just taken the class and compare their grades in the class to the score they got on this test, and then use this to determine if their curve matches up correctly. No, they don’t compare to people at MIT who take 8.012/8.022. And if I remember right, the cut-off for a 5 on AP Physics C Mechanics was actually too high.</p>
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<p>Uhh, maybe this has to do with the fact that they were planning on taking college level analysis anyways? Like, I don’t believe that it is reasonable to expect everyone to learn calculus from Apostle. Even in colleges, people drop classes that use Apostol as a text all the time.</p>
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<p>If someone has taken Pre-Calculus their senior year, and they want to continue on in math and they have mastered the material, they will probably go on to take Calculus. It probably will not be at a level of Apostol. If someone takes Pre-Calculus their junior year, they should want to continue similarly, without having to go into all that theory.</p>
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<p>I’m not sure MIT has posted numbers based on GPA rather than class rank and some comments on the admission rate of valedictorians. Princeton posts tables based on unweighted GPA (or whatever they deem to be your GPA on a 4.0 scale), showing that to reach the overall admission rate of 10.1% for all applicants, one has to get above 3.9, and if you get as high as 4.0 the rate of admission is 16.9%. These are small and flat effects compared to what is seen for SAT in either Princeton’s data or MIT’s. For example, for the MIT class of 2002, the Tech reported: “[Marilee] Jones pointed out that of the 491 students who scored a 1600 on the SAT worldwide, 185 applied to MIT and 127 were admitted”, which means 69 percent admission for those who mastered the easier, recentered SAT. I don’t know of any grade category where people would get into MIT at such rates, even ten years ago, other than ranking #1 in one of a handful of the most competitive high schools in the country. Two years later there was the steeply increasing graph of MIT admission rate by SAT percentile, published in the Revealed Preferences ranking paper (search SSRN).</p>
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<p>I was waiting for someone to mention something like this. I think what faraday, myself and others get at is not that we need things to be at the level of honors level courses at MIT and Caltech. </p>
<p>The problem can be clearly stated, independent of difficulty scale, that when one is covering material, it should be made precise what is being covered. If calculus is being taught, students shouldn’t exit without knowing why things are true, or without at least a serious attempt at understanding these things. Subsequently in college, the abstraction and sophistication level is taken far beyond. </p>
<p>I have a strong feeling that I heard from someone the calculus used to be taught in a much more thorough fashion in the earlier days, and modern courses have watered it down so it can be done earlier. Let’s not belittle calculus and call it utterly bassic – it’s serious stuff by itself and should be respected, and taught properly. I don’t know Apostol’s specifics, but honestly I think a lot of reasonable things can be done with calculus material without expecting crazy abstraction, which aren’t being done. Ditto for physics and all the integrals you take – it’s good to actually define the mathematics behind what you’re doing. That in and of itself makes things not a joke. Further, the serious problems should all be attempted.</p>
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<p>Basic calculus at my university is not Apostol level, but I know people who took the BC exam without anything but a frivolous AB course and got 5’s after prepping the additional material from a prepbook…and then found calculus at my school quite hard, i.e. the material they should have seen in BC. I think it’s a lie to say they had a college level exposure.</p>
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I don’t have a link, sorry, although perhaps Chris will chime in.</p>
<p>On a back-of-the-envelope level, it’s certainly true that MIT’s student body is more working-class than its peer schools, so that would suggest there are fewer parents capable of, e.g., donating a building. :)</p>