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No, I mean the discussion on the previous page of a 790 vs. an 800.</p>
<p>Hi, molliebatmit: I am not really a fanatical perfectionist, although my recent comments have probably made it seem that way. I have posted much earlier (several months ago) that in my opinion, missing 2 questions on the SAT M is understandable, due to misinterpretation of a question, arithmetic errors, etc. This would take a student down to an SAT M score of about 750.</p>
<p>Before someone objects that 750*3 = 2250, so 2250 is equivalent to 2400 after all, let me throw in that this statement requires the assumption that the person could improve across all three areas simultaneously upon retest, or that the person could make large gains in a single area.</p>
<p>On 790 vs. 800: I know a single 790 vs. 800 pair of people, so my data set is poverty-stricken. On the one hand, I would say from observation that there are definite differences in the mathematical thinking of these two people. On the other hand, they each have their strengths, and it would be hard to say which is “better.”</p>
<p>I don’t know what was going on in December, that was all-around a weird test date for me. I ended up with a 780 CR, basically 100 points higher than I’ve ever scored, which was pretty convenient for my superscore. Q&A wasn’t available; I suspected a bubbling error but I’m really not sure.</p>
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<p>I still have to ask where this notion of perfection comes from. It’s so easy to point stuff like this out in hindsight.</p>
<p>More true to the point at hand, let’s look at the performance to failure ratio of, say, the shuttle program. Of 136 shuttle flights, there were two failures. On one we forgot about that o-ring resilience in cold weather, and on another we didn’t consider the foam breaking off on the ET. Now, I’m making a leap at logic here, but it almost seems like you’re claiming that those two problems we missed on the math SAT are somehow related to this.</p>
<p>I am not criticizing NASA–I think the achievements of NASA have been awesome, truly. I really enjoy reading about Gene Kranz, Chris Kraft, and others who have played major roles at NASA.</p>
<p>I realize also that perfection is unattainable.</p>
<p>However, it seems to me that the notion of providing units in science is pretty basic. In our school system, students start to be “dinged” for leaving off the units in 4th or 5th grade. I don’t think including the units with an “answer” is a sign of unhealthy perfectionism.</p>
<p>I can easily see how the o-ring issue might have been missed. The temperatures in Florida at the time of launch were well below the normal range. Even if one considered the lack of flexibility of the o-rings in cold weather, one might well have thought that the rings would warm up quickly during launch. The outcome was tragic, but I blame no one. (I do recognize that there was some political pressure to get the shuttle launched–perhaps some blame attaches there.)</p>
<p>In the second case, with the foam breaking off, I think there was an issue there, of unwillingness to seek military help. As I understand it, at least one of the NASA engineers wanted satellite reconnaissance to check out the condition of the hull of the shuttle (and the military could have provided it), but he was over-ruled. The New York Times carried quite a lot of information about his emails and requests. If the poor condition of the hull had been detected, it is conceivable to me that some alternate plan could have been arranged. For example, was there any possibility of a transfer to the ISS? Or were the astronauts just “as good as dead already” given the problem with the hull?</p>
<p>Neither of these is an issue of attentiveness, in my opinion. Also, I have to apologize for errors of fact that might be present in this post. I am remembering newspaper coverage from the past, and my recollection may be imprecise.</p>
<p>Still, I think that having something like “Oh, the International Date Line!” pop into one’s head is an example where attentiveness does come into play. In this case, fortunately the weather was good and no lives were lost despite the computer crashes.</p>
<p>I never expected my question to spark so much debate. Let me put my spin on standardized testing. On the premise that knowledge of science, math, and general problem solving skills are OBVIOUSLY important in STEM fields, I think that standardized tests should be structured much like Japanese National Exams (bear with me here…) I do not mean to say that we should implement cram schools and what not, simply that a test covering “critical reading,” “writing,” and “math = basic algebra + geometry” does NOT by any means provide a proper scale to measure the wideeeeee distribution of intelligence that is present among America’s teenagers.</p>
<p>It would be interesting to see an AMC 10/12 style math test, because math olympiad style problems can bring out the problem solving spark in a student that no typical standardized test can. That’s the real reason why it’s so hard to differentiate between mathematical talent given an SAT score; honestly, a 780 and 800 could be the matter of an arithmetic error, but those very same people could end up getting a 13 and 5 respectively on the AIME. That’s certainly no passable fluctuation.</p>
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<p>I think the amount of random noise in AMC 12/AIME scores is actually quite a bit given how a small change in score can make a big difference. It seems very possible that a bad day could cost 2+ questions which is a pretty massive change in score. My experience with the AIME is perhaps an extreme outlier but in 10th and 12th grades I got a 10 and in 11th grade I got a 2. Some of that is because the 2011 AIME was more difficult but obviously that doesn’t explain most of the difference. One benefit of using lots of metrics is that random noise like that decreases in importance when using lots of metrics.</p>
<p>QuantMech, can you define what a student being “2-3 years behind” in math means? </p>
<p>MIT is one of the places my son will likely apply to next year and I’m wondering where he would fall on your scale of readiness. He goes to a public high school where the standard sequence for high performing math students is:
Honors Geometry
Algebra
Precalculus
AP Calculus </p>
<p>He is exceptionally talented in math and easily gets A’s in these math courses. He’s also on the school math team where he is one of the top scorers. Would you consider that being behind?</p>
<p>I can’t say authoritatively about MIT. At my institution, being 2-3 years behind in math would normally mean starting in College Algebra and Trigonometry! So you can see that we are pretty accommodating.</p>
<p>I think the fact that your son is on the school math team is a good sign. When you say he is “one of the top scorers,” what is your reference group?</p>
<p>I don’t mean to be discouraging, but I can say that at the local school a few years back, we had 3 9th graders in AP Calculus BC, all of whom had A’s and 5’s on the exam. This was followed by Honors Multivariable Calculus and Honors Differential Equations at the local university, then Matrix Theory, and then some branching, but to include a statistics course with a multi-variable calculus pre-requisite, and abstract algebra. I have known a fair number of students who had more or less this level of preparation going into college. Some took real analysis rather than the abstract algebra course.</p>
<p>MIT does seem to be welcoming to potential math majors with varied backgrounds. I know a few people who have gone to MIT, and a few professors there (and I was a post-doc there ages ago). But I don’t really have current information on the math department at MIT. Your son should be aware that there will be students who are well beyond him at present in math. If that is not discouraging to him, then I would say that he should go for it. </p>
<p>I hope someone who has better information on MIT’s math curriculum will post on this.</p>
<p>Also, a general question about MIT’s math department: How much attention do the undergraduates get from the faculty? Does this vary with the level of the course? Who generally teaches the multivariable calculus course–tenured faculty or visiting professors? Do the Putnam team members get more attention than other math majors? What fraction of math majors participate in undergraduate research, and when do they typically start? Is starting research linked to completion of certain courses? What fraction of students who enter with the intention to major in math wind up actually majoring in math, if that information is available? At Princeton, at least until recently, I think that only about 25% of the students who originally intended to major in math wound up doing so.</p>
<p>euclid76, does your son’s school participate in the AMC competition? Either way, the Art of Problem Solving web site is a good resource to look at.</p>
<p>A 5 on Calc BC will get you credit for 18.01 single variable calculus. After that your son would probably take 18.022 which is a somewhat proof-based version of multivariable calculus. After that your son would probably take 18.03 ordinary differential equations although if he has a strong background in proofs he could take 18.100 Real Analysis. At that point there are more options. If your son has a decent background with proofs he is probably like 1 year behind good (but not the very best) math majors at MIT. If your son doesn’t have any background in proofs it might be closer to 2 years behind those students. However, it’s important to note that those students start off with what would typically be junior level classes at most universities.</p>
<p>I can’t speak about intro classes but there was a decent amount of attention in the more advanced classes I took. I don’t think the Putnam team gets extra attention but I didn’t take the Putnam so I don’t know much about that. I’m not sure about the other questions but I don’t think research is linked to any particular classes.</p>
<p>I think MIT is better than Princeton in that regard as there are ~100 math majors per year and it seems implausible that ~400 out of ~1100 entering freshmen want to major in math.</p>
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<p>Then I don’t think your definition of “attentiveness” is well-defined enough to make a claim that there is a correlation between it and what is reflected by SAT scores.</p>
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<p>That percentage, whatever it is, probably has less to do with MIT and more to do with the fact that MIT has so many choices of technical majors, many of which may appear more marketable than math. This probably is less true at Princeton, where engineering is a comparatively less attractive option than at MIT. </p>
<p>A lot of people who went to MIT ‘wanted’ to be physics majors but weren’t necessarily wedded to it and ended up in a physics-heavy engineering major.
18.02 is always taught by tenured faculty–used to be taught every year by Hartley Rogers. Classes being taught by TAs or visiting faculty is not a problem at MIT partly because it has so many faculty. For instance, in one of my core classes in engineering the president emeritus of the university was my TA. Often tenured faculty are TA’s, at least in engineering where there are so many faculty members.</p>
<p>freeman94, post #174, I don’t think there is a correlation between attentiveness and SAT M score over the full range of scores. I had a narrower situation in mind. That is, the student who has scored 700 on the SAT M and claims that it is essentially equivalent to an 800. If the student did not actually know how to solve the 4 or 5 problems that were missed, then I don’t see how the student could really claim the equivalence–the student doesn’t understanding things the higher scorers do understand. </p>
<p>The situation where I could see the student making the claim of “essential equivalence” is one where all of the errors were in the “stupid” category (as in QMP’s equality 4 *7 = 21) or the student just overlooked some element of the problem or misinterpreted something. Here is where I think that “attentiveness” does come into play, in collecting those last 100 points, assuming that the student otherwise understands the material.</p>
<p>Sorry for the confusion–did not mean that SAT M measures “attentiveness” in general.</p>
<p>Having the introductory multi-variable calculus class taught by tenured faculty at MIT is a real plus, which you would not be guaranteed in a number of other universities–including the large public research universities. I would take that as a positive sign for Euclid76’s son.</p>
<p>I think that many of the would-be mathematicians at Princeton jump ship into economics or finance. Recently, though, the department has gone to some lengths to try to keep the majors engaged in math, and I think the number graduating in math has risen.</p>
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<p>Given that math majors at MIT routinely have the second highest starting salaries (after EECS) it’s not clear that most engineering majors are more marketable than math. Starting salary data can be found here <a href=“http://gecd.mit.edu/resources/data[/url]”>http://gecd.mit.edu/resources/data</a>.</p>
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<p>No, I’m not confused at all. I am saying that it’s highly dubious that those 100 points mean anything related to one’s ability as an engineer. It really seems like you keep moving the goalposts.</p>
<p>QuantMech and others, thanks for the feedback to my questions. </p>
<p>My son did discovery the Art of Problem Solving website and has taken the AMC 12 class and purchased several problem solving books. His school participates in the New England Mathematics League so he is able to compare himself to his peers by looking at the published results.</p>
<p>Based on his scores he is one of the top students in these contests. He just will not have taken any advanced calculus classes when he graduates HS.</p>