Why don't you read the doughnut question and tell me what your opinions are....
This is one of the most famous SAT questions. It's called the doughnut question. And it shows you a doughnut. In the figure above, what is the greatest number of non overlapping regions into which the shaded region can be divided with exactly two straight lines? And people use this--we used this at the kick off news conference that launched Fair Test way back in 1985. And David Owen, who wrote the book None of the Above, showed this to the assembled 40 or 50 press people in the room--who ooed and awed at it. Fifteen years ago, people hadn't seen this. And how simply you solve it, if you have been well- coached.
You read it, what is the greatest number? And you see that, well, this is the last math item in this section. Therefore, it's a very difficult question. You know from looking at the SAT that on every SAT section, exception for memorizing comprehension, items go from the easiest to the hardest. So at the beginning of the section, an obvious answer is right. At the end of a section, an obvious answer is a distracter. It's wrong. You never go for it.
And what coaching courses like the Princeton Review and others teach you, is that you can analyze--without knowing how to solve the problem, you can have a very good chance of getting the right answer. You look at it and say, what is the greatest number? Well the greatest number in the answer's six. That's wrong. That's the distracter answer. It's designed to take somebody who doesn't understand it and make him guess wrong. But you look at it and say, well, the simplest thing I can do is I can divide it into four pieces by cutting vertically and cutting horizontally. But that's too easy too. That's got to be wrong. But I could get four. So, I must be able to get three or two because they're smaller than four. And six is wrong because it's the easy answer. The answer's five. That is the right answer.
I now know how to draw the lines so you can do it. You draw them so they intersect in the middle, inside of the doughnut. So you get two very small triangles and some large ones. But you don't have to know how to solve that problem. And it has nothing to do with math. It has nothing to do with aptitude. And it most certainly has nothing to do with merit. Unless you define merit as being coached.
Can you walk us through a question from the SAT?
P, Q, R and S are four towns. P is farther north than Q and R. S is farther south than P. Q is farther south than R. Which town is the farthest south? P, Q, R, S or, it cannot be determined.
What kind of a question does it strike you as?
A, very coachable. B, not really math, certainly nothing you learn in high school and nothing that will be useful in college. Plausibly a little bit of logic, I'll accept that. But I think more, just a little trick.
It's the kind of thing they do a lot. There are three towns--A, B and C. The distance from A to B is four. The distance from B to C is three. What's the distance from A to C? And of course if you're kind of linear, you would say, well it's seven. It's the two together. But of course, they don't have to be in order. So it could be one. Does it measure what you learned in high school? No. Is that useful in college? No. It's a little trick thing. You'll get it wrong once. Someone will explain it. And then you'll be ready for it.
Why develop a question like that if it's only measuring a test-taking technique?
Because the point of writing an SAT question is not measuring what you learn in high school or how well you'll do in college. It's separating out kids. There are kids who will get that right. And they're generally the kids who have been in math courses where they play with this kind of stuff. Which is to say, upper income. And there are kids who will get it wrong because they don't play with this stuff.
So the question is very good at separating kids. And that's why they have it here.
Money is to bank--a little socioeconomic problem here, but let's go with it--money is to bank, as food is to basket, park is to city, cash is to store, book is library and article is to magazine.
So what you're supposed to do is say, I put money in a bank. And I guess money is kept in a bank in the same way that a book is kept in a library. Maybe it's a vocab question. Do you know the word bank or the word money. I can't believe that it's a logic question. And I can't believe the kid who gets that right is going to be better in college than the kid who gets it wrong. Especially since there are some wrong answers that are pretty attractive here. You know, you sort of think of banks and money. And there's an answer with cash. And you sort of--you know, you're stressed. This is important. You're in a rush. You're in the middle of the SAT, which is a pretty important test. It's nine in the morning on a Saturday. You're probably hung over. And a lot of kids who get that wrong--it's not because they don't speak English. And it's not because they won't do well in college.
Our experience is, a kid who doesn't do well on the SAT--it's not because he gets the toughest questions wrong. It's because they make lots of careless mistakes on easy questions. They get sucked into trap answers a lot. Because they don't have their footing. They don't understand the question. It's not that they can't do it.
So a lot of the course isn't focusing on the toughest questions. It's focusing on making sure you don't get that question wrong.
The doughnut question....
You got a doughnut here. And the question reads: "In the figure above, what's the greatest number of non-overlapping regions into which the shaded region--the doughnut--can be cut with two straight lines? In other words, how many pieces can you cut the doughnut into with two straight lines?"
This is the last question on the test. It's Saturday morning. You're very stressed. You're very tired. And this is really important. So what Joe Bloggs does is, he'll just cross lines. Right? The easy answer there is four. I can make four pieces pretty easily. What are the odds that on the toughest question on the SAT that you've done enough work? Right? They're zero. No way.
And again, a good test-taker's sitting there. And he answers four and goes, god, there must be tougher than this. And he's right. So you cancel four. And of course, since you're able to get four, you cancel three and two also. That's not the greatest number you're able to cut it into. You're able to cut it into at least four. The answer's got to be five or six. And then you sit back for a second and you say, what else would Joe Bloggs do? He'd say, well, they want the greatest number possible. So maybe it's six. Maybe it's the greatest number. So it's not that either. The answer's got to be five.
On the one hand you might way, well that's kind of a goofy way to take the test. That's all testmanship. On the other hand you might say, what is this question telling you about a kids math skill or his ability to do college level work? This is just a good question. And goofy questions deserve goofy preparation.
Here's another one. There are 3 roads from Plattsville to Ocean Heights. And 4 roads from Ocean Heights to Bay Cove. If Martina drives from Plattsville to Bay Cove and back, passes through Ocean Heights in both directions and does travel any road twice, how many different routes for the trip are possible? 72, 36, 24, 18 and 12?
Like, what is this telling you about your son. Like, is it telling you he's stupid that he got it wrong? Is it telling you he shouldn't go to college or he should? What is it telling you? And I would claim it tells you almost nothing. A great question for Games Magazine but a lousy question for Harvard.
Could you look at the doughnut question and tell me what that question is measuring?
In the figure above, what is the greatest number of non-overlapping regions into which the shaded region can be divided with exactly two straight lines? And it gives you four choices.
What it's trying to do is measure mathematics reasoning, spatial relations and one's ability to conceptualize.
Anything else? Is that a true test of how one will perform in college? Should an admissions officer use that information in choosing between candidates?
Well, hopefully no one will base any decisions on a single item on a single test administered on a Saturday. That's why our tests have about 60 mathematics items and 70 verbal items. So--no, an admissions officer should not base any decision on a single item. And what we try to do it state further than no one should base any decision on a single test score. They should use a lot of information.
But what we're trying to do is, we're trying not to recapitulate or repeat the types of computational basic skills, items in terms of addition or subtraction or dividing. What that type of an item and many others on our test are trying to do is, going beyond simple computation. Look at critical thinking skills and reasoning ability. Some of it's visual and perceptual. And others are simply mathematics and the ability to look at analogies or look at memorizing comprehension's and draw meaning from the text.
Are you saying that it's basically not fair given the differences in society?
I'm saying, given the differences across different groups in every way we want to measure it, whether we measure it with the SAT, with the courses taken, with high school grades, college grades or graduation--those differences exist and they exist in any measure that we have including the National Assessment of Education Progress at fourth grade and beyond.
And so when you're prohibited from looking at race and ethnicity--when those differences are so much a part of educational opportunity, of opportunity to learn and of quality of education and teaching--it really is a crime.
What the crime is, is not that the SAT is used for admissions. The crime is that courses like the advanced placement program, qualified teachers, the opportunity to be engaged in more rigorous courses and be expected to perform at higher levels--that opportunity is not uniform across all schools and across all communities, irrespective of where one lives.