9/9/09: Today's SAT QOTD (and why the Math section of the SAT needs to be reworked)

Test Preparation
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<p>And I bring you today's SAT question of the day, assuming you aren't subscribed to it already:</p>

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[quote]

If it is now 4:00 p.m. Saturday, in 253 hours from now, what time and day will it be? (Assume no daylight saving time changes in the period.)</p>

<p>A. 5:00 a.m. Saturday
B 1:00 a.m. Sunday
C. 5:00 p.m. Tuesday
D. 1:00 a.m. Wednesday
E. 5:00 a.m. Wednesday

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<p>This is what the Collegeboard seemingly interprets as a question that evaluates mathematical aptitude. What is it really? It is merely a counting question, designed as a question full of plenty potential pitfalls for the less than meticulous test-taker. Having been reasonably acquainted with the SAT over the past few months, I realize that the SAT is a test of, in addition to aptitude, ability to recognize and avoid certain tricks. This I am okay with; what is not okay, in my opinion, is essentially what the math section of the SAT has become.</p>

<p>For the average math aficionado, the SAT math section isn't exactly a challenge in terms of the degree of difficulty offered. Let's face it; many more people have the capability of mastering the content in the math section of the SAT than the content in the CR section. The topics required are all rather elementary and not in great depth. Hell, just by plugging in numbers several people that I've known have obtained high scores, and these were rather poor math students. Essentially, what I'm getting at is that a score received on the math section isn't really indicative of one's math skills.</p>

<p>What it seems to have evolved into is a section without true challenges to exercise the mind, one that offers only challenges in the sense of tedium, like the problem I initially mentioned. This sense of tedium often leads to carelessness, which is why even USAMOers will sometimes score under 800.</p>

<p>Of course this works for the Collegeboard. They have fooled the public into believing that the two core sections of the SAT, CR and M, are reasonably balanced in terms of difficulty. Their ridiculously steep curves on the math section make this feat possible, and they probably have no urgent sense to alter the way the math section is formatted and curved. But in the process, they harm those whose strengths are in math by reducing their capabilities to a rudimentary level, to a point where the farce of aptitude masks the reality of the math section, that of simplistic, cheap deception. And are there people with similar positions with regard to the other core component of the SAT (the CR)? I'm sure there are, but whereas the CR section at least measures college-level reading ability reasonably in addition to the usual SAT trickery, the same cannot be said about the math section.</p>

<p>What are your opinions on the matter? Do you think the SAT math section should continue to exist in its current form? Do you think it deserves reconstruction? Perhaps you might even advocate the removal of the math section from the SAT, relegating it to solely subject tests? Your feedback on this issue is appreciated.</p>

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<p>I’d also like to add some complaints - why are there multiple levels of Math in the SAT IIs but neither of them include Calculus? Shouldn’t the college board know that there are plenty of people who have taken calculus by the end of Junior year since they record the age of the test takers on the AP Calc tests? Also, wouldn’t the fact that around 10% of test takers get a perfect score on the Math II seem to indicate that the curve isn’t doing its job, or that the subject content should be more difficult?</p>

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I concur with your latter point that the questions are simply too easy. But not many juniors have taken a calculus class. Heck, I go to a rather competitive HS in New York and the typical math track is to take calculus in senior year. Many schools in the nation do not even offer a calculus course. So while the difficulty of the math2c test is lower than it should be, the level of the content is probably where it should be. Perhaps they could introduce a few basic calculus concepts that some precalculus classes may teach (basic derivations and integrations) but even that might be a stretch.</p>

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<p>I don’t see why you need higher level math to make a difficult math test. I mean, the AMC 10 covers very similar material to the SAT, yet has some extremely difficult problems. The USAMO only goes to precalculus but is insanely difficult. There’s more to being good at math than being calculus.</p>

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<p>“Higher level material” means absolutely squat, as UMTYMP so well pointed out. The USAMO, as he mentioned, goes up to “pre-calculus” but ** most mathematicians, even award winning greats ** probably could not do that well on it. </p>

<p>It’s the ability to use the given tools in creative ways that matters, not whether you have a bunch of tools and can use them in a rudimentary fashion. </p>

<p>A more concrete example that we might be familiar with (I’d bet 99+% of us here never made it to USAMO…including myself) would be SAT math v.s. AP Calculus. The SAT math questions require more thinking compared to AP Calculus BC, which is mostly just straightforward application. </p>

<p>The SAT is basically in the style of a math contest not quite at the AMC 10 level, but about at the level of the AMC 8 (AMC 8’s hardest questions are slightly harder than SAT’s, but the AMC 8 covers less material).</p>

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<p>By the way, this problem is actually a very good test of mathematical creativity (at the non-contest level): </p>

<p>Take 253 days and partition them into 240 + 13 days. You know that since there are 24 hours in a day, you can cycle through the 240 hours by simply adding 10 days (240/24 = 10), so that we are now at Tuesday at 5 PM. Then just add on the remaining 13 hours by going to Wednesday (8 hours to do this), then from there go from 12:00 to whatever’s left (5 hours), which takes us to 5:00 am, Wednesday. </p>

<p>^ This is not a “trick”, it’s clear mathematical reasoning that can be expressed and justified. And it’s much more interesting than: </p>

<p>“Some cone is filling up with water, here are a bunch of rates; use the pythagorean theorem like you have 100x before to solve for the rate that its height is increasing”</p>

<p>or </p>

<p>“Write the taylor approximation of this function”</p>

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<p>And, to continue, let me just say that the SAT subject tests are ** boring **. They do not require anywhere near the creative thought as the SAT math section does. It’s straightforward “find the formula”. When I took the SAT, I was happy to solve the problems because they weren’t routine like ** every problem I’ve done in high school **. SAT Math Level 2, on the other hand, was mind-numbingly boring.</p>

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<p>CollegeBoard could learn from the CEMC contest folks down in Canada. The Fermat test would be perfect.</p>

<p>[CEMC</a> - Past Contests - Mathematics and Computing Contests - University of Waterloo](<a href=“http://www.cemc.uwaterloo.ca/contests/past_contests.html]CEMC”>CEMC - Past Contests - Mathematics and Computing Contests - University of Waterloo)</p>

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<p>Your answer is easily found in the historical tables that show the … scores. Before crying for a more difficult test, you might ask yourself why the test had to be made easier a few years ago. Fwiw, the original SAT tests would probably transform many of today’s students into a hysterical bunch. Why? Because simple reasoning has become harder for generations who could not live without the cructhes of a computer program or a Ti-89.</p>

<p>As far as using more SAT Subject Tests, look at what happened to the SAT-II Writing Test. It was merely merged into the “new” SAT Reasoning Test. Then take a look at the Math Level 2 test, isn’t that a test that rewards your mastery of a graphical calulator above everything else? </p>

<p>The reality is that ETS/TCB could make the SAT MUCH more difficult without raising the need for more vocabulary or more “mathematical” knowledge. They could drop the average of the test to a mere 400 overnight, if needed. This is, however, the last thing they need to do since they had to HELP students maintaining an average that is close to about 500. </p>

<p>Oh, and lastly, you should check the percentage of people who MISS those really “ridiculously” easy questions!</p>

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<p>It is NOT a test for the “average math afcionado.” It is a test for the average HS student, many of which never complete Alg II.</p>

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<p>Yup, see point one. </p>

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<p>Again, that is by design. It is a test for the average high school student (with average IQ and average high school math class), not the “average” student on cc who self-teaches Calculus in fifth grade. :)</p>

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<p>A better question is to ask why our society demands that everyone be able to perform well on these tests. The current SAT does not measure mathematical talent. There is very little actual proof or reasoning.</p>

<p>Why do “average” students need to make 500 on the SAT? Surely its purpose should be to measure mathematical ability, not give an ego boost to teenagers with self-esteem issues. Not everyone needs to be good at math, and there is nothing wrong with getting a poor score on a math test if you don’t intend to pursue mathematical fields later in life.</p>

<p>Consider the Fermat test I mentioned above. The score distribution is available at <a href=“http://www.cemc.uwaterloo.ca/contests/past_contests/FermatResults.pdf[/url]”>http://www.cemc.uwaterloo.ca/contests/past_contests/FermatResults.pdf&lt;/a&gt; (find page 14).</p>

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<p>

Typical reading enthusiasts aren’t faced with an exam as insulting to their favorite subject. They are even offered the opportunity to reflect their capabilities through the Lit subject test, which I think many will agree may be the most difficult subject test, barring perhaps a few of the more obscure language exams. How many reading enthusiasts can genuinely claim that an 800 in Lit is a cakewalk? Even an 800 in CR isn’t exactly a breeze through the park for these people because of its slightly tinted ambiguities and occasional use of esoteric vocabulary.</p>

<p>My problem isn’t so much that the math exam uses trickery, but rather that the math exam only tests the most rudimentary of abilities while relying on deception to balance its curve. Furthermore, I am bothered by the face that there isn’t a single math subject test offered that is genuinely challenging for the math enthusiast.</p>

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It is a counting question meant to deter those who are prone to jumbling numbers or make a mere skip in their arithmetic. What highschooler does not understand the concepts of 24 hours in a day, as well as the AM and PM systems?

Like I previously stated, these questions create so many wrong answers because of deception, not difficulty.</p>

<p>Is it not possible to increase the difficulty of the math section while making the math curve much more reasonable? You think they are fighting to keep the 500 score but it seems more like they are fighting to keep it down by instilling ridiculous curves. (A 750 for 2 questions answered incorrectly?? Ridiculous.)</p>

<p>

I’ve never taken the AMC 8, but the SAT is in no way comparable to the difficulty of the AMC 10. The AMC 10’s first 10 questions are about equivalent to the SAT’s hardest, IMO. Assuming that the AMC 8 isn’t a huge drop-off from the AMC 10, I’ll have to disagree with you.</p>

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<p>Sure they are. Look at the other thread on cc where kids compare their CR score and Lit subject test score (some in the 500’s) against a 5 on AP Lit. Both taken in the same year!</p>

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<p>What you call “trickery” or “deception”, test makers call “reasoning”. But, if you don’t like so-called reasoning in the SAT, try the ACT since it’s math is both a higher level (includes trig), and more straightforward. Unlike the SAT, however, the ACT gets its “curve” by requiring speed, such that the “average” kid will run short of time, and others will make a silly math error in their head.</p>

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<p>They don’t. The test is normed such that the average student earns a ~500. It could easily be normed that the average was 650 (thus compressing the top end) or 350…but it’s not.</p>

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<p>

That really doesn’t address my point, which was responding to xiggi’s assertion that

You say that

I don’t understand how this is relevant. Let’s assume that CollegeBoard/ETS increased the rigor of the SAT math section to the point that the average score falls by 100 points. So what? Average students are still average when compared to their peers.</p>

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<p>

AP Lit isn’t exactly what I had in mind, and you know what I meant. People with a literary passion are able to reflect their abilities on high-ceiling exams like the Lit subject test and, arguably, the CR section. There is no such equivalent for people with a mathematics passion.</p>

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<p>SAT and SAT subject tests are not made for math aficianado’s. They are made to test how well you can solve problems of a mathematical or quantitative nature.</p>

<p>Sure they don’t have proofs and in depth reasoning, but what percentage of the population could handle that?</p>

<p>If you want a test that a math enthuisiast can take, go do the AMC10/12. And if you don’t make it to the AIME, then it looks like you found something challenging. Otherwise continue the path.</p>

<p>Edit: Also, collegeboard (as much as they don’t want to show it) cares more than anything about money, why would they make and bother to administer a test that 1% of the population took?</p>

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<p>^ Have you been following the course of discussion? It’s the comparison between the difficulties of the math and CR sections that has me flustered. The math section is only able to maintain a balanced curve at the upper score ranges because of its ridiculous curve. There is essentially no indication of a student’s math skills beyond the 700 range because after that it dwindles down to getting 2-3 questions wrong because of the nature of the exam or getting 0 wrong because of a keen eye for these manipulations. Whereas there is no clear indication of a difference in skills in the 700-800 range, it is clear that an 800 CR scorer is much more developed in terms of reading ability than a 700 CR scorer. The ceiling is much higher for the CR section to reflect abilities. If the math section adjusted its difficulty as well as its corresponding curve, scores would see similar distribution, but those with higher scores would almost more definitely have a higher ability in math.</p>

<p>Many high schools and communities do not offer the AMC exams.</p>

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<p>Just my 2 cents, you don’t really get the whole picture on CC.</p>

<p>As CC posters, 99% of us obviously are top students at our schools and care a lot about college and our future. The SAT is designed to be FAIR for everyone. So what some parts are a bit easier for us than others. </p>

<p>Also, you have to realize that percentiles are pretty accurate. Out of the millions of students who take the SAT/ACT, most CCers drop into the top 1-20% at least. What about the other 80% of students who get lower scores? What happens to them?</p>

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<p>Calculus is not in the standard high school curriculum, which is why it will never be tested in exams such as this.</p>

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<p>

As I said above, the SAT is judged in context. If almost all students score a 400, that 400 will become normal. If only 100 people make an 800, that will become unique. Fair != easy.

I’m going to get flamed for this, but I’ll say it anyway: the majority of people apply to colleges that have extremely lax admissions standards. There is nothing wrong with that, but take a minute and think about what it means. A school that accepts 95% of applicants does not need to know whether a 520 is oh-so-different from a 580. On the other hand, a school only taking 10% of applicants could make excellent use of a test with a clear difference between 720 and 780.</p>

<p>Just my 2¢</p>