A question regarding "Holistic" admissions and "Perfect Scores"

Colleges and Universities A-Z Massachusetts Institute of Technology
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<p>freeman94, I am not an engineer, so I am happy to concede that they don’t have any relation to one’s ability as an engineer. Indeed, I have a relative who is a very successful engineer and did not score an 800 on the SAT M.</p>

<p>On the other hand, I am not moving the goalposts. I have been writing all of the time about the difference between 700-ish and 800 on the SAT M, although the erratic timing of posts over the holidays may have made the context unclear.</p>

<p>As I wrote in the last post, if the reason that a student did not score 800 is that the student <em>could</em> not solve the last few problems, then I don’t see how the student could claim that the scores were essentially equivalent. The 800 scorers (on the same administration) could solve problems that student couldn’t. Most of the 800 scorers I know could solve all of the problems correctly on any administration of the test. I doubt that luck comes into it, except in a few cases.</p>

<p>So, when I wrote about “attentiveness,” I referred to catching the details on the problems that a student could have solved correctly, but didn’t.</p>

<p>Is catching the details not important in engineering? Detail-orientation won’t get a physical scientist very far in the absence of understanding, hard work, and creativity. But on the other hand, in research in physical science, understanding, hard work, and creativity can be reduced to no effect by overlooking an important detail that affects the outcome. In “less bad” cases, overlooking an important detail causes only minor embarrassment + errors in the numerical results; e.g., there is a well-known textbook writer who issued a text with atomic units, specifying that the mass of the electron, the charge on the electron, h bar, the Bohr radius, and c were all equal to one. Unfortunately, no such units are possible. If the first four are equal to one, c is approximately 137. </p>

<p>Perhaps the team size in engineering is larger than in some fields of physical science, so someone is usually around to catch things? (Obviously, the teams in particle physics are huge, but in other areas, not so much.)</p>

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<p>If you don’t understand all the questions on the SAT math or you make careless mistakes on like 15%-20% of your work, you are less likely to be a great engineer than someone who doesn’t have that problem, all things being equal. This is especially true in engineering fields where theory is more important. </p>

<p>Also, some people may have wild vacillations in scores, but these people are obviously more prone to mistakes than people who don’t. Therefore, someone who gets 700 on one test and 800 is probably not as reliable in the math area as someone who doesn’t have such wild swings in performance. Just like someone who gets a B+ in math class is less reliable than someone who has high A’s.</p>

<p>I don’t know why people get offended at statements like this. No obstacle is insurmountable. If you didn’t learn math well in high school or had a particularly bad day, it doesn’t mean you can’t improve. But playing the odds, you are less of a sure bet than people who didn’t have such problems.</p>

<p>Physics Nobel Laureate Steven Chu had mediocre grades in his prep school, but he buckled down during undergrad. However, I still think it is valid that people with mediocre grades are less likely to be stars in physics.</p>

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<p>Dear euclid76
My son went up to Calc BC in high school. At MIT his score of 5 on the AP test (and I am not sure if he also had a placement test or if that was just physics) tested him out of 1st semester math. He was in no way behind an in fact most of his friends did not test of of 1st semester math so he could have even been considered ahead. I know when you see posts here on CC you feel like all kids are taking advanced classes but from my experience both my kids where not behind at all in math with only having gone up to Calc BC in high school.</p>

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<p>The issue is not whether completing only Calc BC will put someone behind the average MIT student [it would put them about average in this group] but among MIT math majors or perhaps serious MIT math majors [those with sufficient preparation for graduate school in mathematics]. I think starting 18.02 and 18.022 (the typical starting math classes from someone whose highest high school math class is Calc BC) is somewhat behind for the second group and I’m virtually certain it’s behind the third group.</p>

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<p>I don’t see how it’s an issue for someone to be behind at all. Someone who starts off with 18.022 can have a very competitive application for top graduate schools.</p>

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<p>I think if you have the talent and a solid mastery of mathematics through calculus, that you will be prepared enough to do well in theoretical math classes at MIT. </p>

<p>However, the issue most people have is that they won’t have any idea of whether they’ll be able to actually be a working mathematician–that is, to solve open problems in math for a living. It takes a lot more than A’s, even from MIT, to do that. That is why some people opt out of the math major.</p>

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<p>To be honest, I really do agree with shravas here. What matters a lot more is that you click with difficult coursework. The most important thing is maturity – if you’ve got that, every time you take a course, it actually sticks, and you build on that foundation. </p>

<p>Research mathematics is giant, and the idea to prepare for it is to have a very good working understanding of the types of things people will want you to be familiar with, not to grab a few extra courses here and there. </p>

<p>One thing people don’t realize is that mathematics kind of stops building linearly on itself after the lower division. And how all-over-the-place your learning really becomes at a certain point. </p>

<p>One point @QuantMech: your discussion of the difference between 700 and 800 is very well taken; I wanted to add, though, that it is unclear how closely correlated the ability to be careful on the SAT and the ability to be careful with large bodies of complicated material in a less strict time limit are correlated. Certainly, I think someone who is at the level mathematically of scoring an 800 might have issues with sloppiness if scoring a 700.
But when one is working in the engineering, physics, or mathematics world, I’d imagine the goal is to produce a very careful product that’s very accurate, without much time pressure at all similar to the kind on the SAT. More like, you’re GOING to make mistakes the first time around, and you should be inclined to go back and fix them with lots of persistence, in a reasonable amount of time.</p>

<p>This extends beyond just carelessness. There’s the additional factor: there’s only so many new things you can learn/do in a day. So if it takes you some significant but not inordinate bit more time than someone else to come up with the idea behind a solution, it may not even really make a terrible bit of a difference with persistence.</p>

<p>It depends what career one is shooting for. I think the real skill at being careful comes with practice, as one understands the ideas better, and gets them enough to be less inclined to make errors, and aware of the kinds of errors that are often made.</p>

<p>For some careers, I confess freely that performing under extreme time constraint is necessary. Nonetheless, I wouldn’t screen based on this for admissions, unless the student’s primary selling point is talent in a related realm.</p>

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<p>Are you saying that students who enter with mathematical maturity but little formal coursework will succeed? I definitely agree with this. Are you are saying that students with only fairly standard high school math (Calc BC, no math competitions) can acquire the requisite mathematical maturity quickly enough? This seems somewhat unlikely to me although definitely possible for very gifted students [I am certainly not that gifted as it took me quite a bit of time to develop any sort of mathematical maturity]. I think part of this is that MIT’s math curriculum is not particularly good at bringing students with whose high math record is Calc BC up to speed. At MIT such students would probably take 18.022 their freshmen fall and 18.03 their freshmen spring. Neither course involves many proofs or is designed for math majors so those students won’t take any serious proof-based class until their sophomore year which seems unideal. Other elite colleges (Harvard, Stanford, Yale, Princeton, Caltech) offer fairly rigorous linear algebra and multivariable calculus classes for motivated freshmen with only Calc BC.</p>

<p>EDIT: 18.014/18.024 is another decent option for freshmen who only had Calc BC in high school although I think it is easier than the above described classes at peer universities.</p>

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<p>It would also be useful if someone could post about how MIT students fare in math graduate admissions (even a rough summary would be very helpful). For the self-exit surveys on the math department’s website about 10-15% of math majors go to graduate school in math. What graduate schools do they attend? Are these drawn exclusively from the best students or from a larger cross-section? What kind of coursework do they typically take?</p>

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<p>Right, but I wouldn’t say time pressure should be an issue. It shouldn’t take you much time to solve the math SAT problems–you should have plenty of time to check at least a significant portion of your work. It’s not a creative essay.</p>

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<p>@collegealum: for the SAT I math? It seems that there’s enough time to get through the test, but that one really can’t work very cautiously. I actually don’t believe much in checking work, so much as getting most of it right on the first pass through (checking for mistakes as you go along). Once you’re done with several questions, if it’s unclear where you made your mistakes, where do you start checking? That’s why I think methodically going through a problem and ensuring a good solution is often better. I don’t think this is really an option on SAT I mathematics. As for the SAT II math, the error margin is so great that an 800 is almost a sure thing if one prepared specifically for that exam with the right prep materials - usually, a strong student scores lower only because of not knowing the right tricks/formulas. </p>

<p>@UMTYMP student: the former. Mathematical maturity does require time to acquire, and not having it can slow one down. I don’t believe the very vast majority of people who get A’s in BC Calculus are anywhere close to the mathematical maturity required to start taking advantage of a strong school’s math curriculum.</p>

<p>As for graduate-school-bound students, the short summary is, coming from very strong schools, it’s unnecessary to have the absolute top of the line letter of recommendation to get accepted to great graduate programs, but getting accepted to programs such as Princeton’s or Harvard’s might be somewhat a matter of luck for anyone who isn’t truly mathematically exceptional (i.e. exceptionally gifted even for an MIT undergraduate, exceptional application, and at this sort of school, has even done significant research and published, although this is hardly necessary to get into a strong program… as many are aware, some programs are expressly structured around student capability to engage in research coming in). Pretty sure a reasonably gifted MIT student with quite strong letters, solid coursework, great results, should be able to make a very good program (Ivy League, top public school, or other strong privates like Chicago).</p>

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<p>mathboy#187, I agree with you that work in physics and mathematics often involves dealing carefully with large bodies of complicated material, with multiple steps in the calculations. One doesn’t have the sense that there is a short time limit. It does generally take a lot of patience, to go back and double-check (or triple-check) work for errors. However, it seems to me that this is harder than scoring 800 on the SAT math–it’s more like scoring 50 800’s back to back, in practice.</p>

<p>re your post #191: What tricks and formulas do you think are needed for the SAT II math? I think it is helpful to know the quadratic formula and the sum of a geometric series, but that’s about it, as I recall. Could you give an example of an SAT II math problem where a trick or formula is required?</p>

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<p>@QuantMech: I seem to remember a large body of calculator tricks was necessary, but have since forgotten what they precisely are, to be honest. Perhaps since I had no had a precalculus class, I felt there was a bunch of memorization involved.</p>

<p>As for double and triple checking: in my experience, most of my checking is done when I actually write the proof. If everything seems pretty internally consistent, and I am not using any facts I should not, it all goes through. Same way if there is a calculation: I note what I am doing carefully each step, and try to ensure there was no error if, say, there was a step with some long integration or something.</p>

<p>That is the major thing I find is a negative with the SAT time limits. It is hard to conceive of slowing down some to really maximize carefulness. Maybe it is just me, but solving 5 complicated exercises
seems to help me focus and check the internal correctness. I found the SAT style unnatural for me, though doable once I took practice exams and familiarized myself.</p>

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<p>Doing the test at a conservative rate such that I am reasonably careful, I remember having time to check 1/3 to 1/2 of the SATI and II math problems. I just start from the beginning and start checking.</p>

<p>I don’t remember calculator tricks helping for the SATII math.</p>

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<p>Perhaps it changed since you took the SAT II - I’m pretty sure collegeboard SAT II and AP exams where they expressly allow for a calculator pretty much require very high familiarity with using it to minimize time spent. I haven’t really used a calculator in probably 7+ years at this point (I didn’t even own one from the start of college), but I remember it being useful back for that exam pretty distinctly, perhaps at least to make sure to get a near perfect score. One could certainly still score high without a calculator. Perhaps the idea of using a calculator is so foreign to me that my memory is a bit skewed :)</p>

<p>I guess if a majority of good math students are finding it easy to check their work, it’s true that there’s no excuse for making mistakes. Somehow, that wasn’t at all my memory of SAT I or II to be honest, although the II allowed a tremendously high error margin. Regardless, I guess my preference always goes to solid performance in fundamental school coursework, and I liked the AP exams better than the purely multiple choice ones.</p>

<p>My (admittedly rusty) memory of SAT type math is that you have around 20 questions to solve in a 30 or so minute interval? I imagine a lot of them are just really easy algebra, or a very simple high school geometry application. Nonetheless, some of them seemed to involve some level of actual manipulation, and given the rough estimate of how much time one has for a question, that is, not even a couple minutes, I can’t say it’s ideal to promote carefulness.</p>

<p>Perhaps one’s view is to suck it up, and just make sure to not make mistakes, or retake the test until mistakes aren’t made. Somehow, I have not connected to that mindset ever. </p>

<p>That said, the difference between a 700 and 800 is reasonably significant in my eyes, but it is somewhat impossible for me to interpret the precise reason for such a difference in scores without assessing all the other competency checks.</p>

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<p>mathboy98, could you come up with any examples of the need for a calculator on SAT Math II, from the book of Real SAT II’s or another source? I don’t actually think a calculator is needed for it at all.</p>

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<p>@QuantMech: admittedly as I said, memory is rusty; however, I’ll say this: it is not specific problems that I remember requiring a calculator so much as that it seems collegeboard designs the exams where it allows a calculator so that you really should use it when it would speed you up to minimize your time wasted. When I took calculus in high school as well, our teacher specifically had us learn to use one, for instance to calculate integrals, because he had seen by experience that it was useful in the calculator section of the exam.</p>

<p>He was assuredly old-school enough that he didn’t really care tremendously for calculators, and likely taught it out of strategy.</p>

<p>All I recall was that I took the SAT II math after I’d finished calculus, and that the calculator familiarity I’d acquired seemed rather useful when I took practice exams, and I think also on the real exam, but less so (I found some prep books were a lot more complicated than the things that showed up on the real exams).</p>

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<p>At least a quick scan at the least official source, a Wiki excerpt, says: </p>

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<p>And I seem to believe it. It’s this that I was getting at. It would be a slightly different story to ask for specific questions where I’d have to use a calculator, so much as, take your average high schooler getting an A in precalculus, and ask them if a graphing calculator helped them get 800 on the SAT II math…was it at least good for speeding up several questions, or is Collegeboard bluffing about the utility of calculators there?</p>

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<p>And a fair number of them require no calculation at all but are just based on intuition.</p>

<p>For example, “which is bigger, x or x^2?” is a question often on the exam.</p>

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<p>I agree that the AP Calc tests are designed for calculator use. One would want a calculator for them, I think. One would certainly want a calculator for AP Stat.</p>

<p>On the other hand, I don’t think that a calculator is even needed for SAT II Math.</p>