New SAT, New Problems(theatlantic.com)
theatlantic.com
New SAT, New Problems
http://www.theatlantic.com/education/archive/2015/01/new-sat-new-problems/384596/?single_page=true
44 comments
More coachable is probably the goal. A big problem for the college board is that insofar as the SAT is difficult, math driven, and g loaded, Asian people tend to score too high.
This creates political pressure for colleges to stop using the SAT in admissions, an existential threat to the college board.
This creates political pressure for colleges to stop using the SAT in admissions, an existential threat to the college board.
>More coachable is probably the goal. A big problem for the college board is that insofar as the SAT is difficult, math driven, and g loaded, Asian people tend to score too high.
How would this help? I've taught SAT courses, and Asian students are overrepresented in those prep courses. Those cultures tend to have a habit of using external prep.
Note for posterity: I'm not saying Asian overrepresentation is a bad thing. Just stating a fact about courses I taught. If the college board's motive is to reduce Asian scores, I don't think they've picked a good method.
How would this help? I've taught SAT courses, and Asian students are overrepresented in those prep courses. Those cultures tend to have a habit of using external prep.
Note for posterity: I'm not saying Asian overrepresentation is a bad thing. Just stating a fact about courses I taught. If the college board's motive is to reduce Asian scores, I don't think they've picked a good method.
They have always tweaked exams to meet with new(old for the rest of us but new for college admissions departments) demands. A few years ago they changed the GRE to include more statistics and probability.
I'm just spitballing here, but I always assume the reason Asians do so much better is because it is game-able and the Asian subculture pressures students to overstudy.
> The main issue is that you kind of have to dumb yourself down to answer the questions - if you start actually thinking critically, you'll run into trouble.
This has always been true on the SAT--especially the math section.
In the math section, it is almost always faster to eliminate answers using backward reasoning than getting the correct answer using forward calculation. For the sample question, answers C&D relate to intercept--answers A&B relate to slope. The question asks about slope so you immediately discard C&D. Now, even a guess is a plus for you.
By the way, that sample question would get removed after statistical norming. It's sufficiently confusing that it won't pass the standard--poor students always miss--mediocre students sometimes hit--good students always get it right--that is required for the SAT to work statistically. The confusion is that choice of slope is arbitrary--there is no particular reason for why which length is on which axis and which is cause and effect.
This was actually one of the unique things about the SAT for me. While "sample" questions always had lots of confusing answers, the SAT questions were absolutely crystal clear. Any SAT section with more than one confusing question was obviously the experimental section.
This has always been true on the SAT--especially the math section.
In the math section, it is almost always faster to eliminate answers using backward reasoning than getting the correct answer using forward calculation. For the sample question, answers C&D relate to intercept--answers A&B relate to slope. The question asks about slope so you immediately discard C&D. Now, even a guess is a plus for you.
By the way, that sample question would get removed after statistical norming. It's sufficiently confusing that it won't pass the standard--poor students always miss--mediocre students sometimes hit--good students always get it right--that is required for the SAT to work statistically. The confusion is that choice of slope is arbitrary--there is no particular reason for why which length is on which axis and which is cause and effect.
This was actually one of the unique things about the SAT for me. While "sample" questions always had lots of confusing answers, the SAT questions were absolutely crystal clear. Any SAT section with more than one confusing question was obviously the experimental section.
> It is fine—good, even—to ask students to carry out these tasks, but in many cases these are skills that students unfortunately haven’t yet mastered. If they aren’t being taught to think about graphs that way, let alone articulate their reasoning in that matter, chances are only the smartest (or well-prepared) teens will be able to arrive at the correct answer under the time and emotional pressure of the test.
But isn't that the point of the SAT? To sort the kids who have mastered these skills from the ones that haven't?
But isn't that the point of the SAT? To sort the kids who have mastered these skills from the ones that haven't?
The original point of the SAT was to measure "aptitude" in order to identify students might perform well in college, but did not have good opportunities to demonstrate that in high school. This was before things like "aptitude" and "intelligence" became dirty words.
Steven Pinker argues for admissions based on standardized tests, in part because he contends that the current Ivy League admissions process suffers from "eye-of-newt-wing-of-bat mysticism that jerks teenagers and their moms around and conceals unknown mischief.":
http://www.newrepublic.com/article/119321/harvard-ivy-league...
http://www.newrepublic.com/article/119321/harvard-ivy-league...
Seems like the math portion is becoming less about math and more like an MBA reading comprehension test.
It's actually become less about wrote manipulation of symbols and more about a deeper understanding of actual math concepts.
The latter is, indeed, harder.
The latter is, indeed, harder.
So some questions can only be answered by smart people. What are they trying to measure exactly?? As a smart kid, I never understand why people were always trying to knock us down. The other kids would brag to me that they got to take their SATs untimed. I got a perfect score and still got rejected from five colleges.
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I know what that graph-line question is trying to ask, but I can't figure out those possible answers.
The answers are so ungrammatical and mystifying that it almost seems like the designers were trying to kill the test on purpose. The "correct" answer is this:
The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone
...as far as I can tell, the answer written for sentient humans would be something like:
As the length of the metacarpal bone increases, so does height.
But my translation is so obvious that I sat there for five minutes wondering if I was looking at some kind of otherworldly trick question. Nope. They just made a wretched problem.
Obviously, the original SAT was an IQ test (as the article says) that allowed poor but smart kids from poor schools to get into college. But that process is self-defeating, as poor areas have all their smartest people leave for everything from state schools to Harvard. As inequality becomes more rigid groups like the College Board are flailing and improvising.
The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone
...as far as I can tell, the answer written for sentient humans would be something like:
As the length of the metacarpal bone increases, so does height.
But my translation is so obvious that I sat there for five minutes wondering if I was looking at some kind of otherworldly trick question. Nope. They just made a wretched problem.
Obviously, the original SAT was an IQ test (as the article says) that allowed poor but smart kids from poor schools to get into college. But that process is self-defeating, as poor areas have all their smartest people leave for everything from state schools to Harvard. As inequality becomes more rigid groups like the College Board are flailing and improvising.
Your translation does not capture what they are saying. They are asking what quantity the slope of the line (as in, rise over run) corresponds to. The answer should be a noun phrase describing some numerical quantity, not a sentence describing a true or false fact about the world.
I think their answer is perfectly sensible and perfectly grammatical. It's also clearly correct according to even the most basic notion of slope as rise over run. I honestly don't see the issue with this question. Not only does your answer not fit grammatically, but it's also less precise.
When I skimmed the list of answers, they also looked wrong to me, but this is because I saw the answers (which start at the top of the page) before the question (which is at the bottom). Because the answers started with capital letters, I initially read them expecting a full sentence, mentally replacing "increase" with "increases":
"The predicted height increases in centimeters for one centimeter increase in the first metacarpal bone." (True, although the height also increases in any other unit for any amount of increase in the bone.)
"The predicted first metacarpal bone increases in centimeters for every centimeter increase in height." (Ditto, but this looks more correct because it has it increasing for every/any centimeter increase in height, rather than specifically one.)
Judging by the parent comment, I think they may have done the same, but failed to notice the correct interpretation? In any case, while as a native speaker, I only saw it that way for a few seconds, I can certainly imagine that someone speaking English as a second language could be thrown off.
The answers also do have odd wording - they refer to the bone itself "increasing", rather than its length, and the first answer's "for one centimeter increase" could be interpreted as either "for (one centimeter) increase", which lacks an article, or "for one (centimeter increase)", which is not ambiguous but not proper terminology either.
I think the design could be improved - first by avoiding the weird inverted question/answer position if at all possible, second by avoiding capital letters, third by using easier to parse wording:
"the predicted increase in height, in centimeters, for every one centimeter increase in the length of the first metacarpal bone"
"The predicted height increases in centimeters for one centimeter increase in the first metacarpal bone." (True, although the height also increases in any other unit for any amount of increase in the bone.)
"The predicted first metacarpal bone increases in centimeters for every centimeter increase in height." (Ditto, but this looks more correct because it has it increasing for every/any centimeter increase in height, rather than specifically one.)
Judging by the parent comment, I think they may have done the same, but failed to notice the correct interpretation? In any case, while as a native speaker, I only saw it that way for a few seconds, I can certainly imagine that someone speaking English as a second language could be thrown off.
The answers also do have odd wording - they refer to the bone itself "increasing", rather than its length, and the first answer's "for one centimeter increase" could be interpreted as either "for (one centimeter) increase", which lacks an article, or "for one (centimeter increase)", which is not ambiguous but not proper terminology either.
I think the design could be improved - first by avoiding the weird inverted question/answer position if at all possible, second by avoiding capital letters, third by using easier to parse wording:
"the predicted increase in height, in centimeters, for every one centimeter increase in the length of the first metacarpal bone"
It seems pretty poor to me. I would think the correct answer should be something like: "The expected height on in centimeters for any person with a first metacarpal bone length between 4 and 5 centimeters." That may not be perfectly technical wording, but I think it's the general message the line conveys.
Edit: Whoops, misread the question. I see it's asking about what the slope of the line means and not just what the line represents in general.
Edit: Whoops, misread the question. I see it's asking about what the slope of the line means and not just what the line represents in general.
It's a very twisted way of asking "do you know that slope is defined as 'rise over run'?"
My bad - made a mistake reading the question (see my edit above). But still, completely agree that the answers are worded very strangely. I think going for "real" math is a fine idea, but if the questions are designed as poorly as this one, it's going to become as much about reading comprehension as math.
Can someone explain why both answers A and B are not valid on the metacarpal problem? If the line indicates a linear relationship between these two values, and the choice of axis is arbitrary, it seems to me you could just as well predict one from the other as vice versa.
The line of best fit changes depending on the choice of independent variable, even for the same data. The quantity being minimized is different for the two cases. (sum of squares of vertical distances between the line and the data points vs. the same for the horizontal distance)
The question is very specifically about the interpretation of the slope, and because the slope would be different for the other case, only one of the answers is correct.
The question is very specifically about the interpretation of the slope, and because the slope would be different for the other case, only one of the answers is correct.
Sure, you could just as well predict one from the other. But the question asks "What is the following is the best interpretation of the _slope_ of the line of best fit in the context of this problem?", and you are expected to interpret "slope" in the usual jargon sense (as the the ratio of vertical change to horizontal change, rather than vice versa).
(By "vertical" and "horizontal" here, I mean with respect to the graph, not the interpretation, although it happens to be the case that the vertical axis corresponds to height and the horizontal axis corresponds to length.)
(By "vertical" and "horizontal" here, I mean with respect to the graph, not the interpretation, although it happens to be the case that the vertical axis corresponds to height and the horizontal axis corresponds to length.)
This then seems like less of a test of math ability and more of a test of whether or not you have effectively absorbed the jargon and conventions around certain math concepts. Maybe that's what they want, but it doesn't really seem like problem solving at all.
See my other response, but I don't think you're giving the question enough credit. The other responses don't mention the fact that the line would likely be different if we swapped the variables. The question tests both whether you know what a line of best fit represents, and also whether you know that the correlation in one direction is not necessarily equal to the correlation in the other direction. This is something that could be covered in an algebra class with a unit on linear regression. I remember seeing a demonstration and explanation of this in mine.
Except that there is no reason to choose the correlation in one direction versus the other in the given problem.
It's a bad question.
It's a bad question.
The definition of slope is an extremely basic fact from middle school math. This isn't exactly crazy trivia.
To be fair, knowing the jargon and conventions is almost just as important as knowing how to solve problems.
If nothing else, in college, most of the problems will be posed in terms of standard jargon and conventions, so it helps to know it.
If nothing else, in college, most of the problems will be posed in terms of standard jargon and conventions, so it helps to know it.
You're right that the graph contains the data for both A and B (and for that matter C and D as well) but the question refers to what the slope means. Here we have a Y = MX + B graph. M indicates how much Y changes for every 1 unit change in X.
So it's A.
So it's A.
Both answers are valid. This question would not survive the statistical norming process that the SAT uses to make sure that questions are "well-behaved" with respect to their answers.
By convention, X is supposed to be the independent variable and Y is supposed to be the dependent variable. Since it is not clear which variable really should be "dependent", the question would get thrown out.
By convention, X is supposed to be the independent variable and Y is supposed to be the dependent variable. Since it is not clear which variable really should be "dependent", the question would get thrown out.
It's very hard to be perfect when you want to get competitive while considering 'no-child-left-behind' in college education. There are many financial aids, the famous affirmative action, the public and private college system separation, local community colleges for some low-incomes, the rich pays more tax while the poor pays none, the K-12 for all etc are all into play, if those are not enough to care for the disadvantaged, we may just open the door to take whoever wants to get into which college on a lottery basis? do we really think that communism world has arrived?
In the 3rd question, if the fee were 6%, would the right answer be 7075 or 7076? I don't know the high school rules of rounding. Are you allowed to round to a number that doesn't satisfy the question? Fortunately they picked values where it is not ambiguous, but that question could be really nasty.
7075.471698 technically rounds to 7075. Less than 0.5, round down. 0.5 or greater, round up.[1]
But saying "what's the least" and then "round your answer" at the same time is silly. If you ask a student "each bus holds 10 people; how many buses do you need to move 32 people?" the answer is 4. I would hate to be asked to "round" that answer.
7075 rupees is too few; 7076 is the first whole number that is "enough."
The real meat of that question comes down to the student being able to figure out "do you multiply by 0.96, or do you divide by 1.04?" And the sample exchange with the fee is pure filler to distract the student.
EDIT Rerad Blackjack31's link, and you will find the original question, which isn't as butchered as it seems at The Atlantic. The present the example rate because they first ask the student to calculate the exchange rate. END EDIT
Plus, what about fluctuations in the daily exchange rate? The student is supposed to assume that isn't changing, but then why in the world are we talking about the daily exchange rate? Say it's a fixed exchange rate.
[1] I had a third grade teacher who insisted you could round to the tenths position and then the unit position, and always get the same answer if you just immediately rounded to the unit position. This is the test case that proves her wrong, but for some reason she didn't want to hear it.[2]
[2] I was in some ways a prat.
But saying "what's the least" and then "round your answer" at the same time is silly. If you ask a student "each bus holds 10 people; how many buses do you need to move 32 people?" the answer is 4. I would hate to be asked to "round" that answer.
7075 rupees is too few; 7076 is the first whole number that is "enough."
The real meat of that question comes down to the student being able to figure out "do you multiply by 0.96, or do you divide by 1.04?" And the sample exchange with the fee is pure filler to distract the student.
EDIT Rerad Blackjack31's link, and you will find the original question, which isn't as butchered as it seems at The Atlantic. The present the example rate because they first ask the student to calculate the exchange rate. END EDIT
Plus, what about fluctuations in the daily exchange rate? The student is supposed to assume that isn't changing, but then why in the world are we talking about the daily exchange rate? Say it's a fixed exchange rate.
[1] I had a third grade teacher who insisted you could round to the tenths position and then the unit position, and always get the same answer if you just immediately rounded to the unit position. This is the test case that proves her wrong, but for some reason she didn't want to hear it.[2]
[2] I was in some ways a prat.
I'm glad you pointed this out to your teacher. It is worth noting, though, that if it weren't for the arbitrary "If it's exactly halfway inbetween, you should just round it up" rule taught as received wisdom in school, your teacher would've been on stronger ground. And it is reasonable that they were attempting, in their way, to convey (or even fully come to terms with themself) the understanding that the nearest integers to a value are always also among the nearest integers to the nearest multiples of 0.1 to that value (and all the generalizations of this); it's just that sometimes there are other nearest integers to nearest multiples of 0.1 as well.
The "0.5 rounds up" is kind of arbitrary, but it has the advantage of "you only need to look one digit out to round."
4.49 obviously rounds to 4.
4.51 obviously rounds to 5.
4.50, since it "should"[1] follow the same rules as any other number that starts with "4.5", thus rounds to 5.
Say I were looking at a real number of arbitrary length, such that it starts with 4.500000000000... and maybe has a non-zero digit somewhere in it before it terminates. With the "round up on .5" rule, I don't have to keep on reading out indefinitely to round it.
[1] This "should" is assertion.
4.49 obviously rounds to 4.
4.51 obviously rounds to 5.
4.50, since it "should"[1] follow the same rules as any other number that starts with "4.5", thus rounds to 5.
Say I were looking at a real number of arbitrary length, such that it starts with 4.500000000000... and maybe has a non-zero digit somewhere in it before it terminates. With the "round up on .5" rule, I don't have to keep on reading out indefinitely to round it.
[1] This "should" is assertion.
This is not really a 'high school rule' but I am almost certain that in a standardized test like the SAT you should round up for such a question, and not round down to a number that doesn't satisfy the question, since that would just be logically wrong and fail to correctly answer the question.
This was the kind of tricky question that would often annoy me in high school or college tests since teachers and professors were not always good at catching such ambiguity and resolving it in the most logical way. Standardized tests are usually pretty good about this.
This was the kind of tricky question that would often annoy me in high school or college tests since teachers and professors were not always good at catching such ambiguity and resolving it in the most logical way. Standardized tests are usually pretty good about this.
Short answer - In general, item writers try to isolate one issue that they want to evaluate so that it is easier to determine where the knowledge/cognitive breakdown occurs.
Longer answer - According to test design principles, one would not use initial values that would lead to a potentially ambiguous rounding issue unless you were specifically testing the knowledge of rounding. In this particular case, there are much better ways to test knowledge of rounding than a two-step problem like the one your proposed.
Longer answer - According to test design principles, one would not use initial values that would lead to a potentially ambiguous rounding issue unless you were specifically testing the knowledge of rounding. In this particular case, there are much better ways to test knowledge of rounding than a two-step problem like the one your proposed.
On the posted question, I don't understand why only A is the right answer, when B is also correct. The two quantities are correlated, so having any one of the two lets you predict with some margin of error the other.
You are right about being able to predict either, but the specific quantity described in A is the slope, while in B it is the inverse of the slope.
Am I the only one who clicked this thinking it was a boolean satisfiability challenge?
Here's a 200 page PDF on the new format with lots of sample questions: https://www.collegeboard.org/pdf/sat/delivering-opportunity/...
The sentence completions are gone; now we have words in context. Essay is twice as long. No independent writing section. Math is more algebra and prob/stats focused, especially with graph and chart interpretations. Geometry has been all but eliminated, coming in at 6 total questions in the Additional Topics in Math (paraphrasing) category.
In my view, the main issue with this exam is that it's more coachable now. I feel you can learn less math/reading/writing now and just exploit the nature of the SAT to do well on the new exam. Good for test prep, not so great for everyone else. The main issue is that you kind of have to dumb yourself down to answer the questions - if you start actually thinking critically, you'll run into trouble.