Why don't you read the doughnut question and tell me what your opinions
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
reading 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
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
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
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
Could you look at the doughnut question and tell me what that question
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
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 reading comprehension's and draw meaning from the text.
Are you saying that it's basically not fair given the differences in
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.
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test score gap |
getting in to berkeley |
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