Stanford and Private School Admissions - A Mystery

Colleges and Universities A-Z Stanford University
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<p>Ramaswami, I am glad that the Stephen Hawkings of the world will go recognized, and your point seems to be that either you're one of these or you ought to be good in other regards than pure academics. I.e. the average IIT student is of the profile of not being a complete outright genius and not necessarily having the qualities that Ivies correlate with holistic success outside of just being good students. </p>

<p>One question. How do you measure the success of an academic student in the university? To my experience, generally a successful student who'll do wonders for the intellectual world is neither Stephen Hawking nor an average engineer. It's merely someone who takes the most rigorous path available in his/her college major, does great research, aces the courses, shows potential as a researcher, and goes on to (hopefully a top notch) grad school - and note, it's probably an insane deal harder to get into say Harvard for its top grad programs than it is its undergrad ones. College isn't a place to just BE a Stephen Hawking. It's a place where some top caliber people will really develop their skills and figure out where they're headed. </p>

<p>So one comment I have is that maybe students with great math and physics skills, for instance, perhaps ought be allowed into some of the top schools, WITHOUT having aced Olympiads or known in senior year of high school that they want to win fields medals. See, a lot of these may not just be generic IIT engineers who ace tests. A bunch may just be exceptionally bright math and physics students who may decide IN college that they want to go to top grad schools in so and so area, and take advantage of the exceptional faculty. </p>

<p>What I'm saying is, there seems to be in my experience a middle ground. Now I'm not claiming I know where they end up - do these guys end up at schools like Ivies ANYWAY (without having other personal qualities or athletic ability or being future Stephen Hawkings)?</p>

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<p>mathboy, good points. In college, how do we measure academic success? The usual route, GPA in declared interest/major, research, etc. The method to recognize the student who is not Hawking in high school but has not yet won Olympiads or caught the attention of teachers who say wow: the question then, how do we know this is a phenomenally bright kid who will blossom in college? We don't. I guess the Ivies will pour over their apps, the advantages or disadvantages they have had, try to decipher potential but if these kids have not taken APs, (not available in school, let us say) do not go to Olympiads, (no mentors, say), do not pester teachers for opportunities, why should they be given a break for college admission over someone who has done some or all of these?</p>

<p>In the end, there is some subjectivity to the process. One can extend your argument and say, why don't elite colleges admit late bloomers? Because they are late bloomers they were not seen in bloom when college admissions time came around.</p>

<p>So, some of these kids will go to other colleges and keep developing their potential in other ways. After all, great scientists come from all sorts of colleges.</p>

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<p>hipster, I don't know much about the SAT writing beyond what I have read. Seems formulaic, seems length gives an advantage, etc. I think its potential is in correlating it with the application essays and catching fraud. Students ought to be asked to send in a graded essay from high school.</p>

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<p>Ramaswami, I see we're at a point where I don't think I any longer disagree with your fundamental point, though in my heart of hearts I'd like things to be different. I think I see what the main problem is, and it might be impossible to fix -- we kind of have to make a choice how many of "my kinds" of students to allow in, and how many not to. Frequently, students who're equipped with incredible firepower to excel in top schools like MIT may be turned down, go somewhere else, do superb things, and then end up at top grad schools after taking their first college courses and being excited by them, and I guess this is why top grad students come from diverse backgrounds, not just from the same old places. I know a 19 year old Berkeley grad student who went to UOP as an undergrad, kind of prodigiously ahead in math. I also know (maybe not all personally, but some even from class) grad students from MIT, Princeton, Duke, Berkeley itself, Stanford, and I'm sure Ivies...but also a bunch from some less known schools. They're definitely on average academically sharper by a long shot than an absolute vast majority of Ivy Leaguers and others, as heck, they made it to superselective Ph.D. programs. And would've shone if we'd implemented my "higher curriculum."</p>

<p>I just wish these people could all have the luxury of top faculty at their disposal as undergrads. It seems like it's just a matter of choice - to let them in, or to let other kinds of exceling students in. I am obviously biased towards the academic ones. </p>

<p>I'd still like a better designed curriculum for purposes of exciting students early in high school about their subjects, but I see adding it wouldn't alter the Ivies' fundamental motive. There's something good about the Ivy system, but I see something good about my own in a sense (which is far from an IIT sort of system) - mine just leans a little bit on the "conservative" end, which is to say favors standard academics more, than the current one.</p>

<p>Though, I think we can both agree that given resources, something very great would be achieved if a higher curriculum were made an option. I'm sure you're aware that at many universities, they have a few levels of the same math courses - often a standard and an honors. Maybe if there were a higher version of the current AP, for students who're into so and so subjects, but aren't yet obsessed, it'd SPARK that obsession earlier, and these guys would go on to do more with their new sparks. I think a lot of good would be achieved of my proposal, given feasibility, and exclusive of bashing the current system.</p>

<p>My major problem now is that as you say, LOTS of students don't show the spark early given our current measures, and a "super AP curriculum" addition (maybe even independent of the current one) which better reflects college rigor might actually discover or even catalyze the spark earlier. For instance, a large number of math students really get excited and KNOW they want to go forward with math only after they get a good taste of purer, more theoretical math, which nobody but this tiny minority (like me -- who went much ahead with math in high school after calculus) really does taste. </p>

<p>However, whether there will be space in the top schools for all these students, who knows. </p>

<p>Oh and as a note -- please read this long post carefully! Because in it, I actually haven't disagreed with anything, only made constructive remarks. And have acknowledged why things may have to remain how they are.</p>

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<p>"So, some of these kids will go to other colleges and keep developing their potential in other ways. After all, great scientists come from all sorts of colleges."</p>

<p>In short, I wish with greater consistency, these guys' sparks would be identified early and also that schools with top academic faculty had space for them. But I may be too demanding.</p>

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<p>mathboy, then there will be those who will be identified early but fizzle out. Personal experience can be very misleading, small biased sample and all that but here I go anyway. I know of two south Asian kids who supposedly excelled in math (Johns Hopkins advanced courses, summer school, acceleration, the whole nine yards) went to college and abandoned math altogether, one said that doing math was his way of earning parental approval which in turn was mistaken by IIT engineer father for math precociousness, etc. And then we know of those who specialized too early and regretted it.</p>

<p>The Ivy method leaves room for the true prodigy who will show his talents early and allow the rest to bloom in their own time, allows a fuller development of the person and more forgiving of early dead ends, so to speak.</p>

<p>Regarding your higher curriculum, it already exists. Anyone can take AP exams, you don't need to take the classes, and your kind of sharp student can excel in the two math APs and the 3 or 4 science ones plus do advanced work directed by HS teacher. In other words, there is the higher curriculum, such students take classes at nearby colleges, etc. It does not make sense to institute a higher curriculum when the vast majority of high school kids cannot handle even regular non- AP classes, and those that take APs are a distinct minority and those that excel in the existing APs are minuscule. Curriculum development is hugely expensive, both costly and labor intensive and it would be foolish to do that for the sake of perhaps 3000 students in the country who have at their disposal, access to nearby community colleges and universities.</p>

<p>If a student turns out in freshman or sophomore year of a non Ivy college to be very gifted in math / science to the extent that everyone is in agreement that he/she should not have been turned down by the Ivy or MIT/Caltech (assuming he was turned down) then the next question to be asked, was this potential evident in high school, evident in the sense of objective records (since responders with current evidence of his college performance will in hindsight exaggerate his high school prodigy status)? If it was, was it presented to the Ivy? If so, and he was turned down, then a mistake has been made. I wager that not too many such mistakes are made.</p>

<p>It seems to me that more kids blossom in the second year of college than at any time in their scholastic history until that point and to argue based on that (you are not arguing in this vein) that they should have been admitted earlier will miss the fact that this potential was not so readily obvious when they first applied for college.</p>

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<p>Good points from you as well. Yeah I think the consensus we have reached is that it is on average very, very, very tough to predict how academic types will bloom in college, unless they were superstars to begin with (no telling how many will become superstars in college). </p>

<p>"It seems to me that more kids blossom in the second year of college than at any time"</p>

<p>HEAVILY HEAVILY agree with this. Because that's usually when students take a "real" class for their major, and figure out how into the stuff they really are. </p>

<p>I still, however, would say that the curricula at schools could be refined with a positive result in one definitive way as even an educator. That is, independent of college admissions altogether. IDEALISTICALLY! (So bear with me, and forget finances just for a second =]). </p>

<p>See, so we have for lower level courses in high school this distinction between honors and regular, right? Most students in America probably BARELY will touch an honors course. Even fewer will touch an AP course. Why offer AP courses at all? Well, we've decided some threshold of interest in them is being met, and students who can handle a taste of college work should have a chance to. In short, there is a pretty big difference, you and I both would agree, between someone who tries to take advantage of AP curricula and someone who refuses to. This is just a plain philosophical difference. What I'm saying is that I think there is a similar philosophical difference, however, between those who take calculus just because they take it, and those who really are into math. Difference, similarly, between those who just take AP Physics, and those who really are into physics. Difference between those who're into English, and those who just take AP English. I think a clear, clear difference existed in every one of these cases in high schools for me. </p>

<p>I'd say that given resources, an <em>option</em> of just one (not two or more) higher level that teaches calculus in a proof-based sense would be beautifully received by those who like math.</p>

<p>The point is that those who take courses past calculus, I think, are WAY smaller in number than those who take calculus. A grad student told me that he took these special "calculus for math majors" courses in college, and that's what sparked his interest in math! So you know, since AP Calculus is in my experience such a more widely taken course than, say the subsequent math courses are, having a more substantial version would do wonders to excite future math types (similar remarks for other fields). </p>

<p>The problem is there is NO course right now in high school, which would genuinely excite a math major in the making - no proofs or anything required in AP. Similar for physics, I think (though I speak with less certainty). Even if statistically most find these courses hard...statistically, most people know much, much less than calculus, and the threshold we've drawn as educators as to how far we're going to take curricula may be neglecting something.</p>

<p>BTW - I like the IB curriculum for math a lot more than AP. Received info about it from someone (other than a poster in this thread). I'd have favored taking it myself!!</p>

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<p>mathboy, some math professors would argue that a) simply introducing higher math courses in high school is not enough since high school teachers do not have the skills to teach these higher courses b) even if high school teachers teach courses titled XYZ they are really not the same as those taught in college, they are simply there to pander to those few kids who fancy they are tops c) that even if all these issues are ironed out kids are really COGNITIVELY ready for such courses until they are 18 or 19. Remember, the brain's capacity for abstraction really grows only in late teens and early adulthood d) the opportunities for those proof based classes are there: go take them at the nearest college and e) better to delay introducing them so that like the students at a Zen monastery the ability to handle delay itself is part of the training.</p>

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<p>Hmm. Interesting. As a disclaimer, again most of what I'll write now is more directed towards your opinion on education than on admissions. So, as I've said, I guess I did follow what you said, which is to say I went out and learned a bunch more math on my own, and had lots of exposure to proofs and such things by the time I went to college. </p>

<p>I guess I wonder -- at what point is math considered too abstract? Even calculus at the AP level requires likely more abstraction than the earlier subjects, and is considerably less of a plug and chug deal. What is the barrier? Because the line I'm drawing isn't an arbitrary one based on difficulty, it's based on thoroughness of coverage of the topics the AP is allegedly to cover - are we actually covering the material in more than a plug and chug fashion whenever we can without having to introduce more machinery. Are we explaining where everything comes from. </p>

<p>I guess the question is -- how do we know the AP isn't too hard itself? Why did we draw the line at this level, rather than at a more thorough one, when AP itself is meant to be something not every student can handle (however easy top students think it is)?</p>

<p>Also, as a note - technically I am not introducing a higher topics math course, I just want a thorough version of the one which exists. Not sure about other subjects as much, but this is purely out of my interest in the math education.</p>

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<p>Because, it strikes me that a thorough version of calculus is <em>considerably</em> less abstract than college math at higher levels (for instance, the first pass with analysis is the course which generalizes lots of calculus notions), and could provide exactly the healthy balance which a) will excite prospective math majors, and b) not force a level of abstraction which could have been handled much more productively at a slightly later age. (For those who can handle more abstraction, obviously doing extra math reading is an option, so we'll forget about them.)</p>

<p>Notice that in a sense, from the standpoint of completeness of education, NOBODY needs to offer a proof-based calculus course, not even colleges, but some do. Because students can just head to upper division math and get all the knowledge they ever needed to - learn more general versions of the results they could've done earlier. But, does this mean we do no theory whatsoever in the calculus courses?? Offering some can be a healthy first step, and also really excite students. </p>

<p>I mean, to me right now, the word "proof" is like...well, that's all I DO. I don't even think twice before writing. But I remember, the first time I learned, it was definitely a formative experience. When that experience comes can significantly change, I would guess, how excited someone is about math.</p>

<p>However, I remain curious what you have to say about when abstraction really is too much -- some qualitative answer is great.</p>

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<p>mathboy, with all respect I am lost, your posts are all over the place and I don't understand what you are trying to say.</p>

<p>We begin to develop abstract abilities around age 14, not all develop them, not all develop them to the fullest extent or at the same rate or to the same extent. Depending on the area of math, irrespective of course title, and depending on the nature of the teacher and the ability of the student that area may be abstract to a greater or lesser extent.</p>

<p>For most people, proof based math is best done later than earlier, and there is no precise point which is later or earlier. Newton was capable at age 16 but that won't apply to most others. I am no math expert nor am I an expert on education, with those caveats let me say that I am told that a few decades ago calculus was not even taught in high schools. That there has been a downward drift toward earlier and earlier teaching. Whether this is good or bad I don't know. </p>

<p>I have no objection to a stronger curriculum or a stronger math/sci national test. I don't believe the expense will justify the added benefit. And for the sake of fairness we must then have stronger English and stronger history curriculums, and stronger art and stronger whatever.</p>

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<p>OK, I think I get what mathboy is saying.</p>

<p>AP self-proclaim itself to be "college-level" and yet the level taught in the math and sciences are just ridiculous: nothing more than plug-and-chug on the AP exam.</p>

<p>What mathboy (and I) probably demand for is that AP level actually becomes what it is professed to be, not just a hypocrytical system that boosts people egos. Many people will take AP courses, and repeat that equivalent course in college, and even get a lower grade on the course they repeated. What I, and mathboy want, is that AP level becomes what it is professed to be.</p>

<p>Example 1: Calculus is not just a system of rules to compute derivatives and integrals. There are Delta-epsilon proofs, ideas about continuity, Real number system (define What's a real number), what does it mean to diverge? Converge? Tend? Can series of functions "approach" a certain function? (OK, this may be more Real analysis)</p>

<p>THose ideas are not what I call "abstract." They are necessary components of doing mathematics, and require what I would call rigorous and sharp thinking, not abstraction. And they can be taught in high school, if proofs become the way we live, breathe and do math. Which is what I would envision a real college level class to be.</p>

<p>Example 2: Physics.</p>

<p>Introduce the idea of vector rigorously. You don't "multiply force by whatever" (common misnomer at the high school and current AP level). You can "dot" or "cross" a vector with a vector.</p>

<p>Introduce the idea of vector field, of vector operations, noninertial frames (Newton's laws don't work everywhere do they?? :D) etc.. All those terminology issues are not what I would call abstraction but more of precision and *rigorosity<a href="not%20sure%20if%20grammatically%20correct">/I</a>.</p>

<p>As it is currently taught, most physics teacher are simply teaching wrong material. If your physics teacher uses correct vector notation and operators, then you are very lucky and rare. If you want a more precise idea of what I mean by correct terminology, you are more than welcome to visit MIT's opencourseware website and watch Walter Lewin's 8.01/8.02 lectures on physics. That's where I discovered the discrepancy between the fluffy high school AP and college level.</p>

<p>Now there are 2 reasons why AP don't/can't teach those stuff often:</p>

<ol>
<li><p>Because the AP exam is easy and does not require precise reasoning. Most physics problems are special cases where our "fluffy" uses of scalar operations instead of vectors are correct.</p></li>
<li><p>Because teachers are not able to teach those things. Well, I expect an AP teacher to at least have 1-2 yr worth of college level knowledge in their subjects. If they don't know their vector operations, then they probably shouldn't teach AP.</p></li>
</ol>

<p>PS: If US high school students aren't able to handle such material, then AP exams and courses shouldn't be called college level to boosts people's egos. And secondly, if 16-17 yr old brains are not wired to take "abstract" (I don't like that word) math/science, then we are not supposed to take "AP" level classes. AP should be for those that are ready to take them. Otherwise, it should not be called "college-level"</p>

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<p>Proofs in math are the equivalent of essays in english. How can you even think about learning math without doing proofs? And they certainly do not require "abstract" knowledge. They require precise terminology, some logic and sometimes (not always) creativity. I don't even believe it is necessary to teach calculus to teach proofs. We can introduce the importance of proofs to middle-school people with geometry, algebra and other elementary topics, something that is lacking in the current system. </p>

<p>Here is a comparison. I have a taiwanese friend and her math exam (not college-level, not AP) was basically 6 proofs questions. She is not a in a college-prep math intensive course or anything like that.</p>

<p>Our exam is a bunch of plug and chug problems, with numerical answers.</p>

<p>Ramaswani, I have a question to you, who seem to be so knowledgeable about admission officers. Are AP scores more important academic factors and SAT's and SAT subject tests? If so, then my fears about academic frivolity of college admissions are greatly alleviated.</p>

<p>PS: apologies to ramaswami for what I said. That does not mean, however, that I believe in using SAT's to weed down the numbers and to use as an academic gauge of people's abilities.</p>

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<p>Yeah I apologize if my post was a bit tough to follow, but faraday clarifies it exactly. The idea is that no matter how hard the AP is or isn't for the average student, and no matter how few students can do well in the AP, I believe pedagogically it's unsound to give a foundation in math the way it's done. Similar in physics, as faraday states, though I'll say I'm not quite as good a judge on that material. </p>

<p>Proofs are, as he states, just a way of expressing things clearly, and calculus taught rigorously is actually not more abstract, just more thorough. While students can take our shallow AP and head to higher math and wait to get excited about it then, I think it's a GREAT refinement to the system to teach it appropriately now. Think about it - if you actually explain calculus thoroughly, it even seems like a student exiting the class would feel more sort of "at peace." There's something disconcerting about just exiting a class having had unstable foundations to tread on, and sort of communicating based on guesswork. </p>

<p>Abstraction gets introduced more later in college, I think. </p>

<p>As you say, we already have a fairly good means of giving students exposure to college level stuff, the AP. Now, by not making a "super test" but just teaching it in a sound way, I think I'll be much happier looking at someone who did well in calculus and say - hey good chance he/she will be happy doing some more math. Wherever the given student ends up. </p>

<p>The AP's have it right in principle, but the way they're written, they do not force rigorous thinking. A few other little improvements - making the AP Physics tests <em>standard</em> length, not half the length for mechanics and half for the electricity/magnetism.</p>

<p>In short, I am not proposing that we make EVERYONE take one level of math earlier, just teach what we do teach in a thorough way. I feel very confident it won't break the backs of the AP-ers, but will make them less complacent but even perhaps happier with their AP education. </p>

<p>Also, again I'd favor the IB system over the AP for math. They seem to offer a great track for students to learn useful skills - the AP kind of ends the fun too soon.</p>

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<p>Name of the game - rigor and clarity, not abstraction, which I agree the vast majority are most ready for later in the game. =]</p>

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<p>"There's something disconcerting about just exiting a class having had unstable foundations to tread on, and sort of communicating based on guesswork"</p>

<p>It is more disconcerting when "top" students actually become complacent because they aced a gazillion AP's. Many of them will enter college assuming they got the key to what physics/math is about, when they have no clue at all. And the reason for such ignorance is the shallow education system. I know many people who boast they can compute X,Y,Z integral, or mechanically (the best word I found to describe it) compute the magnitude of whatever force, and using those tools scored 5's on their AP's thinking they knew what calculus and physics was. Many of them don't even realize the vector nature of angular momentum, or what a dot product is, but the AP fooled them into thinking they are well prepared for college.</p>

<p>There are two consequences of the frivolous system currently used:
1. It boosts people's egos to a dangerous level, and thus that ego will lead to disappointment in college.
2. For more informed persons who know about their ignorance, it gives a certain feeling of inadequacy.</p>

<p>I judge myself to be in situation 2. I definitely feel I've been cheated out of an education by believing the AP bluff of our math/science teachers, and the AP exams I aced. Trust me, I was quick to get college science/math books to supplement my knowledge, realizing how much I would become unprepared for college had I been complacent. Then, I realized how much of the beauty of science I had missed out, how much there was yet to learn, how long I rehashed AP stuff, which obscured and concealed the beauty of the physical world.</p>

<p>Let me give an example of case 1 highlighted above. In High school, how many people think they are good at math? At my school, at least 20-30% think they are good at math and physics, and pretty much ace those classes. How many of those end up majoring in math/physics? very few. That tells us a certain discrepancy between the professed AP-college-level curriculum and what math and physics is about. That ego-inflation seems to be deflated too late, namely in college. I believe high school should be more than an ego-inflator.</p>

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<p>Funny thing is...I never cleaned up a bunch of my knowledge officially. I sort of ended up reading a bunch of math on my own, and realized "OH, I could've done so and so physics more rigorously as such..."</p>

<p>I wonder what people think about the other AP tests. Which are actually <em>good</em>? </p>

<p>I know AP Bio has to be fishy if I got a 5 on it, LOL. Just took that for no reason, have no inclinations towards Bio, and wrote utter nonsense on the free response.</p>

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<p>mathboy and faraday, I am ignorant about the teaching of math and physics in high school and I have forgotten most of my math and physics. I will take your word that the teaching is bad, that it can be done better, that other countries do better, that it can be made more rigorous.</p>

<p>You may want to write a detailed proposal to the College Board.</p>

<p>Both of you have good things to say but I am afraid the clarity of your presentation can be improved quite a bit. </p>

<p>Faraday, I lost your on admissions and AP and SAT etc. What are you trying to say? My point is this: it may well be that the current AP tests have a low ceiling, that they do not allow the top students to show their true ability, etc. I concede this readily. But my point regarding admissions is this: between SAT and SAT subject tests, and APs and teacher recs and counselor recs and ECs (remember, a math/sci person could have a ton of science related ECs) and community college courses and summer college courses and high school courses and classroom performance etc etc the adcoms do a fine job. Not a perfect job.</p>

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<p>"Both of you have good things to say but I am afraid the clarity of your presentation can be improved quite a bit."</p>

<p>I am trying! What can I clarify, if anything in particular?</p>

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<p>As for faraday's point on the AP and SAT's - I think he means that if the AP's are taken a bit more seriously than he thinks they are, more so at least than the other tests, he is happier than he was with the admissions process [i.e., he's request your opinion since you seem to have some insight into what admissions offices actually think.]</p>

<p>"You may want to write a detailed proposal to the College Board."</p>

<p>I sometimes wonder how many complaints it's received. I.e. I don't know how many people complain as much as faraday and I do =] as legitimate as I think our complaints are.</p>

<p>I think in general our complaints are less even that admissions made are all invalid, and more that the so-called highest curriculum in high school is taught how it is. Even if it made no difference on college admissions, I would love for there to be a curriculum revamping.</p>