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THE WHITE HOUSE
Office of the Press Secretary
For Immediate Release
October 20, 1997
PRESS BRIEFING BY
SECRETARY OF EDUCATION RICHARD RILEY
The Briefing Room
1:12 P.M. EDT
SECRETARY RILEY: Thank you so much. I just have
returned from traveling with the President to Brazil, and some of you
were there, and I'm here today to release a major report and also to
brief you on the week ahead -- this is a very important week, as you
know for education -- on the President's education agenda.
The President, as you know, used his Saturday morning
radio address to praise a bipartisan effort to support charter school
legislation that is now moving through the Congress. He also used
the radio address to endorse another bipartisan legislative
initiative that is being led by Congressman John Porter and
Congressman David Obie to fixing failing schools. We know how to fix
failing schools, and the Porter-Obie initiative is targeted funding
to help get that job done.
Now, today we're releasing a major report entitled,
"Mathematics Equal Opportunity." That conveys three powerful
messages: first, that young people who go on to college, by
overwhelming numbers -- 83 percent -- take the serious math courses
like algebra I and geometry. Second, that taking these gate-keeping
courses is especially important for low-income students. Seventy-one
percent of low-income students who took algebra I and geometry went
on to college, compared to 27 percent of low-income students who did
not take these courses.
Now, I just met with a group of young people from Prince
George's County who were part of the College Board-sponsored Equity
2000 Initiative to get more young people to take algebra early.
These young people have gotten the message that getting ready for
college is their responsibility, and that means taking the serious
math courses.
But we need to make sure that everyone gets this
message. Only 63 percent of all young people take algebra and
geometry, and only 43 percent of low-income students take these math
courses. And that's precisely why the President has called for
voluntary national tests in 4th grade reading and 8th grade math.
I assure you that these tests will shake up the status quo and will
make things happen.
The third message of this report is that taking the
right courses is more important than what type of school you attend,
whether it's public or private. The latter point, I think, deserves
some attention. Many voucher proponents argue that giving parents
public tax dollars to send their children to private school is the
key to educational renewal.
This report says there is a much more important choice
that's being overlooked entirely, and that is the choice of courses.
That is a choice, also, and a very important one. Taking the right
courses matters a lot more in terms of going to college than whether
your school is private, public, or parochial. There are very good
schools in all categories, as we know, all across the country and
mediocre schools and others that need a lot of help. But the type
school that a child attends turns out under these numbers not to be
as significant in terms of going to college as to the choice of
courses they take.
Now, let me go on and tell you a little bit about the
rest of the week, then I will respond to questions. Tomorrow, the
President will meet with college and university leaders who have
endorsed his America Reads challenge. We have thousands of energetic
college students signed up to be reading tutors and ready to go, and
we're excited about that.
We also want the Congress to act on the President's
request for legislation. I'm concerned that the House is starting to
get stuck in the usual partisan rut and losing sight of what is
really important in education. I think it's a sad day when a reading
initiative, a reading initiative, becomes a political pawn because
some members of Congress do not support the President's call for
voluntary national tests in reading and math.
Now, making sure that all of our young people are
literate is a grand goal that has full support of the American
people. Congress needs to fulfill its part of the bargain. Let's
remember that the reading initiative was part of the budget
agreement. And for his part, Vice President Gore, then, will be
visiting Louisiana State University and give a major address on race
and education at Southern University Law Center.
And on Wednesday, I will join Larry Summers, who is the
Deputy Secretary of the Treasury, at a press conference with
Representative Charlie Rangel to once again reaffirm the
administration's strong opposition to the Coverdell IRA-education
proposal. The Coverdell proposal is bad tax policy. It is outside
the balanced budget framework, and it has little if anything to do
with improving public education.
On Thursday, the President, the Vice President, the
First Lady and several members of the Cabinet, including Donna
Shalala and myself, will participate in the White House Child Care
Conference. Then on Friday, both the President and the Vice
President will once again focus on education. The President will
meet with several hundred teachers who are part of the effort
surrounding the National Board for Professional Teaching Standards.
The President's goal, as you've heard, is to have 100,000
board-certified teachers in the next 10 years.
For his part, Vice President Gore will announce a new
public-private partnership to match computers donated from federal
agencies to low-income schools. Now, this is a very busy week for
the administration when it comes to education, and that's the way it
should be. Education is President Clinton's number one priority, and
we need to pick up the pace in order to get all of America's children
ready for the 21st century.
Education matters to parents all over America, and the
President is determined to get things done. The President's
education agenda is comprehensive and it gets to the heart of the
issues that need to be resolved to improve American education --
things like higher standards, better-trained teachers, safe schools,
computers in the classroom, more accountability, more public school
choices, and an absolute commitment to making sure that all of our
children -- all of our children -- have mastered the basics once and
for all.
My biggest concern is that the Congress is fiddling at
the margins and not focusing on these essential and central issues
that define American education. The President wants some action and
I think that the American people want to see some movement as well.
The administration is prepared to work with the Congress
in a
bipartisan way, but we do need to get on with the business of
improving American education.
Now I will be happy to respond to any questions.
Q
Secretary Riley, is the President still committed
to vetoing the D.C. appropriations bill if there are these vouchers
included in there?
SECRETARY RILEY: And we just got back from South
America, you and I, and I'm not positive if there's been any
statement in the last day or so. As I recall, certainly senior staff
has indicated that they would recommend that the President veto that
if that measure is in there, and I think that's where the status is
right now.
Q
Could you explain in your own words, obviously, why
poor children in the District of Columbia would be denied the
opportunity to go to a better private parochial school or to go to a
suburban school, that the President would take this opportunity away
from 2,000 poor kids in the District of Columbia?
SECRETARY RILEY: Well, I would be glad to. First of
all, we're into trying to help solve problems, to build better
schools, to help states and school districts and schools get better.
The idea of giving someone a ticket out of the school solves no
problems whatsoever. It is a non-solution to major problems. We
know what to do to improve schools. We could take that same $7
million that they propose to come in and pay for vouchers for 2,000
children and impact in a very significant way probably as many as
40,000 children. Having school reform measures like the Slavins
program and Comers program and others, and new American schools, all
of those efforts that are there waiting to come in -- we're doing
that, by the way, in a number of elementary schools here in
Washington, D.C., and I think we're seeing some real positive
results.
So what do you do? You pull 2,000 kids off, and who
decides who it's going to be and where they're going to go? They'll
be going to some -- perhaps many of them -- to a parochial school, a
religious school. So the answer that they have in there is some
governmental body appointed by the House and Senate and the President
comes in and says this religious school is all right, this one isn't.
Or do they say all of them are all right? Or who is to judge? Once
you get into that judging process, you have made them public. That
doesn't help private and parochial education. I strongly support
quality private and parochial schools. But the idea of siphoning
people off to an unidentified place chosen by public officials to me
distorts the great mix we have now with public, private and
parochial. Now, the idea of improving the schools in Washington,
D.C. is very important, and all of us ought to be into it, especially
those of us in the federal government. And we are, ourselves, into
it and we are prepared to get as much into it as the Congress would
enable us to.
We think that we could really make a big difference, and
that is, as I say, beginning to happen. But vouchers would in no way
solve any of the problems in the Washington schools.
Q
Mr. Secretary, why is it okay for the President to
threaten to veto the education appropriations bill, but it's
outrageous, in your view, for Congressman Goodling to threaten the
America Reads program over the national standards and tests policy
dispute with the administration?
SECRETARY RILEY: Well, you know, you have a reading
proposal that I think everyone is ready to get busy on. We have
these college students that are ready, we've got grandparents and
senior citizens, we've got teenagers -- everybody is excited about
the reading program. And to say that somehow it's going to help
education by holding that up or holding it hostage because the
President wants to have a voluntary testing program tied to NAEP --
NAEP is in all 50 states now, it's a sample test. We're simply
saying to make the sample test individual so a parent can see how
well their child is doing in very basic skills -- not in
controversial subjects; we're talking about reading in the 4th grade
and math in the 8th grade with algebra, just like this study says is
so important.
So we think that's a very clear, clear issue and to tie
then the reading measure to that is certainly not any way in the
world to interpret that as being helpful to education. Then, when
you look at vouchers, in my judgment, vouchers are harmful to public
education. I think they've harmful to private and parochial
education, too, as I've just said. You need -- something that you
think is harmful to public education I think you should veto, and
that's what I would advise the President to do.
Q
Secretary Riley, in terms of the economics of a
family budget, if vouchers were to go through as they've been
proposed in various forms, could they ever provide a school
opportunity to a very poor family that would need to use only the
voucher to finance the education of their child, or would vouchers
even, under the best of circumstances, only be a subsidy to families
that are already better off?
SECRETARY RILEY: Well, I think that's a very good
question and, of course, the answer would be mixed. Some families
would be totally dependent on the voucher, they would have certain
serious limitations of choices then as to what the voucher would
afford. Others who could afford private school can make a very good
argument that if you're going to give the person sitting next to me a
voucher, then I'm entitled to one, too -- that person might be poor,
also.
So, I mean, you start getting into this very mixed up
and confusing interrelationship; you're mixing up public and private,
and religion. It's clear to me that if you are a very poor person
and you are uneducated, and you are subject to entrepreneurs and you
have a voucher for $3,200, that, too, worries me as to who could
convince you to come to their school, or whatever. I think the whole
scheme is just replete with problems and, as I say, I think it is
harmful to the public schools and the private schools, also.
Q
Mr. Secretary, I have a question about this report
that you're putting out today. It's sort of a chicken and egg
question. Doesn't it seem common-sensical that students who plan to
go to college would take algebra and geometry and students who don't
would not, and so that's what your study shows, rather than showing
if you take algebra and geometry, that somehow propels you to go to
college?
SECRETARY RILEY: Well, I think that's right if you had
children making adult choices very early. And the problem is, we
need in the school systems in the states and the school districts and
the schools need to let children know very early that we expect more
of them. We expect them to think about college.
An awful lot of kids are either told or signaled at a
very young age that they're not college material, that's for someone
else, way before they have had a chance to prepare themselves to go
to college. So I think the schools need to take all young people and
make them think better of themselves and make them have higher
expectations about what they can do.
And then when they approach middle school, we do very
well on the early basics. The TIMSS test
4th
grade showed we were second in the world only to Korea in science --
in the 4th grade. That's poor children, wealthy children -- to hold
this very diverse, large country.
Then you get on up into the 8th grade; we drop down to
where we're just about barely average. So we're very high in the 4th
and we drop down to about average in the 8th grade.
So what happens between the 4th and the 8th? Well, in
math, our observation is -- and some of these studies are showing it
-- we just kind of continue on with arithmetic, and let's wait -- you
might, can't handle anything more than that. Of course, we used to,
unfortunately, have tracks into general math, or whatever, which was
a ticket to nowhere.
So what we think is that counselors, people who are
planning for schools' curriculum, course work and so forth in the 7th
and 8th grade should realize the very serious importance for all
children taking algebra in the 8th grade. If they do, it then opens
up the 9th grade for geometry. And then if they want to go on to
advanced math, the door is wide open to do that. If they don't take
algebra in the 8th grade, they get on into high school and it's
amazing how that just pulls the curtain down on their future. We
think that's very good information.
But to say that a young child who is planning,
themselves, to go to college so they choose to take algebra is
probably right, but then there's another 75 percent of the children
out there who should be told that if they work hard, if they take
these tough courses, they, too, can go to college.
Q Mr. Secretary, what significant opposition is there
to broadening the offering of algebra in the 8th grade, and how does
that in any way relate to the President's push for national student
tests?
SECRETARY RILEY: Well, it relates a lot. First of
all,, there's no real opposition, but only 25 percent of American 8th
graders have had algebra. And in Japan it's 100 percent. There's a
reason for that. The Japanese have very clearly figured that out,
the very thing that this longitudinal study shows. So we think that
is very, very important to get that 25 percent to 100 percent.
That's one thing.
And then you ask how does it connect up with the
President's test? It's very clear. The test in the 8th grade is
tied to NAEP. NAEP then has algebra and some geometric principles in
the 8th grade test. That's what the sample test is now. It's not
like we're adding anything new. But then, obviously, if the test
then is a national test, states decide to take it, school districts
decide to take it, then they'll say we've got to prepare these
children to be able to take algebra in the 8th grade. And they
should. And that's then -- we see a very powerful focus then being
made on reading in the 4th grade, math in the 8th grade including
algebra, and that that will just have all kinds of good results in
this country, by focusing school districts and schools on those two
subjects at those grades.
Q You would use the test then to encourage the
broadening of 8th graders taking algebra. But is there not another
way to do that? I mean, if this is standard knowledge, the benefits
of it, why don't schools adopt it more on their own? Why is the test
necessary to increase --
SECRETARY RILEY: Well, the test -- and you're asking a
very good question, because it gets to the real root of why the test
is important, to me. The test focuses the nation -- the nation --
not a school, not your child, or whatever -- you get the information
on your child, but it focuses the nation on a priority. And the test
doesn't tell you how to teach math, it doesn't tell you what you do
to prepare for it or whatever; all it tests is what you know. Then
the school district and all decides that. But if it's a national
test and Americans have bought into it, that all of our children
ought to be able to read independently by the 4th grade, do basic
math by the 8th grade including algebra -- if that's done, I'll tell
you it would be revolutionary in terms of the success we would have
in education. So I think it's enormously important.
Q Mr. Secretary, maybe I'm dense, but isn't it the
obvious that if you achieve within -- every teacher sets out a lesson
plan and says this is what you need to do to master this particular
subject, is it absolutely necessary that a national test be adhered
to in order to know what the obvious is? You ought to know if your
kid is achieving or not in a particular subject.
SECRETARY RILEY: Well, there's two ways to look at
that, too. You know, you've seen the chart we've had looking at
various states on the NAEP test, but the NAEP test which is given out
there now and looks at in a sample way -- you understand, just a
sample test. If you took the test you might take one-seventh of it
and you come out with a national average. This test you take the
whole test and we know how you stood on math in 8th grade and reading
in 4th. But NAEP then looked at the various states and it looked at
-- I'm reluctant to call states, but one was South Carolina, one was
Louisiana, Wisconsin, as I recall -- the local test there said
reading in the 4th grade up in the range of 80 percent proficient
readers. That's the state test.
NAEP, the national sample test taken in the same state,
said it was in the range of 15 percent to 20 percent. And don't hold
me to the exact numbers, but I've got the charts. But that came from
the NAEP test.
So you see, a kid, then, in one of these states could
think -- their parents could think they're reading wonderfully well.
Compared to a national scale, they are doing very poorly and they
don't know it. And what we are saying is, there's no reason in the
world to keep that information from a parent. And people say, well,
you know, children over here in a poor section don't do well, so why
give them a test? Well, that's a terrible thing to say in this
democracy. You give them a test because every child there is
important and every child there must know how to read and every child
there should know basic math and algebra in the 8th grade. And every
individual there is important, and don't group this school, or it's
done poorly or whatever, and say it's that way, so let's get over
here and worry about college.
So I think it's very, very important to single in on
every child and then to have a national challenging test to raise
those levels of interest. And I'll tell you this: When the test is
given, there are going to be a lot of disappointed, concerned people,
because it's a high challenging test.
Then, that's when the important part comes. That's when
the system reacts to the tests, and the parents say, wait a minute,
my child's in the 4th grade and can hardly read. Then, the school
district and the school can all come together. You look in Seattle.
I was so pleased reading an article in Seattle the other day.
Seattle gave a tough test. And I mean it was -- everybody was very
concerned about it. They did poorly; a lot of kids did poorly. So
the reaction was very positive. Not criticize the children, not kill
the test, but let's improve the schools to where the kids do well in
the test.
Q
So you have all these battery of tests that
students are already taking. How could they possibly be so out of
whack with what should be obvious levels of achievement?
SECRETARY RILEY: Well, they are.
Q
In that test I think --
SECRETARY RILEY: I know. And the fact is they're all
over the ball park. Delaware's local test is much harder than NAEP.
I mean, you could test in Delaware reading basic, and in NAEP you
would be reading proficient. You see what I mean? Delaware is way
up here and Louisiana is down here. That's just the way it is. So,
really, it makes a lot of sense to have a national test so everybody
will know how their children stand, teachers will know what basic
improvements are needed, but the important thing is to focus the
nation on these basic skills of reading and math.
Q
Mr. Secretary, two questions about the national
test. Number one, a few minutes ago in making the case about why the
administration opposes the voucher program for Washington, D.C., you
said essentially we know where the problem is and we know how to
better spend the money to solve the problem in this Washington, D.C.
Isn't that precisely what opponents of the national tests say, that
we ought not spend the money, we know how to fix schools and the
money would be better spent fixing the schools rather than testing?
That's number one, and I've got a follow-up.
SECRETARY RILEY: Let me follow that again. You say the
opponents of testing --
Q
Yes, the opponents of testing say we don't need
tests, we know how to fix schools --
SECRETARY RILEY: Yes, the answer I just gave -- let me
answer that first -- that I gave this gentleman is the answer to that
in my judgment, every student is important. And if you say this
school does poorly, why test the children; they're poor, so don't
worry about them.
Q
What they're saying is don't spend the money on the
test, apply the money that you would have spent on the test to fixing
that school. Bypass the test, go in and fix the school.
SECRETARY RILEY: I guess it was Deming who said, you
can't improve something you can't measure. Really, measurement is
very, very important -- real measurement. If I'm a parent and my
child is in that school and they say, you know, we don't need to test
your child, we know he's going to do poorly; well, I want to know
that. And if he does poorly, I want to know how. What is he weak
in, in reading? What is he weak in, in math?
Every parent's entitled to that in this country, in my
judgment and not to be grouped into some -- you're in this poor
neighborhood, so we know you're going to do poorly, why test you?
That's not fair to any child in that neighborhood.
Tell me the other.
Q
The second question, if I could follow up, which is
-- you talk about how, once you did the national tests, that will
force school districts -- "force" is my word, not yours --
SECRETARY RILEY: Challenge --
Q -- to change their curriculums in order to better
-- to do better on the test. Isn't that precisely what opponents of
the test fear, that it becomes the federal government's through its
test, forcing alternations in local school district policy? You say
for good reasons; they say for bad reasons.
SECRETARY RILEY: Yes.
Q
Isn't that the nub of the debate?
SECRETARY RILEY: Well, of course, what I say is that we
don't tell them how to teach reading. All we propose is to test can
the child read. And if they -- you can have two completely different
ways of teaching reading. And you can look, then, if this child can
read and this one can't, then that's good information for them. We
don't say which is best or which is worst; all we propose to do is to
test the child in reading, which is a very basic skill, we don't get
into history and science and some of those very controversial
ideological things; basic skills -- you either read or not. And
then, with math it's the same way, and algebra. So we say it's very
basic skills and it's a very fair way to look at it.
And you say -- some say that that might control
curriculum, and all I say to that is we don't get into curriculum at
all. All we test, all we propose -- and it's voluntary. If somebody
is worried about that, all they have to do is say we don't want the
test. We think it's going to catch on and we think the people in
this country are going to almost look at it as a patriotic thing, to
get involved in getting this country to read well, getting this
country to do math well, and getting our children ready for college
and important jobs.
Q
But you do think it will influence curriculums,
sir, when you said a moment ago these tests will shake up the status
quo and make things happen.
SECRETARY RILEY: Absolutely.
Q
Well, then --
SECRETARY RILEY: Well, I'm saying we don't control
curriculum. We're looking at can a child read, and if a child can't
read it ought to shake up something. There's curriculum, it might be
text books, it might be teacher preparation, it might be parent
involvement, it might be technology, it might be violence in the
school, drugs, construction. It will shake up something. And we
want something shook up. That's what we want to do because if
they're not reading then something needs to happen. But we don't get
into curriculum. I want to make that clear, and I'll get 7,000
letters. We don't get into curriculum; we simply propose to measure
basic skills, what they can do, and not how they learned it.
Q
Where are the teachers unions with you on this?
SECRETARY RILEY: On the testing? I think they support
it. I think they -- as far as I know, they -- I was trying to think
-- there's two of them and I know the AFT -- I think both teacher
organizations support the testing proposal that we made.
Q
Secretary Riley, since you say mathematics is the
opportunity, speaking at today's event, why is it that your office
hasn't mandated algebra and geometry for every child?
SECRETARY RILEY: Because our office cannot do that and
we would not like to do that. Education is, as I've said many times
to you all and to others, is a state responsibility and it's a local
function. The control of education is in the state, basically under
our system. It's very similar to Brazil, by the way, which was very
interesting, and in my trip to Brazil that's all they wanted to talk
about, was education. But it's a state responsibility. It is
illegal really for us to put out a federal curriculum.
So we want to do things to help the states and help the
school districts, and measurement is one of them. We think that is
real accountability. Anybody who is into accountability ought to be
into true measurement because that makes -- that encourages,
challenges states and school districts to improve their schools.
Q
Secretary Riley, can I ask a follow-up to an answer
you gave to Leo on vouchers? Do you think private and church schools
really will try to scam people out of their vouchers? And also, did
you mean to suggest that poor people aren't bright enough to know
that they're being scammed by these schools?
SECRETARY RILEY: No. I started off saying that I've
got great confidence in private and parochial schools. Some of them
are the highest quality schools in the country. And we are involved
with them in some ways, as you well know, with Title I and we've been
all through that Aguilar versus Felton. But if you have a private
school and you've got a voucher, then there is a complication in
making that -- keeping that private or having public accountability.
I mean, I think anybody can see that. That's not saying anything
about any strong private or parochial school.
But a lot of the stronger schools, of course, charge
more than $3,200 a year tuition. Some of them don't. Some of them,
they could come within that range, and some of those are full. But I
still say -- and I don't want to in any way infer that private and
parochial schools are any kind of a bad choice. I think it's a
wonderful choice for people to have, but I think they ought to stay
private, stay parochial, and that vouchers is a very bad system.
And I don't quite understand what you're saying, but if
you have -- I do think this -- that if you have poor people with a
voucher, it certainly could cause entrepreneurs to then try to move
into that zone. Now, that's not to say those good private and
parochial schools -- I'm not talking about them, obviously. I have
to handle higher education gate-keeping, and it is hard. I've had to
close down -- not close down, but deny federal funds, Pell Grants and
so forth, student loans, to, like, 700 colleges and universities and
schools. And it, in substance, closes them down. And that's hard.
That's a job, though. That's connecting up with them. And I don't
know how that would be done on a K through 12 system, but that's the
problem in higher education. Some of those schools aren't schools at
all and we have to then come in and say that. And that is very, very
difficult and it's an accountability responsibility that is very,
very difficult.
Q Can I just follow that last point? So, as a matter
of principle, the principle of the federal government subsidizing
colleges and universities, private and parochial schools at the
college level, it's okay, but it's not okay as a principle, assuming
you could get around this one issue that you just raised, in
secondary or elementary schools?
SECRETARY RILEY: It's two totally different things.
The state constitutions primarily, or state law -- usually, it's the
state constitution -- says that the state will provide free public
education for every child in the state. That, of course, under court
interpretation is K through 12. That is the state's responsibility;
not the federal government, but the state. And it covers all
children. It covers disabled children; it covers brilliant children;
it covers whatever.
And then after grade 12, there's no such state
constitutional or legal requirement to provide free public education.
So in higher education, you get out of the 12th grade, then our
programs deal with the individual. They're adults then, too, but
there's no state control of the system and the state responsibility.
So as far as a child going to a religious school in college, it's no
different with us -- we deal with the child -- than if they're going
to a private school or a public school. But it's totally different.
One is K through 12; that's state. And the other is adults who are
not in the state-protected system.
Q
What do you think of the salaries college
presidents are getting, Mr. Secretary? Did you read about that? Did
you read about these high salaries these college presidents are
getting?
SECRETARY RILEY: I haven't, no. Something recent?
Q Yes.
MR. MCCURRY: It looks like a good line of work, though.
(Laughter.)
SECRETARY RILEY: I recommend Mike -- (laughter.)
THE PRESS: Thank you.
END
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Final
MATHEMATICS
EQUALS
OPPORTUNITY
White Paper prepared for
U.S. Secretary of Education Richard W. Riley
October 20, 1997
OF
* UNITED STATES OF AMERICA *
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A Letter from the Secretary of Education
Many parents, students, and educators in the United States are beginning to understand that
mastering mathematics is a gateway to college. The key to the "gate" is taking algebra or
courses covering algebraic concepts by the end of the 8th grade. However, many 8th and 9th
graders may be behind in their course taking to get on the road to college.
Recent analyses by the U.S. Department of Education indicate that high school students who take
algebra, geometry, and other rigorous mathematics courses arc more likely to go on to college.
This is true regardless of their family income. In fact, the benefit of taking rigorous courses is
greatest for students from low-income families. Students who take chemistry, a subject that
requires a firm grasp of mathematics, are also more likely to go to college. Other research tells
us that the advantages of a solid mathematics background are not limited to the college bound.
Workers who have mastered mathematics earn more and are less likely to be unemployed than
workers who are less proficient in mathematics.
However, not all students have access to rigorous mathematics courses -- either because their
school does not offer everyone a full selection of challenging courses, or because not all students
are prepared for and encouraged to take them. The results of the recent Third International
Mathematics and Science Study (TIMSS) confirm that many students enter high school without a
solid grounding in mathematics, closing doors very early for further education and better careers.
The implication is clear: The 8th grade is a critical point in mathematics education.
Achievement at that stage gives students a leg up on taking rigorous high school mathematics
and science courses important for later success.
As a nation, we must ensure that all our students develop the mathematics foundation they need
by the end of the 8th grade--and then build on it throughout high school. We challenge parents,
schools, community groups, higher education, and employers to ensure that all children have
access to rigorous mathematics courses and a chance at college. The U.S. Department of
Education stands ready to assist them by providing financial aid to college students and
supplementing Advanced Placement Exam fees for students who demonstrate need.
Additionally, the Department provides funding through Title 1 and other programs of the
Elementary and Secondary Education Act (ESEA) to assist schools in upgrading mathematics
teaching and learning nationwide. It is also offering a voluntary national test in 8th grade
mathematics, so that parents and schools can benchmark their students' performance. Together,
we will help to ensure that all students arc given the opportunity to excel.
Sincerely,
Richard W. Riley
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Table of Contents
Page
Executive Summary
3
Mathematics and Future Opportunities
5
The Importance of Mathematics for College Entrance
5
Mathematics in College the Workplace, and the 21st Century
9
Middle School: Getting on the Road to Challenging Mathematics and Science Courses
12
Laying the Foundation
12
Course-Taking Patterns in Middle School
13
Parent and Student Attitudes about Mathematics and Science
14
Mathematics in the U.S. Today
16
International Comparisons of Middle School Mathematics and Science
Proficiency
16
Promising Practices
18
Next Steps
24
Six Things Educators, Policymakers and Community Members Can do
24
Six Things Parents Can do
24
Resources
26
Appendix
28
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Executive Summary
In the United States today, mastering mathematics has become more important than cvcr.
Students with a strong grasp of mathematics have an advantage in academics and in the job
market. The 8th grade is a critical point in mathematics education. Achievement at that stage
clears the way for students to take rigorous high school mathematics and science courses-keys
to college entrance and success in the labor force. However, most 8th and 9th graders lag so far
behind in their course taking that getting on the road to college is a long way off.
This report highlights the following findings:
Students who take rigorous mathematics and science courses arc much more likely to
go to college than those who do not. Data from the National Educational Longitudinal
Study (NELS) reveal that 83 percent of students who took algebra I and geometry went on to
college within two years of their scheduled high school graduation. Only 36 percent of
students who did not take algebra I and geometry courses went to college. While nearly 89
percent of students who took chemistry in high school went to college, only 43 percent of
students who did not take chemistry went to college.
Algebra is the "gateway" to advanced mathematics and science in high school, yet most
students do not take it in middle school. Students who study algebra in middle school and
who plan to take advanced mathematics and science courses in high school have an
advantage: approximately 60 percent of the students who took calculus in high school had
taken algebra in the 8th grade. However, 1996 NAEP data reveal that only 25 percent of
U.S. 8th graders enrolled in algebra, and that low-income and minority students were even
less likely to take algebra in the 8th grade.
Taking rigorous mathematics and science courses in high school appears to be
especially important for low-income students. Low-income students who took algebra I
and geometry were almost three times as likely to attend college as those who did not.
While 71 percent of those who took algebra I and geometry went to college, only 27 percent
who did not take those courses went on to college. By way of comparison, 94 percent of
students from high-income families, and 84 percent of students from middle-income
families who took algebra I and geometry in high school went on to college. Sixty percent
of students from high-income families and 44 percent of students from middle-income
families who did not take algebra I and geometry went to college.
Despite the importance of low-income students taking rigorous mathematics and
science courses, these students are less likely to take them. Students from higher-income
families are almost twice as likely as lower-income students to take algebra in middle school
and geometry in high school. They are more than twicc as likely to take chemistry.
3
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Other important findings include:
Mathematics achievement depends on the courses a student takes, not the type of
school the student attends. Students in public and private schools who took the same
rigorous mathematics courses were equally likely to score at the highest level on the NELS
12th grade mathematics achievement test.
Students whose parents are involved in their school work are more likely to take
challenging mathematics courses early. Students whose parents were involved in their
education were more likely to take courses like algebra and geometry in the 8th and 9th
grade than students whose parents were not involved.
The results of the Third International Mathematics and Science Study (TIMSS) reveal
that the middle school mathematics curriculum may be a weak link in the U.S.
education system. While U.S. 4th graders scored above the international average in
mathematics and science, U.S. 8th graders scored below average in mathematics, and only
slightly above the international average in science. Initial analysis of TIMSS data also
shows that the middle school mathematics curriculum in the U.S. is less challenging than in
other countries. The curriculum of average 8th-grade mathematics classrooms in the U.S.
resembles 7th grade curriculum elsewhere. Although algebra and geometry are integral
elements of the middle school curriculum in other countries, only a small fraction of U.S.
middle schools offer their students these topics.
Algebra in the Curriculum
Making a successful transition from arithmetic to more advanced mathematics, including
algebra and geometry, has often been difficult for students. As a result, many mathematics
programs in the U.S. are now systematically incorporating some fundamentals of algebra and
geometry into the upper elementary grade curriculum. In these programs; 5th, 6th and 7th
grade students are representing and solving equations, characterizing patterns and rates of
change among variables, and using other fundamental algebraic concepts.
In addition, some middle and high schools are taking a new approach to advanced topics.
While many schools offer the traditional model of separate courses for pre-Algebra, Algebra I,
Gcometry, Algebra II, Trigonometry, pre-Calculus and Calculus, these schools are integrating
them. This approach is consistent with practices in other industrialized nations, which
integrate algebra, geometry, and other topics throughout the elementary, middle, and high
school years and offer a significant component of algebra in the 8th grade. Building a firm
foundation in algebra during the elementary and middle school years eases the shift from
arithmetic to advanced topics, whatever the format of students' new curriculum. NELS and
NAEP, the two sources of national mathematics course-taking data analyzed in this brief,
employ traditional courses titles, such as "algebra I" and "geometry." Thus, these titles arc
used throughout the brief.
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Mathematics and Future Opportunities
The Importance of
Mathematics for College
Entrance
Figure 1
College Attendance by Course-Taking
Students who take rigorous
% attending college
mathematics and science courses are
100%
much more likely to go to college
83%
80%
than those who do not. Data from a
longitudinal survey of students who
60%
were in the 8th grade in 1988
(National Educational Longitudinal
40%
36%
Study or NELS) revcal that 83 percent
of students who took algebra I and
20%
gcometry enrolled in college¹ within
0%
two years of their scheduled high
Took Algebra 1
Did Not Take
school graduation. Only 36 percent of
and Geometry
Algebra I and
students who did not take algebra I
Geometry
Source: Analysis of NELS data
and geometry went to college (Figure
1). Similarly, students who take
rigorous science courses in high school are much more likely to go to college. While nearly 89
percent of students who took chemistry entered college, only 43 percent who did not take
chemistry went to college.
Students who take more rigorous mathematics courses also show higher gains in mathematics
achievement (measured by the mathematics achicvement test given as part of NELS) than
students who take less challenging courses, even when controlling for initial achievement. For
example, among students who initially began at the same level of mathematics proficiency in the
8th grade, students who had taken algebra II or geometry by the 10th grade experienced greater
gains, on average, than students who had taken no algebra or only algebra I during that period.
1 Throughout this report. the term "college" is used to refer to any postsecondary education taken at a public,
private not-for-profit, or private for-profit institution.
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Students of all income levels who
take rigorous mathematics and
science courses in high school are
Figure 2
more likely to go to college, and
College Attendance by Income and
among low-income students
Course-Taking
(students in the bottom third of the
income distribution), the difference
Took Algebra I and Georratry?
No
III
Yes
is particularly dramatic. Students
from low-income families who took
% attending college
algebra I and geometry were almost
Lowincome
three times as likely to attend college
as those who did not. While 71
Middle-income
percent of low-income students who
took algebra I and geometry went to
college, only 27 percent of low-
High-income
income students who did not take
algebra I and geometry went on to
0
20
40
60
80
100
Income divided into thirde
college. The differences are also
Source: Analysis of NELS data
dramatic among students from
middle- and high-income families: 94
percent of students from high-income
families, and 84 percent of students from middle-income families who took algebra I and
geometry went on to college, while 60 percent of students from high-income families and 44
percent of students from middle-income families who did not take geometry still went on to
college (Figure 2).
Unfortunately, many students, in particular low-income students, do not take these rigorous
mathematics and science courses. According to NELS, 63 percent of all students took algebra I
and geometry and 50 percent took chemistry. Students from low-income families, however, were
far less likely than their more advantaged peers to take these rigorous courses. Among students
in the bottom third of the income distribution, 46 percent took algebra 1 and geometry and only
33 percent took chemistry. By way of comparison, fully 81 percent of students in the top third of
the income distribution took algebra 1 and geometry, and 72 percent took chemistry. The
differences are similar for other rigorous mathematics courses (Table 1).
²Income data are based on total family income reported by parents. Low, middle, and high income groups each
contain approximately one-third of the sample. The "all" category includes additional observations with
missing income data.
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Table 1: Course-Taking Patterns of NELS Students
Percent of Students Taking Course
All
Bottom Income
Middle Income
Top Income
Algebra Iand
63
46
68
81
Geometry
Trigonometry
18
10
19
30
Chemistry
50
33
52
72
Accounting for course-taking patterns dramatically reduces the difference in the rate of
college-going between low- and high-income students. Students from high-income families are
almost twice as likely to attend college as students from low-income families (86 percent
compared to 44 percent) when course-taking patterns are not accounted for. However,
comparing only students who have taken rigorous courses to one another, students from low-
income families go to college at rates much more similar to students from middle- and high-
income families (Table 2). For example, among students who took chemistry in high school, 95
percent of high-income students, 89 percent of middle-income students, and 79 percent of
low-income students went to college. When low-income students take rigorous courses, income
effects on college entrance rates diminish greatly, although they do not disappear.
Table 2: College Attendance by High School Course-Taking Patterns of NELS Students
Percent of Students Attending Postsecondary Education
All
Bottom Income
Middle Income
Top Income
All
63
44
69
86
Algebra Land
Yes
83
71
84
94
Geometry
No
36
27
44
60
Trigonometry
Yes
94
90
92
98
No
59
42
66
83
Chemistry
Yes
89
79
89
95
No
43
31
50
68
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Public Versus Private
Achievement Depends on Course-Taking,
Not the Type of School
In general, the mathematics courses students take in high school determine achievement
more than the type of school they attend. While recognizing that a great deal of diversity
exists in public and private schools, it is uscful to note that when coursc-taking patterns are
accounted for the mathematics achievement of students in both categories of school is very
similar. Public and private, school students who took the same mathematics courses were
almost equally likely to score at the highest level on the NELS 12th grade mathematics
achievement test. This was also true for low-income public and private school students
Additionally, among both public and private school students of all incomes, students who had
taken more rigorous mathematics courses were much more likely to score at the highest
achievement level (Figure 3).
Figure 3
Mathematics Achievement by
Highest Mathematics Course Taken
All Students
Public
Algebra II
Private
Trigonometry
or Higher
Low Income
Students
Algebra II
Trigonometry
or Higher
0%
20%
40%
60%
80%
100%
Percent of Students Scoring at the Highest Level of the
NELS 12th Grade Mathematics Achievement Test
Achievement divided into thirds; Students in highest level scored in the top third
Source: Analysis of NELS data
Private schools include non-religlous, Catholic, and other private schools
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Mathematics in College, the Workplace, and the 21st Century
The benefits of taking rigorous mathematics and science courses extend to students heading
into the job market and to both two- and four-year colleges. As technology becomes prevalent
in the workplace, more and more workers will find they need to have strong backgrounds in
mathematics and science--backgrounds which will have begun to form even before high school.
Rigorous mathematics and science preparation is also important to students intending to go to a
two- or four-year college or university. The level and number of mathematics courses that a
student needs to take before and during college depend on the college and the major that the
student wants to pursue. Mathematics- and science-related disciplines typically require that
students have taken rigorous mathematics courses. Many other popular courses of study require
advanced mathematics as well.
Two-year colleges often require all students to gain an understanding of intermediate algebra
prior to graduation, regardless of their course of study. Many two-year colleges require all
degree-seeking students to take mathematics placement exams prior to enrollment. High scorers
may be exempt from taking certain mathematics courses, while low scorers may have to take
remedial mathematics courses. Many of the most popular majors at two-year colleges--including
Business, Nursing, and Computer Science-require more rigorous mathematics course work, such
as statistics.
Four-year colleges and universities typically require more high school mathematics
preparation for admission. Typical state four-year colleges and universities recommend, and in
some cases require, that all students take at lcast three, and sometimes four, years of mathematics
in high school. Data collected by the College Board reveal that in 1997, 68 percent of incoming
freshmen at four-year colleges and universities had taken four years of mathematics in high
school. Furthermore, almost all of these students had taken algebra and geometry, and more than
half had taken trigonometry. Most state colleges require students to take mathematics placement
exams upon enrollment. Colleges look favorably on Advanced Placement courses and often
place students who have taken them out of introductory mathematics courses. While graduation
requirements differ depending on the students' major, many popular majors, such as Business
and Psychology, require students to take several more rigorous courses in mathematics or
science.
In the job market, workers who have strong mathematics and science backgrounds are more
likely to be employed and generally earn more than workers with lower achievement, even if
they have not gone on to college. A national survey found that by age 30, high school graduates
who had not furthered their education but had scored in the top quartile on the mathematics
portion of the Armed Services Vocational Aptitude Battery (ASVAB--administered to civilians
for study purposes) earned, on average, 38 percent more per hour than high school graduates who
had not gone to college and had scored in the bottom quartile of the mathematic portion of the
ASVAB. Similarly, the unemployment rate among high school graduates who scored in the top
quartile of the mathematics test was only 4.4 percent. The unemployment rate was 10.3 percent
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among high school graduates who scored in the lowest quartile. Workers who scored in the top
quartile of the science section of the ASVAB also earned more, on average, and were less likely
to be unemployed.
Mathematics ability will be even more important for well-paying jobs in the future. Some
major firms already require job applicants to pass standardized mathematics and reading tests.
For example, Diamond-Star Motors, a joint venture of Chrysler and Mitsubishi, tests all
applicants for production and maintenance positions on their ability to do high school level
mathematics. Authors Richard Murnane and Frank Levy have identified a set of "New Basic
Skills," in their book of the same name, that non-collegc-bound high school graduates should
master in order to get well-paying jobs in the modern labor market. The "New Basic Skills" that
workers will need in order to cam a good wage include the ability to use mathematics skills and
concepts at least at the 9th grade level.
Shortages in workers skilled in mathematics and science could affect U.S. performance in
global markets. According to a recent report, America's New Deficit: The Shortage of
Information Technology Workers, from the Office of Technology Policy at the U.S. Department
of Commerce, as computer and data processing become more important to the economy, more
and more workers skilled in mathematics- and science-related disciplines will be needed to
maintain the U.S.'s international competitiveness. The report cites a survey by the Information
Technology Association of America indicating that 50 percent of company executives in
information technology report a lack of skilled workers as "the most significant barrier" to their
companies' growth during the next year. Howcver, the number of bachelor level computer
science degrees awarded by U.S. colleges and universities declined more than 40 percent
between 1986 and 1994, indicating that these problems are likely to persist.
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Mathematics and Science in the Modern Job Market
Many jobs in today's labor market require a mathematics or soience background. A number
of these are among the fastest growing occupations nationally, and are not oncs ordinarily
thought of as "technical." Projections from the Bureau of Labor Statistics (BLS)
Occupational Outlook Handbook indicate that between 1994 to 2005, jobs requiring the most
education and training will be the fastest growing and highest paying. BLS predicts that
occupations requiring a bachelor's degree or higher will average 23 percent growth, almost
double the 12 percent growth rate projected for occupations that require less education and
training
Many jobs that once required little background in mathematics now call for specific skills in
algebra, geometry, measurement, probability, and statistics. According to an industry-wide
standard, an entry level automobile worker needs to be able to apply formulas from algebra
and physics to properly wire the electrical circuits of any car. The National Coulition for
Advanced Manufacturing has defined 25 specific standards of mathematics and measurement
among their national skill standards for what a competent worker should know and be able 10
do
Several of the fastest growing job areas will reflect growth in computer technology and health
services-fields that can roquire substantial mathematics and science preparation. Generally
speaking, fields requiring a strong science base also require substantial mathematics
preparation, as most academic science programs build upon a strong background in
mathematics. Below are some of the jobs which BLS indicates require a mathematics or
science background; while many of these jobs require mathematics OF science course work
beyond the high school level, all require at least a high school level background. The
occupations that BLS projects will be among the fastest growing during the period from 1994
to 2005 are noted with a star (*).
Computer Scientists (*)
Surgical Technologists
Systems Analysts (*)
Dieticians and Nutritionists
Occupational Therapy Assistants and Aides (*)
Optometrists
Chemical Engineers
Physical Therapists (*)
Civil Engineers
Roufers
Aerospace Engineers
Tool and Die Makers
Medical Assistants (*)
Photographers
Dentists and Dental Hygienists
Financial Managers
Surveyors
Budget Analysts
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Middle School:
Getting on the Road to Challenging Mathematics
and Science Courses
Laying the Foundation
"Mathematics is the language of science, and
Algebra is the "gateway" to rigorous
algebra is the minimum vocabulary that
mathematics courses. Rigorous mathematics
scientists of every discipline use to describe
courses build upon the skills and concepts
their work.
that students learn in carlier mathematics
Dr. George Castro, Associate Dean of the
courses. Traditionally, students cannot take a
College of Science at San Jose State
rigorous mathematics course in high school
University
until they have successfully completed one or
more prerequisite courses. Algebra I, or
another course that covers basic algebraic concepts, is the prerequisite for more rigorous
mathematics in high school.
Students who plan to take advanced mathematics and science courses during high school and
begin to study algebra during middle school are at a clear advantage. A rigorous sequence of
mathematics spans several years. The traditional sequence of mathematics courses involves one
year courses in algebra I, geometry, and algebra II, followed by a half-year course in
trigonometry, a full- or half-year course in pre-calculus, and then calculus or an Advanced
Placement course. Increasingly, schools are covering these rigorous content areas in courses that
integrate algebra, geometry and other areas of mathematics such as statistics and probability,
rather than teaching each separately. According to NELS, approximately 60 percent of the
students who took calculus in high school had taken algebra in the 8th grade. The typical high
school sequence of rigorous science courses (biology, chemistry, and physics) also necessitates
an early background in algebra and geometry.
Students who do not take courses covering algebraic concepts early in their educational career
risk closing the door on many important opportunities, including opportunities to take courses
outside of mathematics and science. Some high schools require students 10 complete a specific
package of courses, including mathematics and science, in order to graduate. By the junior and
senior years, students who have not planned ahead have fewer options in choosing which courses
they take. Students who do not complete prerequisite and required courses early enough not only
risk being unable to take more rigorous courses in those disciplines later, but also may not have
time in their schedules to take other courses that can help prepare them for college or a career,
including foreign language, art, Advanced Placement, and "tech prep" courses.
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Course-Taking Patterns in Middle School
Despite recent increases in the proportion
of students taking algebra I in the 8th grade,
Figure 4
in 1996, most students were not enrolled in
Proportion of Eighth-Graders Enrolled in Algebra, 1996
this course. The proportion of 8th-graders
All
25%
taking the National Assessment of
Educational Progress (NAEP) mathematics
assessment who reported taking algebra has
While
27%
increased. In 1992, only 20 percent of
students reported taking algebra. In 1996, the
Black
20%
next year the NAEP mathematics assessment
was administered, 25 percent reported taking
algebra. This increase may be due to a
Hispanic
20%
number of factors, including the National
Council of Teachers of Mathematics'
0%
20%
40%
60%
80%
100%
(NCTM) call for including algebraic topics in
Scurce: 1005 NAEP A M a teckground questionnaire
the middle school curriculum.
Minority and low-income students continue to be less likely to take challenging mathematics
courses in middle school than other students. The 1996 NAEP data reveal that minority
students are less likely to report being enrolled in algebra in the 8th-grade (Figure 4). The data
also indicate that students from disadvantaged backgrounds are less likely to be enrolled in
algebra during the 8th grade: While 29 percent of students who were not eligible for the national
school lunch program reported being enrolled in algebra during the 8th grade, only 15 percent of
students who were eligible for the national school lunch program were enrolled in algebra.
While the number of students taking algebra courses has increased, recent evidence suggests
that the content of these courses has remained rigorous. Many states have recently increased
mathematics requirements for high school graduation, often requiring that students take more
years of mathematics than were required in the past, or mandating that students complete certain
courses. A recent study supported by the National Science Foundation (NSF) examined the
content of mathematics courses in schools in several of the states making the most substantial
changes in mathematics requirements. The study focused on basic courses, such as algebra 1,
which had experienced large enrollment increases because of more stringent graduation
requirements. Despite the larger numbers of students enrolling in the courses, the study found
that the content of these courses was essentially unchanged, indicating that more students were,
in fact, being exposed to rigorous mathematics.
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Parent and Student Attitudes about Mathematics and Science
Large proportions of
middle school students
indicate that they do not
Figure 5
plan to take mathematics
Students Plan to Drop Matherratics, But Want to Go to College
and science courses
All
Black
Hispanic
beyond what their schools
require. A nationally
100%
90%
91%
92%
93%
representative survey of
86%
83%
public school students and
80%
parents conducted by Louis
Harris Associates for the
63%
60%
60%
National Action Council
51%
for Minorities in
Engineering (NACME),
40%
Inc. found that large
proportions of students
20%
would like to stop taking
mathematics and science
0%
courses as soon as they can.
Child plans to drop
Child wants to
Parent expects child
Fifty-one percent of the 5th
matherratics
go to college
to go to college
through 11th grade students
Source NACME Survey
surveyed indicated that they
would take mathematics
classes only as long as required, while 47 percent reported they would study science only as long
as it is required. Distressingly, young minority students--5th through 8th graders who will soon
be facing major decisions about which courses to take--were more likely to indicate that they
planned to drop mathematics and science as soon as they were able to (61 percent planned to
drop mathematics, and 58 percent planned to drop science). Minority students of all ages were
more likely than other students to say that they would like to stop taking mathematics and science
as soon as they could (Figure 5).
However, the same students indicate that they would be interested in going to college, and
taking college-level mathematics courses. Eighty-six percent of all students surveyed said that
they would like to go to college. Although less than half of the 9th- to 11th-grade students said
that they planned to take trigonometry or algebra II in high school, nearly two-thirds said that
they were interested in taking Advanced Placement courses. These contrasts signal that many
students do not understand the importance of, and requirements for, taking rigorous mathematics
and science courses in high school, including the need to take algebra by the 8th grade. In fact,
only 25 percent of minority and 42 percent of non-minority 5th- through 8th-grade students
recognized that if they did not take algebra they would not be able to take other mathematics
classes in the future.
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Parent and teacher involvement may make a large difference in students' decisions about
mathematics and science. According to the NACME survey, ninety-four percent of students
indicated that their parents' or guardians' advice was important to them in deciding what they
would study in school, and 88 percent indicated their teachers' advice was important. Ninety-one
percent of parents want their children to continue their education beyond high school. However,
when 9th- through eleventh-graders were asked who decided which mathematics classes they
would take, 79 percent indicated that they had made the decision by themselves.
Analysis of the NELS data indicates that students with greater levels of parental involvement
are more likely to take advanced mathematics courses. Analysis of the coursc-taking patterns
of the NELS students who were in 8th-grade in 1988 reveals that regardless of whether the level
of parent involvement was reported by the student, the parent, or the teacher, higher levels of
parental involvement were consistently associated with higher likelihoods of taking rigorous
mathematics courses. While only 8 percent of those students who said that they did not discuss
programs at school with their parents took algebra I by the 8th grade, 17 percent of those who
said that they discussed school programs three or more times during the previous semester took
algebra I by the 8th grade. Students whose parents or teachers indicated greater levels of parental
involvement were also more likely to take advanced courses. Thirty-seven percent of students
whose parents said that they rarely talked to their child about high school plans took geometry by
the 10th grade, while 48 percent of those students whose parents said they regularly spoke to the
child about high school plans took geometry by the 10th grade, While 27 percent of students
whose teachers said their parents were not involved took geometry by the 10th grade, a full 63
percent of the students whose teachers said that their parents were very involved took gcometry
by the 10th grade.
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Mathematics in the U.S. Today
International Comparisons of
Middle School Mathematics and
Science Proficiency
U.S. Performance on TIMSS,
Relative to International Average
Recent findings from the Third International
Fourth grade
Eighth Grade
Mathematics and Science Study (TIMSS),
indicate that the mathematics curriculum
Mathematics
from grades five through eight may be a weak
link in the U. S. educational system. Newly
available data from TIMSS (the most
Above average
Below average
comprehensive international comparison of
schools and students ever undertaken) reveal
Science
that U.S. 4th graders scored above the
international average in both mathematics and
Above average
Above average
science. Among 25 other participating nations,
only Korea performed better than the U.S. in
4th grade science, and only 7 of the 25 other
countries did better than the U.S. in 4th grade mathematics. These findings are in contrast to
earlier findings from TIMSS that indicate that U.S. 8th graders perform slightly below the
international average in mathematics, and only slightly above the international average in
science. In fact, only one country-the U.S. in mathematics--falls from above the international
average at 4th grade to below the international average at 8th grade.
The U.S. expects less of its middle school students compared to high performing nations.
TIMSS data suggest that one reason U.S. students do less well at 8th grade is that the middle
school mathematics curriculum in the U.S. is significantly less challenging than curricula in other
countries. In Germany and Japan, virtually all students in grades 5 through 8 move beyond
arithmetic to the foundations of algebra and geometry. By 8th grade, mathematics courses in
virtually all other countries participating in TIMSS include significant algebra and geometry,
while in the U.S., only students in college-preparatory classes receive significant exposure to
algebra, and very few students study geometry. As a result, the content taught in U.S. 8th grade
mathematics classrooms is usually at a 7th-grade level compared to the 40 other nations in the
TIMSS study.
TIMSS also found that U.S. mathematics classes require students to engage in less high-level
mathematical thought and solve fewer multi-step problems than classes in Germany and
Japan. A U.S. mathematics teacher's typical goal is to teach students the mechanics of solving a
problem versus understanding the concepts behind it, while a Japanese teacher's goal is to help
them learn the basics as well as understand the relevant mathematical concepts. In a typical U.S.
classroom, students follow the teacher as he or she leads them through solutions to mathematics
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problems. In Japan, students are asked to solve problems, present them to the class, and describe
how they approached the problem to increase their own understanding.
How Does Our Curriculum Compare Internationally"
The 8th grade mathematics curricula in both Germany and Japan are more advanced than in the
United States. The TIMSS analysis of U.S. curricula examined both the content of textbooks and how
it is implemented in classrooms,
An analysis of curricula in the U.S. and other countries found that algebra and geometry
occupy more space¹ in German and Japanese textbooks than they do in the textbooks
used by a majority of U.S. 8th graders (Figure 6).
Analyses of curriculum implementation make clear that in the middle school years, the U.S. still
focuses on arithmetic. For example, 40 percent of U.S. 8th grade mathematics lessons included
arithmetic topics, whereas only 13 percent of Germany's and none of Japan's lessons at the 8th
grade level included these topics. The major focus of curriculum taught in these countries is on
algebra and geometry.
Figure 6
Algebra in 8th Grade Textbooks
% of space devoted to algebre in 8th grade mathemalics textbooks
50%
40%
40%
30%
25%
20%
10%
10%
0%
Germany
Japan
U.S.
Source:
The Third International Mathamatics and Science Study (TIMSS)
Space is defined in terms of the percentage of a textbook or guidebook that is devoted to particular topics/blocks
Topics include such items as formulas, geometry, numbers, and estimation. Blocks are sub-units of topics that are
parts of it textbook and which might include individual pedagogical suggestions, individual examples, individual
testing, narrative blocks, graphic blocks. suggested activities, and mathematical problems.
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Promising Practices
Across the country, there are many promising mathematics and science practices underway.
Many of these are responsible for increases in the numbers of students taking rigorous courses in
mathematics and science. Just as important, many students are finding that they do quite well in
these more advanced courses. There is, of course, no one formula to success. Highlighted here
are a number of places that demonstrate effective strategies.
Taking the Right Courses. In 1990, the College Board launched EQUITY 2000 to increase
minority enrollment in college preparatory mathematics courses. Originally piloted in six
communities, EQUITY 2000 requires participating school districts to phase out lower-level
mathematics in favor of all students taking college preparatory curriculum--beginning with
algebra and geometry. EQUITY 2000 influences policies, curricula and student academic
development at all grade levels, but particularly grades six through nine. These are critical years
for mathematics education. During this period, parents, students, and educators make key
decisions about which courses students should take and how they should begin planning for
education and careers after high school. Equity 2000 provides on-going professional
development to help teachers work with mixcd-ability classes. It also trains administrators and
teachers to use student enrollment and achievement data to drive school-based decision-making,
helps schools establish support services for students who need extra time and effort to learn
challenging content, and encourages and supports parents to become advocates on behalf of their
children.
Increased parental involvement is a priority in Equity 2000. It recognizes the important role that
parents play in nurturing and reinforcing their children's desire to attend college. Equity 2000
has sponsored Saturday and summer academics on college campuses for entire families. It also
sponsors Family Math nights in which parents and students learn mathematics concepts together.
Results at the six pilot sites indicate that:
All sites dramatically increased the percentage of students enrolled in algebra I
by the 9th grade, and in three pilot districts, all 9th graders enrolled in
algebra I.
The percentage of students passing algebra I did not decline significantly, and
in some cases rose, as more students from the discontinued lower tracks began
enrolling in algebra classes.
Contact:
Vinetta Jones
Equity 2000
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The College Board
1717 Massachusetts Ave., NW
Washington, DC 20036
(202) 822-5900
www.collegeboard.org/equity/html/indx001.html
Advanced Placement Participation and Scores on the Rise. The College Board's Advanced
Placement (AP) Program was started nearly four decades ago to enable students to complete
college-level studies while still in high school and to obtain college credit or placement. AP
courses are widely recognized as setting the standard for high levels of academic achievement in
high school. Today more than 500,000 students in about half of the nation's high schools take at
least onc AP course. Dramatically increased participation in AP courses in Texas and South
Carolina illustrate the success of AP-based reform initiatives in two states.
Texas: The Advanced Placement Incentives program was developed in the Dallas, Texas area by
O'Donnell Foundation in reaction to low rates of college attendance and poor college preparation.
The Advanced Placement Incentives program reward results in AP courses in mathematics,
science, English, and the arts by providing performance-based financial incentives to teachers,
school and students. Teachers arc given financial incentives as well as registration and fees for
attending College Board AP teacher training during the summer, and to teach AP courses.
Students who complete the Advanced Placement course may take the AP exam at half-cost (the
total cost for an AP exam is about $73). Those who score a three or better (on a five point scale)
are given financial incentive and reimbursed for the cost of the exam.
In five years of operation in nine Texas public schools, the O'Donnell foundation reports that:
The year before the program began in nine typical public high schools, 48 students took
AP exams in mathematics, science, and English, and received a three or better. In the fifth
year of operation, 1,099 students took AP exams and 521 received a score of three or
better.
In nine high schools in the Dallas Independent School District, the eighth largest inner-city
school district in the country, with 85 percent minority enrollment, growth in AP
participation has been outstanding. Students took 312 AP in mathematics, science, and
English in May 1995, the year before the program started in the Dallas schools. In May
1997, the second year of the Dallas program, this number has grown to 1,750. The
number of students scoring three or higher during that time period grew from 139 to 559.
The Dallas school program has experienced proportional growth among female and
minority students. The ycar before the program started, 94 females took exams in
mathematics, computer science, and the sciences. In the program's second year, 452
female students took these exams.
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Minority participation has also grown in Dallas, from 64 7 African-American and Hispanic
students taking AP mathematics, science, and English exams the year before the program
began, to 734 in the program's second year.
South Carolina: With former Governor Riley's school reform package of 1984, South Carolina
became one of the first states to legislate funding and other actions to boost student participation
in AP classes. The state appropriated funds to train AP teachers and to help pay for AP exams, as
well as required that public colleges accept AP courses if the student scored 3 or higher on the
exam. As a result, from 1984 to 1997 South Carolina experienced:
An increase in the number of students taking AP exams from 2,799 to 9,748.
An increase in the number of AP exams from 3,461 to 14,890, with the mean grade
remaining stable at approximately 2.7 - 2.8.
An increase in the number of AP science exams (Biology, Chemistry, Physics) from
27 to 2,414.
An increase in the number of AP math exams (Calculus AB and BC) from 46 to
2,767.
Ninety-three percent of all the public high schools in the state participating in AP
(184 of 197 public high schools).
AP participation rates above the national average.
AP Exams Taken
(Eleventh and Twelfth Graders)
1984
1997
Percent increase
South Carolina
3,161
14,890
430 percent
National
223,888
843,399
380 percent
Sources: College Board. Advanced Placement Program, National and South Carolina Summary Reports, 1984 -
1997.
Contacts:
Macarthur Goodwin
South Carolina Department of Education 1429 Senate St.
Columbia, SC 29201
(803) 734-8382
www.state.sc.us/sde
Patrick Moore
O'Donnell Foundation
100 Crescent Ct.
Suite 1660
Dallas, TX 75201
(214) 871-5800
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Strengthening Curriculum and Instruction. Sponsored by the University of Pittsburgh's
Learning Research and Development Center, the Quantitative Understanding: Amplifying
Student Achicvement and Reasoning (QUASAR) Project aims to raise low levels of student
participation and performance in mathematics. QUASAR is an urban middle school
demonstration project that fosters the development and implementation of improved mathematics
instructional programs in economically disadvantaged communities. The program revolves
around three key principles: (1) all students are able to learn a broad range of mathematical
content; (2) all students can acquire a deeper and more meaningful understanding of
mathematical ideas; and (3) all students can demonstrate proficiency in mathematical reasoning
and complex problem solving.
In QUASAR schools, teams of mathematics teachers, school administrators and "resource
partners"-- generally mathematics educators from local universities -- collaborate to develop,
implement, and refine mathematics instruction. All project schools have climinated most forms
of academic tracking, replacing it with the development of deeper student understanding and
high-level thinking and reasoning for all students. While curricula, teaching strategies, and
approaches to professional development vary, all QUASAR sites include extensive attention to
professional development and teacher support. Additionally, the University of Pittsburgh's
Learning Research and Development Center provides schools with ongoing support and updated
information on their progress.
Data indicate that QUASAR schools build teachers' capacity to improve the quality of their
mathematics instruction. Students increase their capacity to think, reason, solve complex
problems, and communicate mathematically and they do so while continuing to learn basic skills.
QUASAR school students, particularly those who are from minority groups and whose English
proficiency is limited, have increased their understandings across a range of important
mathematical ideas. Additionally, QUASAR students in grade 8 performed as well as other
students on basic and traditional items of the 1992 NAEP Mathematics Assessment. They
performed better than their peers on less traditional middle school mathematics content.
Contact:
Edward Silver
QUASAR
Learning Research Development Center 3939 O'Hara St.
Pittsburgh, PA 15260
(412) 624-3231
www.lrdc.pitt.edu/quasar/quasar.html
Raising the Standard. The New York Regents Exam has spurred thousands more high school
students to take and pass college-preparatory mathematics courses. In 1993 then New York
Chancellor Ramon Cortines required all students to take tougher Regents-level mathematics and
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students to take and pass college-preparatory mathematics courses. In 1993 then New York
Chancellor Ramon Cortines required all students to take tougher Regents-level mathematics and
science courses traditionally reserved for college-bound students. Beginning in 1995, the state
required that all students take Regents-level classes. The number of Hispanic and black students
who passed the science portion of the Regents Exam more than doubled over the previous year.
The state is now requiring all students take and pass Regents Exams. In addition, Commissioner
of Education Richard Mills recently called for an increase in the rigor of the state's requirements
for graduation from high school, including adding another year of both mathematics and science
to the current two years required in each.
Contact:
Edward Lalor
New York State Department of Education
Education Building, 111 Washington Ave.
Room 675
Albany, NY 12234
(518) 473-7880
www.nysed.gov
Living Up to Potential. Twenty school districts from Chicago's North Shore joined forces in
1995 to provide their students with a world class education in mathematics and science. Calling
themselves the First in the World Consortium, their first challenge was to determine what a
"world class" education looked like. They then measured their current performance against that
benchmark and developed an improvement strategy.
The Consortium's directed its efforts toward three objectives: (1) benchmarking performance
against international standards in mathematics and science, using the Third International
Mathematics and Science Study as a guide; (2) creating a forum to clarify world-class education
standards for business leaders, policy makers, educators, and community members; and (3)
establishing a network of learning communities for educators, parents, and community leaders
within the Consortium school districts and beyond.
Students in grades 4, 8, and 12 in First in the World Consortium districts took the TIMSS
assessment in Spring 1996. Fourth and eighth graders' results placed them among the top
performers in the world, well exceeding U.S. performance generally.
The Consortium attributes its success to the fact that:
Fifty percent of its 8th grade students took algebra or geometry compared to 25 percent of
students nationally who take algebra;
it had high expectations for students and teachers; and
it had gained broad-based community support for improved student performance.
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The First in the World Consortium is not resting on its success. Its "community of learners"
approach continues to promote teacher participation and provide a context for long-term
commitment to the consortium's goals and to growth in student learning. To this end, it has
created teacher learning networks to strengthen curriculum standards, models of instruction,
assessment, and use of technology.
The resources of the First in the World Consortium place it at an advantage. Yet, what truly
distinguishes it is its willingness to identify its weaknesses and address them. The consortium
credits both state and federal support for helping it focus on its goals. Its experiences
demonstrate that, when given the opportunity, U.S. students can perform as well as, or better
than, students anywhere.
Contact:
Paul Kimmelman
West Northfield School District 31, First in the World Consortium
3131 Techny Rd.
Northbrook, IL 60062
(847) 272-6880
www.ncrel.org/sdrs/firstwor.htm
Next Steps
Six things educators, policymakers and community members can do:
1. Provide all students the opportunity to take algcbra 1 or a similarly demanding course that
includes fundamental algebraic concepts in the 8th grade and more advanced math and science
courses in all four years of high school.
2. Build the groundwork for success in algebra by providing a rigorous curriculum in grades K-7
that moves beyond arithmetic and prepares students for the transition to algebra.
3. Ensure that all students, parents, teachers, and counselors understand the importance of
students' early study of algebra as well as continued study of rigorous mathematics and science in
high school.
4. Provide teacher preparation and professional development to teachers of mathematics to
increase their knowledge and skills in mathematics and the teaching of mathematics.
5. Support mathematics achievement outside the classroom through math clubs, tutoring, and job
shadowing for students who may nccd cxtra help.
6. Support parent involvement in their children's mathematics education.
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Six things parents can do:
1. Discuss your children's mathematics homework with them.
2. Visit your children's mathematics teacher to find out what your children are learning and how
you can help.
3. Insist that your children enroll in algcbra I or a similarly demanding course that includes
fundamental algebraic concepts in the 8th grade and more advanced math and science courses in
high school SO they can keep all of their future options open.
4. Ensure that your children are gaining the groundwork for success in algebra through a rigorous
curriculum in grades K-7 that moves beyond arithmetic and prepares them for the transition to
algebra.
5. Help your children understand the importance of taking challenging mathematics and science
courses to their future by visiting colleges, familiarizing them with college requirements, and
exploring financial aid options available to students.
6. Show the importance of mathematics for career choices by talking with your children about the
use of mathematics in your work or the work of adults they know.
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Resources
Everson, Howard T. and Marlene Dunham "Signs of Success-EQUITY 2000, Preliminary
Evidence of Effectiveness.' New York, NY: The College Board, 1996.
Hawes, Mark, Kimmelman, Paul, and Krocze, David. "Becoming 'First in the World' in Math
and Science: Moving High Expectations and Promising Practices to Scale." Phi Delta
Kappan, Volume 79, Number 1, September 1997.
Jones, Vinetta C. "What A Difference A Standard Makes." In D. Bartels & J. Opert Sandler
(Eds.), This Year in Science: Implementing Science Education Reform." Washington, DC:
American Association for the Advancement of Science, in press.
Levy, Frank and Richard Murnane. Teaching the New Basic Skills: Principles for Educating
Children to Thrive in a Changing Economy, New York: The Free Press, 1996.
National Action Council for Minorities in Engineering. Uninformed Decisions: A Survey of
Children and Parents about Math and Science, Conducted for National Action Council for
Minorities in Engineering, By Louis Harris and Associates, 1995.
The National Commission on Teaching and America's Future. What Matters Most: Teaching for
America's Future, September, 1996. http://www.tc.columbia.edu/-teachcomm/index2.htm
Porter, Andrew. "The Effects of Upgrading Policies on High School Mathematics and Science."
Consortium for Policy Research in Education, 1997, and in Brookings Papers on Education
Policy, 1997.
Schmidt, William H., McNight, Curtis C., and Raizen, Senta A. A Splintered Vision: An
Investigation of U.S. Science and Mathematics Education, East Lansing, MI: U.S. National
Center for the Third International Mathematics and Science Study, Michigan State
University, 1996. ttp://kapis.www.wkap.nl/kapis/CIG-BIN/WORLD/book.htm70-7923-
4441-3
U.S. Department of Education. National Center for Education Statistics. Education and the
Economy: An Indicators Report, Washington, D.C.: U.S. Government Printing Office, 1997.
http://nces.ed.gov/pubsearch/infopage.idc?cid=97269XXXXX
U.S. Department of Education. National Center for Education Statistics. NAEP Facts: Eighth-
Grade Algehra Course-Taking and Mathematics Proficiency, Washington, D.C.: U.S.
Government Printing Office, 1996. http://nces.ed.gov/pubs/96815.html
U.S. Department of Education. National Center for Education Statistics. Pursuing Excellence: A
Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum, and
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Achievement in International Context, Washington, D.C.: U.S. Government Printing Office,
1996. http://nces.ed.gov/timss/
U.S. Department of Education. National Center for Education Statistics. Pursuing Excellence: A
Study of U.S. Fourth-Grade Mathematics and Science Achievement in International Context,
Washington, D.C.: U.S. Government Printing Office, 1997. http://nces.ed.gov/timss/
U.S. Department of Education. National Center for Education Statistics. Statistics in Brief:
Changes in Math Proficiency Between 8th and 10th Grades, Washington, D.C.: U.S.
Government Printing Office, 1996.
http://nces.ed.gov/pubsearch/infopage.idc?cid=93455XXXXX
U.S. Department of Education. Planning and Evaluation Service. Analysis of NELS:88
Follow-Up Data: Factors That Affect College Enrollment, Forthcoming.
U.S. Department of Labor, Bureau of Labor Statistics. Occupational Outlook Handbook,
Washington, D.C.: U.S. Government Printing Office, 1997.
http://stats.bls.gov:80/ocohome.htm
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Appendix
The NELS:88 data. The National Education Longitudinal Study of 1988 (NELS:88) initially
surveyed a nationally representative sample of 26,000 public and private school 8th grade
students in 1988. The data collected include responses to student questionnaires, scores on
standardized achievement tests, high school transcripts, and interviews with parents and teachers.
Since the initial survey in 1988, the students have been resurveyed every two years, with the most
recent data available gathered two years after their scheduled high school graduation in 1994.
The analyses in this report are based on a sub-sample of over 13,000 individuals from whom data
were collected in all three follow-up surveys. Analysis of course-taking patterns is based on
student reports of 8th-grade course-taking and high school transcript data. The actual titles of
mathematics courses as they appear on the transcripts may vary, despite covering similar content
(for example, geometric concepts); accordingly, we have attempted to include all courses under
the traditional course names (i.e. "geometry," "algebra II") reflective of their content.
27
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inder.com/@@m2UNfQUA5SX03FXE/AIPolitics/Latest/story.cgi/1997Oct20/332
PATHFINDER
Report: Getting Math Early Helps
By LAWRENCE L. KNUTSON
Associated Press Writer
what's new!
WASHINGTON (AP) Early exposure to serious math, algebra and geometry,
opens the gate to college for large numbers of students, including minorities and
those from low-income families, an Education Department report says.
TIME
The report, "Mathematics Equals Opportunity," was released Monday by
Congressional Quarterly
Education Secretary Richard Riley, who said it offers evidence that the choice of
Associated Press
subjects determines access to college, not whether the school itself is public,
Washington E-mail
private or parochial.
"These courses demand discipline, they demand hard work and they demand
responsibility," Riley said as he unveiled the new report in a ceremony at the Old
Executive Office Building. "They make a powerful difference in terms of going
to college."
The problem, he said, is that only about 25 percent of U.S. eighth-graders
enrolled in algebra classes last year.
President Clinton took the report as a new reason to support his proposal for
voluntary national tests of reading in the fourth grade and math in the eighth
grade "to ensure that all our children meet the high standards of academic
excellence they'll need to succeed in tomorrow's world."
Many Republicans oppose such testing, and Clinton said: "I call upon Congress
to end the delays. Our children are counting on us."
Riley said that by proposing the tests, Clinton is "laying down a challenge to
shake up the status quo."
"If these critics are going to be serious about improving American education, I
would urge them to read this report and join us in this call for higher standards,"
Riley said. "Sometimes you need to put politics aside and get serious about
education."
"The voluntary tests will focus like a laser beam on making sure we get the
basics right," he said.
The report had three central conclusions:
Eighty-three percent of young people who go on to college take "the important
gateway math courses," starting in the eighth grade. Riley said: "That is a very
important finding that goes against the conventional wisdom that a family's
status and income are the determining factors."
1 of 2
10/20/97 17:37:17
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..inder.com/@@m2UNfQUA5SX03FXE/AIPolitics/Latest/story.cgi/1997Oct20/332
Low-income students who took algebra and geometry were nearly three times as
likely to attend college as those who did not. Seventy-one percent of those who
took such courses went on to a higher education.
Taking these courses is more important than the type of school attended. The
report suggested that students in public and private schools who took rigorous
math and science classes were equally likely to score in the highest levels of
12th-grade math tests.
Many Congressional Republicans contend that giving parents tax dollars in the
form of vouchers to shift their children out of public schools and into private or
parochial schools is the answer to improving their education.
"The report says that there is a much more important choice that is being
overlooked entirely and that is the choice of courses," Riley said.
(20 Oct 1997 16:09 EDT)
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Math cited as key to achievement
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WASHINGTON - High school students who take algebra, geometry and other
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rigorous math courses are much more likely to be successful at college or in the
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workforce, says a U.S. Education Department report out Monday.
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Students with a grasp of higher level math achieve regardless of family income
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The proportion of students who take algebra I and geometry who head to
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Conversely, only 36% of those not taking algebra I and geometry went to
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Students headed for the workforce with a solid math background earned, on
average, 38% more per hour than peers without it.
Yet while algebra is the "gateway" to advanced math and science in high
school, most students do not take it in middle school, Riley says.
He cites a 1996 report by the National Assessment of Educational Progress
showing that only 25% of U.S. eighth-graders enrolled in algebra, and that
low-income and minority students were even less likely to take it. Japan and
Germany offer much more advanced math at an earlier grade.
The release of the findings comes as the administration gears up for tough
education battles. At issue are different House and Senate bills on voluntary
national tests, allowing poor students to use tax-supported vouchers to attend
private schools and creating "Education IRAs" to pay for private and parochial
schools.
By Tamara Henry, USA TODAY
Go to Lifeline
Go to People news
Go to Life front page
1 of 2
10/20/97 11:59:46
OCT. 17. 1997 3:12PM
DEPT ED/OFC OF SEC.
NO. 5659 P. 3/3
* changes in italics as of 3:00 pm, October 17th
U.S. Department of Education
"Mathematics Equals Opportunity"
Agenda
#450 Old Executive Office Building
October 20, 1997
NOT FOR RELEASE
12:00pm
I.
Secretary Richard Riley
Announces the release of report
"Taking tough courses are important for going to college"
High, rigorous national standards are important
introduces the Superintendent
12:10pm
II.
Superintendent Jerome Clark
Former need in district to improve math
What is Equity 2000?
Changes in the district
Results from Equity 2000
introduces the teacher
12:15pm
III.
P.G. County Teacher, Bernadette Dantley
Classroom experiences with Equity 2000
introduces the students and the Secretary's discussion
12:20pm
IV.
Secretary Riley and Prince George's County students
Interactive discussion with the Secretary on their personal experiences with tough
math courses, planning for the future
12:30pm END
V.
Few minutes of one-on-one press availability with participants
Contact: Erica Lepping (202)401-2571, Office of Public Affairs
Math Report 10/97
SUNTUM_M@A1
10/20/97 09:53:00 AM
Record Type:
Record
To:
William R. Kincaid, Joshua Silverman
CC:
Subject: Radio actuality by the President
THE WHITE HOUSE
Office of the Press Secretary
For Immediate Release
October 20, 1997
RADIO ACTUALITY OF THE PRESIDENT
THE PRESIDENT: A new study released by the Department
of Education today confirms what most of us knew instinctively
already - students, especially low income students, who challenge
themselves with rigorous math and science courses in high school are
much more likely to go on to college.
I've worked hard to make college affordable for all
Americans. Our increased Pell Grants and work study positions, the
new Hope Scholarship tax credits for the first two years of college
and other tax credits in education IRAs for the remaining years,
graduate school and other training all these will truly open the
doors of college to all who are willing to work for it.
We've addressed the economic barriers, now we have to
tackle the academic ones. While the studies show that taking algebra
in middle school was essential to preparing for advanced math and
science classes, just 25 percent of our 8th graders took algebra in
1996. We must do better. That's why I call upon all Americans to
support our voluntary national tests for 4th grade reading and 8th
grade math, to ensure that all our children meet the high standards
of academic excellence they'll need to succeed in tomorrow's world.
Our math test will make sure our children master algebra and prepare
for math and science courses that lead to college.
I call upon Congress to end the delays. Our
children are counting on us.
OCT. 17. 1997 3:12PM
DEPT ED/OFC OF SEC.
NO. 5659 P. 2/3
0
UNITED STATES
THE
DEPARTMENT OF EDUCATION
NEWS
UNITED name 0 THE
**ADVISORY**
**ADVISORY**
**ADVISORY**
WHO:
U.S. Secretary of Education Richard W. Riley
Prince George's County Public Schools Superintendent Jerome Clark
Equity 2000 Director Vinetta Jones
Suitland High School Mathematics Teacher Bernadette Dantley
Prince George's County students
WHAT:
Will participate in a press conference announcing the release of white paper,
"Mathematics Equals Opportunity"
WHEN :
Monday. October 20, 1997
12:00 pm
WHERE:
# 450 Old Executive Office Building
17th and G Streets, NW
Washington. D.C.
Secretary Riley will deliver highlights from the report "Mathematics Equals Opportunity" which provides
information on the link between taking tough math courses early, such as algebra and geometry, and going
on to college and succeeding in the job market. The secretary will emphasize the importance of achieving
to high standards and remark on the new financial opportunities students have to attend college. Prince
George's County students and a teacher involved in Equity 2000 will also join the secretary in a discussion
about the importance of taking tough math courses and preparing for college.
For security clearance into the event. please call Erica Lepping at (202)401-2571 and leave the spelling of
your full name, social security number and date-of-birth. You should plan to be at the Old Executive
Office Building no later than 11:30am, in light of the clearance process.
CONTACT:
Erica Lepping (202) 401-2571, Pager 1-800-SKY-GRAM, pin# 211-9840
###
PRESIDENT WILLIAM J. CLINTON
RADIO ACTUALITY
OCTOBER 17, 1997
A new study released by the Department of Education
today confirms what many of us knew instinctively.
Students -- especially low-income students -- who
challenge themselves with rigorous math and science
courses in high school are much more likely to go on to
college.
I have worked hard to make college affordable for all
Americans. Our increased Pell Grants and work study
positions, the new HOPE Scholarships and other tax
credits will truly open the doors of college to all who are
willing to work for it.
1
We have addressed the economic barriers. Now we
must tackle the academic ones. While the study showed
that taking algebra in middle school was essential to
preparing for advanced math and science classes, just 25
percent of eighth graders took algebra in 1996. We must
do better. That is why I call upon all Americans to
support voluntary national tests in fourth grade reading
and eighth grade math to ensure that all children meet
high standards of academic excellence. Our math test will
make sure our children master algebra and prepare for the
math and science courses that lead to college. I call upon
Congress to end the delays. Our children are counting on
us.
2
OCI. 17. 1997 4:00PM
OFFICE vr SECRETARI
DRAFT
Statement of
Richard W. Riley
U.S. Secretary of Education
Briefing for White House Reporters
October 20, 1997
Good afternoon. I have just returned from traveling with the President to
Brazil. Some of you were down there as well. I am here today to release a
major report and brief you on the week ahead on the President's education
agenda. This is a very busy week for the President and the Vice-President
when it comes to education.
The President, as you know, used his Saturday radio address to praise a
bipartisan effort to support charter school legislation that is now moving
through the Congress. He also used the radio address to endorse another
bipartisan legislative initiative that is being led by Congressman John Porter
and Congressman David Obey to fixing failing schools.
This is a very important initiative because it would support proven models of
success that are helping to turn around failing schools all across the country.
Some of these models are being used this year for the first time here in the
District of Columbia. We need to remember, as the President so often says,
that for every problem in American education there is already a solution and
part of our job is to make the match. We know how to fix failing schools and
the Porter-Obey initiative is targeted funding to help us get the job done.
OCT. 17. 1997
2
Today, we are releasing a major report entitled Mathematics Equals
Opportunity that conveys three powerful messages. First, that young people
who go on to college by overwhelming numbers -- 83 percent -- take the tough
math courses like algebra I and geometry.
Second, that taking these gate-keeping courses is especially important for low-
income students. Seventy-one percent of low income students who took
algebra I and geometry went on to college compared to only 27 percent of
low-income students who did not take these courses.
I just met with a group of young people from Prince George's County who are
part of the College Board sponsored Equity 2000 initiative to get more young
people to take algebra. These young people have gotten the message that
getting ready for college is their responsibility and that means taking the tough
math courses. But we need to make sure that everyone gets that message.
Only 63 percent of all young people take algebra and geometry and only 43
percent of all low-income students takes these math courses.
The third message of this report is that taking the right courses is more
important than what type of school you attend, whether it is public or private.
This latter point deserves some attention. Many vouchers proponents argue
that giving parents public tax dollars to send their children to private schools
is the key to educational renewal.
UCI, 17. 1997 4.00PM
OFFICE vr SEORETARI
3
This reports says that there is a much more important choice that is being
overlooked entirely and that is the choice of courses. Taking the right courses
matters a lot more in terms of going to college than whether your school is
public, private or parochial.
The President worked very hard to create the Hope Scholarship and the
Lifetime Learning Tax credit so young people have the financial support they
need to go to college. But young people have a responsibility as well to get
ready academically. This report tells them why it is so important.
Now, let me go on and tell you about the rest of the week.
Tomorrow, the President will meet with college and university leaders who
have endorsed his American Reads Challenge. Making sure that every child in
America can read well by the end of the third grade is a national goal that we
can achieve with the help of thousands of energetic college students who have
signed up to be reading tutors.
But we also want the Congress to act on the President's request for legislation.
I am concerned that the House is starting to get stuck in the usual partisan rut
and losing sight of what is important. It's a sad day when a reading initiative
has become a political hostage which seems to be the thinking of some
members of Congress.
SECRETARI
4
Making sure that all of our young people are literate is a grand goal that has
the full support of the American people. Congress needs to fulfill its part of
the bargain. Let's remember that the reading initiative is part of the budget
deal.
For his part, Vice-President Gore will be visiting Louisiana State University
and give a major address on race and education at Southern University Law
Center.
On Wednesday (not confirmed yet)the President and the Vice President will
meet with a group of high tech business leaders who strongly support the
President's call for voluntary national tests in reading and math.
On Wednesday
Later on during the day, I will join Larry Summers, the Deputy Secretary at
Treasury, at a press conference with Rep. Charlie Rangel (and Cong. Dick
Gephardt?) to once again reaffirm the Administration's strong opposition to
the Coverdell IRA education proposal. .
The Coverdell proposal is bad tax policy, a budget buster and it has little if
anything to do with improving public education. The Administration supports
the Rangel alternative which has a much more targeted focus and helps us
deal with the problem of school overcrowding.
SECRETARY
NO. 4020
1,
U
5
On Thursday, the President, the Vice-President, the First Lady and several
members of the Cabinet including Donna Shalala and myself will participate
in the White House Child Care Conference.
On Friday, both the President and the Vice-President will focus in on
education. The President will meet with several hundred teachers who are
part of the effort surrounding the National Board for Professional Teaching
Standards. This is a Initiative led by Governor Jim Hunt to establish nationally
accepted credentials for excellence in teaching. There are only 500 teachers in
America who have now met these high standards. The President's goal is to
have 100,000 board-certified teachers in the next ten years.
For his part, Vice-President Gore will announce a new public-private
partnership to match computers donations to low-income schools from federal
agencies.
This is a very busy week for the Administration when it comes to education
and that's the way it should be. Education is President Clinton's number one
priority and we need to pick up the pace to get all of America's children ready
for the 21 St century. Parents all over America are tuned into education as
never before. We need to take their concerns seriously and that is one thing
that the President is doing. Education matters and the President is determined
to get things done. Now, I will be happy to answer any of your questions.
Daily Education News
Friday, October 17, 1997
1. Forbes
October 20, 1997
American schoolkids score relatively well through
fourth grade. Why do they lag so badly in subsequent
years?
Claiming credit where no credit is due
By Peter Brimelow
BILL CLINTON GOT A LOT OF PUBLICITY this summer when he claimed credit for American fourth-graders'
second-place ranking in science, as measured by the Third International Mathematics and Science Study (TIMSS). The
previous year, American eighth-graders came in seventeenth.
"There are a lot of people who never believed that U.S. children would score in the top two in the world on any of
these tests," Mr. Clinton reportedly said. "Now they know they were wrong."
Bunk, says Barbara Lerner of Chicago-based Lerner Associates, public policy consultants. American fourth-graders
have always done about this well on international tests, Lemer points out. Where they do badly is where it really matters-as
17-year-olds-at the end of the K-12 educational process.
"Older students resist," Lerner says. And American educators apparently don't want to oppress them. Somewhere
between the fourth grade and graduation, American students tend to fall behind.
According to NAEP, the National Assessment of Educational Progress U.S. 17-year-olds score about the same or
slightly below the levels of knowledge in science, math and reading achieved nearly 30 years ago. Recently, scores have
basically been moving sideways.
The NAEP scores do represent a rebound from the 1970s, when achievement levels were falling sharply-a dark
episode in American education history that has been called "The Great Decline."
"But NAEP only began gathering data when the decline was well under way," says Lerner. "So today's 17-year-olds
are still probably below the levels of the early 1960s."
Minority scores in some areas have actually rebounded better than white scores. But they still lag significantly. And
there have been some recent retreats.
The lack of real progress comes in spite of the huge sums that the educational establishment has been extracting from
the American taxpayer. The U.S. spends a higher proportion of its GDP on K-12 education than the Organization for
Economic Cooperation and Development (OECD) average and many industrialized countries (see chart, upper left). (We threw
in Korea because it and Japan tied for first place in the recent TIMSS study.)
And because the U.S. economy is so much larger, this translates into a massive excess of per-pupil spending.
Conversely, Korea's per-pupil spending is at a strikingly low level.
To some extent, higher per-pupil spending is inevitable in the industrialized world because higher living standards
bid up higher labor costs. But most industries compensate with higher productivity.
And it's not just the amount of U.S. education spending but the distribution that is extraordinary (see chart, lower
left). For example, the Germans spend almost as much per pupil on early childhood and secondary education. But neither they
nor the Koreans put anything like the same resources into college students. Do Americans go to college to learn what Germans
and Koreans are taught earlier?
10/17/97 04:34 FAX 202 208 7751
VOLUNTARY NATIONAL TEST
003
1. San Diego Union-Tribune
October 17, 1997
More math urged at 8th-grade level
By Sharon L. Jones
STAFF WRITER
America's middle-school mathematics courses are intellectual wastelands, an expert said yesterday as he urged
educators to join a national effort to have all eighth-graders study algebra and geometry.
According to an international study of mathematics and science, students around the world generally are introduced to
eight new topics between fifth and eighth grade, said researcher William Schmidt.
In the United States, however, students study generally the same things they studied in elementary school, such as
addition, subtraction, multiplication and division, he said.
No wonder they grow bored and lose motivation to take advanced mathematics classes, said Schmidt.
"We simply have a conception of basic that is static, flat, dormant at the fourth-grade level," said Schmidt, while
speaking at a conference organized by the U.S. Department of Education.
About 1,600 people have registered to participate in the 1997 Regional Conference on Improving America's Schools,
which runs through tomorrow at the Town and Country Convention Center in Mission Valley.
The conference is titled "A call to action: Working together for equity and excellence." It is being broadcast on the
World Wide Web at the following address: http://www.iaswebcast.org/
Yesterday's opening session featured a roundtable discussion of five assistant secretaries of education.
In videotaped remarks, President Clinton stressed the importance of setting voluntary national standards of academic
excellence and national tests to measure whether students are meeting the standards.
"Our children will grow according to the expectations we have of them, so let's all work together to raise those
expectations, to strengthen and improve all our schools, and to help all our children reap the promise of the 21st century,"
Clinton said.
Clinton wants national tests to measure students' reading skills at the end of fourth grade and to measure their math
skills at the end of eighth grade.
House Republicans say such a test would duplicate the work of existing standardized tests.
In a session on standards and accountability, Gerald Tirozzi, assistant secretary in the office of elementary and
secondary education, said testing is key to holding the nation's schools accountable for student performance.
He said a school accountability system starts with academic standards that define what students should know and be
able to do at each grade level. Instructional materials and teacher training should support those standards, and tests should
measure whether students are meeting the standards, he said.
Tirozzi said educators agree that students should be able to read for comprehension by the end of fourth grade and
perform algebraic equations by the end of eighth grade. Students who haven't mastered these skills at these grade levels generally
never catch up to their peers and attend college at much lower rates, he said.
Tirozzi said many educators are uncomfortable with the idea of holding schools accountable for student performance,
but the public is frustrated by the lack of accountability.
If educators don't respond by making themselves accountable, there will be more retired military officers running
school systems, educational vouchers for private education, and privatization of schools, he said.
"People are looking for different ways to improve our schools," he said.
In a session on mathematics, Schmidt explained the results of the Third International Mathematics and Science Study.
U.S. students scored about the international average in fourth grade, but below the international average in eighth grade.
American eighth-graders outperformed only seven countries in mathematics.
Schmidt said the United States must radically change the way it is teaching mathematics, or it won't have a work force
that is able to compete. "This global society isn't rhetoric anymore; it's reality," he said.
029
Figure 1
College Attendance by Course-Taking
% attending college
100%
83%
80%
OPP/PES
60%
40%
36%
3036
20%
10/16/97 19:13 T202 401
0%
Took Algebra I
Did Not Take
and Geometry
Algebra I and
Geometry
Source: Analysis of NELS data
2030
Figure 2
College Attendance by Income and
Course-Taking
Took Algebra I and Geometry?
No
Yes
% attending college
OPP/PES
Low-income
Middle-income
10/16/97 19:14 T202 401 3036
High-income
0
20
40
60
80
100
Income divided into thirds
Source: Analysis of NELS data
Figure 3
031
5
Mathematics Achievement by
Highest Mathematics Course Taken
All Students
Public
Algebra Il
Private
Trigonometry
or Higher
OPP/PES
Low Income
Students
Algebra II
10/16/97 19:15 6202 401 3036
Trigonometry
or Higher
0%
20%
40%
60%
80%
100%
Percent of Students Scoring at the Highest Level of the
NELS 12th Grade Mathematics Achievement Test
Achievement divided into thirds; Students in highest level scored in the top third
Source: Analysis of NELS data
032
Figure 4
Proportion of Eighth-Graders Enrolled in Algebra, 1996
All
25%
White
27%
OPP/PES
Black
20%
10/16/97 19:16 6202 401 3036
Hispanic
20%
0%
20%
40%
60%
80%
100
Source: 1996 NAEP Mathematics Assessment background questionnaire
033
Figure 5
Students Plan to Drop Mathematics, But Want to Go to College
All
Black
Hispanic
100%
90%
91% 92% 93%
86%
83%
80%
OPP/PES
63%
60%
60%
51%
40%
10/16/97 19:16 6202 401 3036
20%
0%
Child plans to drop
Child wants to
Parent expects child
mathematics
go to college
to go to college
Source: NACME Survey
10/16/97
18:48
202 401 3036
OPP/PES
001
10/16/97
U.S. Department of Education
Office of Under Secretary, Planning and Evaluation Service
600 Independence Avenue, SW
Room 4168, FOB10
Washington, DC 20202
FAX COVER SHEET
Fax Number: (202) 401-3036
TO :
Bill Kincaid
FAX NO.: 456-7028
(Number of pages, including cover sheet: 36)
FROM: Melissa Chabran
PHONE NO.:401-1265
Message:
Bill,
Attached is the most recent version of the mathematics brief entitled,
"Mathematics Equals Opportunity."
Melissa Adiss
10/16/97
18:48
202 401 3036
OPP/PES
002
MATHEMATICS
EQUALS
OPPORTUNITY
Information brief prepared for
U.S. Secretary of Education Richard W. Riley
for speech at the White House, Washington, D.C.
October 20, 1997
STATEMENT OF
*
*
UNITED STATES OF AMERICA
A Letter from the Secretary of Education
Many parents, students, and educators in the United States are beginning to understand that
mastering mathematics is a gateway to college. The key to the "gate" is taking algebra or
courses covering algebraic concepts by the end of the 8th grade. However, many 8th and 9th
graders may be behind in their course taking to get on the road to college.
Recent analyses by the U.S. Department of Education indicate that high school students who take
algebra, geometry, and other rigorous mathematics courses are more likely to go on to college.
This is true regardless of their family income. In fact, the benefit of taking rigorous courses is
greatest for students from low-income families. Students who take chemistry, a subject that
requires a firm grasp of mathematics, are also more likely to go to college. Other research tells
us that the advantages of a solid mathematics background are not limited to the college bound.
Workers who have mastered mathematics earn more and are less likely to be unemployed than
workers who are less proficient in mathematics.
However, not all students have access to rigorous mathematics courses -- either bccause their
school does not offer everyone a full selection of challenging courses, or because not all students
are prepared for and encouraged to take them. The results of the recent Third International
Mathematics and Science Study (TIMSS) confirm that many students enter high school without a
solid grounding in mathematics, closing doors very carly for further education and better careers.
The implication is clear: The 8th grade is a critical point in mathematics education.
Achievement at that stage gives students a leg up on taking rigorous high school mathematics
and science courses important for later success.
As a nation, we must ensure that all our students develop the mathematics foundation they need
by the end of the 8th grade--and then build on it throughout high school. We challenge parents,
schools, community groups, higher education, and employers to ensure that all children have
access to rigorous mathematics courses and a chance at college. The U.S. Department of
Education stands ready to assist them by providing financial aid to college students and
supplementing Advanced Placement Exam fees for students who dcmonstrate need.
Additionally, the Department provides funding through Title I and other programs of the
Elementary and Secondary Education Act (ESEA) to assist schools in upgrading mathematics
teaching and learning nationwide. It is also offering a voluntary national test in 8th grade
mathematics, so that parents and schools can benchmark their students' performance. Together,
we will help to ensure that all students are given the opportunity to excel.
Sincerely,
Richard W. Riley
10/16/97
18:49
202 401 3036
OPP/PES
5
003
Table of Contents
Page
Executive Summary
3
Mathematics and Future Opportunities
5
The Importance of Mathematics for College Entrance
5
Mathematics in College the Workplace, and the 21st Century
9
Middle School: Getting on the Road to Challenging Mathematics and Science Courses
12
Laying the Foundation
12
Course-Taking Patterns in Middle School
13
Parent and Student Attitudes about Mathematics and Science
14
Mathematics in the U.S. Today
16
International Comparisons of Middle School Mathematics and Science
Proficiency
16
Promising Practices
18
Next Steps
24
Six Things Educators, Policymakers and Community Members Can do
24
Six Things Parents Can do
24
Resources
26
Appendix
28
2
10/16/97
18:49
202 401 3036
OPP/PES
004
Executive Summary
In the United States today, mastering mathematics has become more important than ever.
Students with a strong grasp of mathematics have an advantage in academics and in the job
market. The 8th grade is a critical point in mathematics education. Achievement at that stage
clears the way for students to take rigorous high school mathematics and science courses-keys
to college entrance and success in the labor force. However, most 8th and 9th graders lag so far
behind in their course taking that getting on the road to college is a long way off.
This report highlights the following findings:
Students who take rigorous mathematics and science courses are much more likely to
go to college than those who do not. Data from the National Educational Longitudinal
Study (NELS) reveal that 83 percent of students who took algebra I and geometry went on to
college within two years of their scheduled high school graduation. Only 36 percent of
students who did not take algebra 1 and gcometry courses went to college. While nearly 89
percent of students who took chemisury in high school went to college, only 43 percent of
students who did not take chemistry went to college.
Algebra is the "gateway" to advanced mathematics and science in high school, yet most
students do not take it in middle school. Students who study algebra in middle school and
who plan to take advanced mathematics and science courses in high school have an
advantage: approximately 60 percent of the students who took calculus in high school had
taken algebra in the 8th grade. However, 1996 NAEP data reveal that only 25 percent of
U.S. 8th graders enrolled in algebra, and that low-income and minority students were even
less likely to take algebra in the 8th grade.
Taking rigorous mathematics and science courses in high school appears to be
especially important for low-income students. Low-income students who took algebra I
and geometry were almost three times as likely to attend college as those who did not.
While 71 percent of those who took algebra I and geometry went to college, only 27 percent
who did not take those courses went on to college. By way of comparison, 94 percent of
students from high-income families, and 84 percent of students from middle-income
families who took algebra I and geometry in high school went on to college. Sixty percent
of students from high-income families and 44 percent of students from middle-income
families who did not take algebra I and geometry went to college.
Despitc the importance of low-income students taking rigorous mathematics and
science courses, these students are less likely to take them. Students from higher-income
families arc almost twice as likely as lower-income students to take algebra in middle school
and geometry in high school. They are more than twice as likely to take chemistry.
3
Other important findings include:
Mathematics achievement depends on the courses a student takes, not the type of
school the student attends. Students in public and private schools who took the same
rigorous mathematics courses were equally likely to score at the highest level on the NELS
12th grade mathematics achievement test.
Students whose parents are involved in their school work are more likely to take
challenging mathematics courses early. Students whose parents were involved in their
education were more likely to take courses like algebra and geometry in the 8th and 9th
grade than students whose parents were not involved.
The results of the Third International Mathematics and Science Study (TIMSS) reveal
that the middle school mathematics curriculum may be a weak link in the U.S.
education system. While U.S. 4th graders scored above the international average in
mathematics and science, U.S. 8th graders scored below average in mathematics, and only
slightly above the international average in science. Initial analysis of TIMSS data also
shows that the middle school mathematics curriculum in the U.S. is less challenging than in
other countries. The curriculum of average 8th-grade mathematics classrooms in the U.S.
resembles 7th grade curriculum elsewhere. Although algebra and geometry are integral
elements of the middle school curriculum in other countries, only a small fraction of U.S.
middle schools offer their students these topics.
Algebra in the Curriculum
Making a successful transition from arithmetic to more advanced mathematics, including
algebra and geometry, has often been difficult for students. As a result, many mathematics
programs in the U.S. are now systematically incorporating some fundamentais of algebra and
geometry into the upper elementary grade curriculum. In these programs, 5th, 6th and 7th
grade students are representing and solving equations, characterizing patterns and rates of
change among variables, and using other fundamental algebraic concepts.
In addition, some middle and high schools are taking a new approach to advanced topics.
While many schools offer the traditional model of separate courses for pre-Aigebra, Algebra 1,
Geometry, Algebra II, Trigonometry, pre-Calculus and Calculus, these schools are integrating
them. This approach is consistent with practices in other industrialized nations, which
integrate algebra, geometry, and other topics throughout the elementary, middle, and high
school years and offer a significant component of algebra in the 8th grade. Building a firm
foundation in algebra during the elementary and middle school years eases the shift from
arithmetic to advanced topics, whatever the format of students' new curriculum. NELS and
NAEP, the two sources of national mathematics course-taking data analyzed in this brief,
employ traditional courses titles, such as "algebra 1" and "geometry." Thus, these titles are
used throughout the brief.
4
10/16/97
18:52
202 401 3036
OPP/PES
005
Mathematics and Future Opportunities
The Importance of
Mathematics for College
Entrance
Figure 1
College Attendance by Course-Taking
Students who take rigorous
% attending college
mathematics and science courses are
100%
much more likely to go to college
83%
80%
than those who do not. Data from a
longitudinal survey of students who
60%
were in the 8th grade in 1988
(National Educational Longitudinal
40%
36%
Study or NELS) reveal that 83 percent
of students who took algebra I and
20%
geometry enrolled in college¹ within
0%
two years of their scheduled high
Took Algebra I
Did Not Take
school graduation. Only 36 percent of
and Geometry
Algebra I and
students who did not take algebra I
Geometry
Source: Analysis of NELS data
and geometry went to college (Figure
1). Similarly, students who take
rigorous science courses in high school are much more likely to go to college. While nearly 89
percent of students who took chemistry entered college, only 43 percent who did not take
chemistry went to college.
Students who take more rigorous mathematics courses also show higher gains in mathematics
achievement (measured by the mathematics achievement test given as part of NELS) than
students who take less challenging courses, even when controlling for achievement. For
example, among students who initially began at the same level of mathematics proficiency in the
8th grade, students who had taken algebra II or geometry by the 10th grade experienced greater
gains, on average, than students who had taken no algcbra or only algebra I during that period.
¹Throughout this report, the term "college" is used to refer to any postsecondary education taken at a public,
private not-for-profit, or private for-profit institution.
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Students of all income levels who
take rigorous mathematics and
science courses in high school are
Figure 2
more likely to go to college, and
College Attendance by Income and
among low-income students
Course-Taking
(students in the bottom third of the
income distribution)², the difference
Took Algebra I and Geometry?
No
Yes
is particularly dramatic. Students
from low-income families who took
% attending college
algebra 1 and geometry were almost
Low-income
three times as likely to attend college
as those who did not. While 71
Mddle-income
percent of low-income students who
took algebra I and geometry went to
college, only 27 percent of low-
High-income
income students who did not take
algebra I and geometry went on to
0
20
40
60
80
100
Income divided into thirds
college. The differences are also
Source: Analysis of NELS data
dramatic among students from
middle- and high-income families: 94
percent of students from high-income
families, and 84 percent of students from middle-income families who took algebra I and
geometry went on to college, while 60 percent of students from high-income families and 44
percent of students from middle-income families who did not take gcometry still went on to
college (Figure 2).
Unfortunately, many students, in particular low-income students, do not take these rigorous
mathematics and science courses. According to NELS, 63 percent of all students took algebra T
and geometry and 50 percent took chemistry. Students from low-income families, however, were
far less likely than their more advantaged peers to take these rigorous courses. Among students
in the bottom third of the income distribution, 46 percent took algebra I and geometry and only
33 percent took chemistry. By way of comparison, fully 81 percent of students in the top third of
the income distribution took algebra 1 and geometry, and 72 percent took chemistry. The
differences are similar for other rigorous mathematics courses (Table 1).
2 Income data are based on total family income reported by parents. Low, middle, and high income groups each
contain approximately one-third of the sample. The "all" category includes additional observations with
missing income data.
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Table 1: Course-Taking Patterns of NELS Students
Percent of Students Taking Course
All
Bottom Income
Middle Income
Top Income
Algebra 1 and
63
46
68
81
Geometry
Trigonometry
18
10
19
30
Chemistry
50
33
52
72
Accounting for course-taking patterns dramatically reduces the difference in the rate of
college-going between low- and high-income students. Students from high-income families are
almost twice as likely to attend college as students from low-income families (86 percent
compared to 44 percent) when course-taking patterns are not accounted for. However,
comparing only students who have taken rigorous courses to one another, students from low-
income families go to college at rates much more similar to students from middle- and high-
income families (Table 2). For example, among students who took chemistry in high school, 95
percent of high-income students, 89 percent of middle-income students, and 79 percent of
low-income students went to college. When low-income students take rigorous courses, income
effects on college entrance rates diminish greatly, although they do not disappear.
Table 2: College Attendance by High School Course-Taking Patterns of NELS Students
Percent of Students Attending Postsecondary Education
All
Bottom Income
Middle Income
Top Income
All
63
44
69
86
Algebra 1 and
Yes
83
71
84
94
Geometry
No
36
27
44
60
Trigonometry
Yes
94
90
92
98
No
59
42
66
83
Chemistry
Yes
89
79
89
95
No
43
31
50
68
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Public Versus Private
Achievement Depends on Course-Taking,
Not the Type of School
In general, the mathematics courses students take in high school determine achievement
more than the type of school they attend A great deal of diversity exists in public and
private schools. It is useful to note that accounting for coursc-taking patterns makes the
mathematics achievement of students in both types of schools very similar. Public and
private school students who took the same mathematics courses were almost equally likely
to score at the highest level on the NELS 12th grade mathematics achievement test. This was
also true for low income public and private school students Additionally, among both public
and private school students of all incomes, students who had taken more rigorous
mathematics courses were much more likely to score at the highest achievement level
(Figure 3)
Figure 3
Mathematics Achievement by
Highest Mathematics Course Taken
All Students
Public
Algebra II
Private
Trigonometry
or Higher
Low Income
Students
Algebra II
Trigonometry
or Higher
0%
20%
40%
60%
80%
100%
Percent of Students Scoring at the Highest Level of the
NELS 12th Grade Mathematics Achievement Test
Achievement divided into thirds; Students in highest level scored in the top third
Source: Analysis of NELS data
Private schools include non-religions, Catholic, and other private schools
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Mathematics in College, the Workplace, and the 21st Century
The benefits of taking rigorous mathematics and science courses extend to students heading
into the job market and to both two- and four-year colleges. As technology becomes prevalent
in the workplace, more and more workers will find they need to do high levels of mathematics
and science. The backgrounds they will need for doing this will have begun to form even before
high school. Rigorous mathematics and science preparation is also important to students
intending to go to a two- or four-year college or university. The level and number of
mathematics courses that a student needs to take before and during college depend on the college
and the major that the student wants to pursue. Mathematics- and science-related disciplines
typically require that students have taken rigorous mathematics courses. Many other popular
courses of study require advanced mathematics as well.
Two-year colleges often require all students to gain an understanding of intermediate algebra
prior to graduation, regardless of their course of study. Many two-year colleges require all
degree-secking students to take mathematics placement exams prior to enrollment. High scorers
may be exempt from taking certain mathematics courses, while low scorers may have to take
remedial mathematics courses. Many of the most popular majors at two-year colleges--including
Business, Nursing, and Computer Science--require more rigorous mathematics course work, such
as statistics.
Four-year colleges and universities typically require more high school mathematics
preparation for admission. Typical state four-year colleges and universities recommend, and in
some cases, require, that all students take at least three, and sometimes four, years of
mathematics in high school. Data collected by the College Board reveal that in 1997, 68 percent
of incoming freshmen at four-year colleges and universities had taken four years of mathematics
in high school. Furthermore, almost all of these students had taken algebra and geometry, and
more than half had taken trigonometry. Most state colleges require students to take mathematics
placement exams upon enrollment. Colleges look favorably on Advanced Placement courses and
often place students who have taken them out of introductory mathematics courses. While
graduation requirements differ depending on the students' major, many popular majors, such as
Business and Psychology, require students to take several more rigorous courses in mathematics
or science.
In the job market, workers who have strong mathematics and science backgrounds are more
likely to be employed and generally carn more than workers with lower achievement, even if
they have not gone on to college. A national survey found that by age 30, high school graduates
who had not furthered their education but had scored in the top quartile on the mathematics
portion of the Armed Services Vocational Aptitudc Battery (ASVAB--administered to civilians
for study purposes) earned, on average, 38 percent more per hour than high school graduates who
had not gone to college and had scored in the bottom quartile of the mathematic portion of the
ASVAB. Similarly, the unemployment rate among high school graduates who scored in the top
quartile of the mathematics test was only 4.4 percent. The unemployment rate was 10.3 percent
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among high school graduates who scored in the lowest quartile. Workers who scored in the top
quartile of the science section of the ASVAB also earned more, on average, and were less likely
to be unemployed.
Mathematics ability will be even more important for well-paying jobs in the future. Some
major firms already require job applicants to pass standardized mathematics and reading tests.
For example, Diamond-Star Motors, a joint venture of Chrysler and Mitsubishi, tests all
applicants for production and maintenance positions on their ability to do high school level
mathematics. Authors Richard Murnane and Frank Levy have identified a set of "New Basic
Skills," in their book of the same name, that non-college-bound high school graduates should
master in order to get well-paying jobs in the modem labor market. The "New Basic Skills" that
workers will need in order to earn a good wage include the ability to use mathematics skills and
concepts at least at the 9th grade level.
Shortages in workers skilled in mathematics and science could affect U.S. performance in global
markets. According to a recent report, America's New Deficit: The Shortage of Information
Technology Workers, from the Office of Technology Policy at the U.S. Department of Commerce, as
computer and data processing become more important to the economy, more and more workers
skilled in mathematics- and science-related disciplines will be needed to maintain the U.S.'s
international competitiveness. The report cites a survey by the Information Technology Association
of America indicating that 50 percent of company exccutives in information technology report a lack
of skilled workers as "the most significant harrier" to their companies growth during the next year.
However, the number of bachelor level computer science degrees awarded by U.S. colleges and
universities declined more than 40 percent between 1986 and 1994, indicating that these problems are
likely to persist.
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Mathematics and Science in the Modern Job Market
Many jobs in today's labor market require a mathematics or science background. A number
of these are among the fastest growing occupations nationally, and are not ones ordinarily
thought of as "technical." Projections from the Bureau of Labor Statistics' (BLS)
Occupational Outlook Handbook indicate that between 1994 to 2005, jobs requiring the most
education and training will be the fastest growing and highest paying. BLS predicts that
occupations requiring a bachelor's degree or higher will average 23 percent growth, almost
double the 12 percent growth rate projected for occupations that require less education and
training
Many jobs that once required little background in mathematics now call for specific skills in
algebra, geometry, measurement, probability, and statistics. According to an industry-wide
standard, an entry level automobile worker needs to be able to apply formulas from algebra
and physics to properly wire the electrical circuits of any car. The National Coalition for
Advanced Manufacturing has defined 25 specific standards of mathematics and micasurement
among their national skill standards for what a good competent worker should know and be
able to do.
Several of the fastest growing job arcas will reflect growth in computer technology and health
services fields that can require substantial mathematics and science preparation. Generally
speaking, fields requiring a strong science base also require substantial mathematics
preparation, as most academic science programs build upon a strong background in
mathematics. Below are some of the jobs which BLS indicates require a mathematics or
science background; while many of these jobs require mathematics or science course work
beyond the high school level, all require at least EL high school level background. The
occupations that BLS projects will be among the fastest growing during the period from 1994
to 2005 are noted with a star (*)
Computer Scientists (*)
Surgical Technologists
Systems Analysts (*)
Dieticians and Nutritionists
Occupational Therapy Assistants and Aides (*)
Optometrists
Chemical Engineers
Physical Therapists (*)
Civil Engineers
Roofers
Aerospace Engineers
Tool and Die Makers
Medical Assistants (*)
Photographers
Dentists and Dental Hygienists
Financial Managers
Surveyors
Budget Analysts
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Middle School:
Getting on the Road to Challenging Mathematics
and Science Courses
Laying the Foundation
"Mathematics is the language of science, and
Algebra is the "gateway" to rigorous
algebra is the minimum vocabulary that
mathematics courses. Rigorous mathematics
scientists of every discipline use to describe
courses build upon the skills and concepts
their work
that students learn in earlier mathematics
Dr. George Castro, Associate Dean of the
courses. Traditionally, students cannot take a
College of Science at San Jose State
rigorous mathematics course in high school
University
until they have successfully completed one or
more prerequisite courses. Algebra I, or
another course that covers basic algebraic concepts, is the prerequisite for more rigorous
mathematics in high school.
Students who plan to take advanced mathematics and science courses during high school and
begin to study algebra during middle school are at a clear advantage. A rigorous sequence of
mathematics spans several years. The traditional sequence of mathematics courses involves one
year courses in algebra I, geometry, and algebra II, followed by a half-year course in
trigonometry, a full- or half-year course in pre-calculus, and then calculus or an Advanced
Placement course. Increasingly, schools are covering these rigorous content arcas in courses that
integrate algebra, geometry and other areas of mathematics such as statistics and probability,
rather than teaching cach separately. According to NELS, approximately 60 percent of the
students who took calculus in high school had taken algebra in the 8th grade. The typical high
school sequence of rigorous science courses (biology, chemistry. and physics) also necessitates
an early background in algebra and geometry.
Students who do not take courses covering algebraic concepts early in their educational career
risk closing the door on many important opportunities, including opportunities to take courses
outside of mathematics and science. Some high schools require students to complete a specific
package of courses, including mathematics and science, in order to graduate. By the junior and
senior years, students who have not planned ahead have fewer options in choosing which courses
they take. Students who do not complete prerequisite and required courses early enough not only
risk being unable to take more rigorous courses in those disciplines later, but also may not have
time in their schedules to take other courses that can help prepare them for college or a career,
including foreign language, art, Advanced Placement, and "tech prep" courses.
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Course-Taking Patterns in Middle School
Despite recent increases in the proportion
of students taking algebra I in the 8th grade,
Figure 4
in 1996, most students were not enrolled in
Proportion of Eighth-Graders Enrolled in Algebra, 1996
this course. The proportion of 8th-graders
taking the National Assessment of
All
26%
Educational Progress (NAEP) mathematics
assessment who reported taking algebra has
increased. In 1992, only 20 percent of
White
27%
students reported taking algebra. In 1996, the
next year the NAEP mathematics assessment
was administered, 25 percent reported taking
Black
20%
algebra. This increase may be due to a
number of factors, including the National
Hispanic
20%
Council of Teachers of Mathematics'
(NCTM) call for including algebraic topics in
the middle school curriculum.
0%
20%
40%
60%
80%
100%
Source: 1956 NAEP Mathematics Assessment background questionnaire
Minority and low-income students continue
to be less likely to take challenging
mathematics courses in middle school than other students. The 1996 NAEP data reveal that
minority students are less likely to report being enrolled in algebra in the 8th-grade (Figure 4).
The data also indicate that students from disadvantaged backgrounds are less likely to be enrolled
in algebra during the 8th grade: While 29 percent of students who were not eligible for the
national school lunch program reported being enrolled in algebra during the 8th grade, only 15
percent of students who were eligible for the national school lunch program were enrolled in
algebra.
While the number of students taking algebra courses has increased, recent evidence suggests
that the content of these courses has remained rigorous. Many states have recently increased
mathematics requirements for high school graduation, often requiring that students take more
years of mathematics than were required in the past, or mandating that students complete certain
courses. A. recent study supported by the National Science Foundation (NSF) examined the
content of mathematics courses in schools in several of the states making the most substantial
changes in mathematics requirements. The study focused on basic courses, such as algebra 1,
which had experienced large enrollment increases because of more stringent graduation
requirements. Despite the larger numbers of students enrolling in the courses, the study found
that the content of these courses was essentially unchanged, indicating that more students were,
in fact, being exposed to rigorous mathematics.
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Parent and Student Attitudes about Mathematics and Science
Large proportions of middle school
students indicate that they do not
plan to take mathematics and science
Figure 5
courses beyond what their schools
Students Plan to Drop Mathematics, But Want to Go to College
require. A nationally representative
All
Black
survey of public school students and
Hispanic
parents conducted by Louis Harris
100%
Associates for the National Action
90%
91%
92%
83%
86%
83%
Council for Minorities in Engineering
80%
(NACME), Inc. found that large
proportions of students would like to
63%
60%
60%
stop taking mathematics and science
51%
courses as soon as they can. Fifty-one
percent of the 5th through 11th grade
40%
students surveyed indicated that they
would take mathematics classes only
20%
as long as required, while 47 percent
reported they would study science only
0%
as long as it is required.
Child plans to drop
Child wants to
Parent expects child
Distressingly, young minority
mathematics
go to college
to go to college
Source: NACME Survey
students--5th through 8th graders who
will soon be facing major decisions
about which courses to take--werc more likely to indicate that they planned to drop mathematics
and science as soon as they were able to (61 percent planned to drop mathematics, and 58 percent
planned to drop science). Minority students of all ages were more likely than other students to
say that they would like to stop taking mathematics and science as soon as they could (Figure 5).
However, the same students indicate that they would be interested in going to college, and
taking college-level mathematics courses. Eighty-six percent of all students surveyed said that
they would like to go to college. Although less than half of the 9th- to 11th-grade students said
that they planned to take trigonometry or algebra II in high school, nearly two-thirds said that
they were interested in taking Advanced Placement courses. These contrasts signal that many
students do not understand the importance of, and requirements for, taking rigorous mathematics
and science courses in high school, including the need to take algebra by the 8th grade. In fact,
only 25 percent of minority and 42 percent of non-minority 5th- through 8th-grade students
recognized that if they did not take algebra they would not be able to take other mathematics
classes in the future.
Parent and teacher involvement may make a large difference in students' decisions about
mathematics and science. According to the NACME survey, ninety-four percent of students
indicated that their parents' or guardians' advice was important to them in deciding what they
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would study in school, and 88 percent indicated their teachers' advice was important. Ninety-one
percent of parents want their children to continue their education beyond high school. However,
when 9th- through eleventh-graders were asked who decided which mathematics classes they
would take, 79 percent indicated that they had made the decision by themselves.
Analysis of the NELS data indicates that students with greater levels of parental involvement
are more likely to take advanced mathematics courses. Analysis of the course-taking patterns
of the NELS students who were in 8th-grade in 1988 reveals that regardless of whether the level
of parent involvement was reported by the student, the parent, or the teacher, higher levels of
parental involvement were consistently associated with higher likelihoods of taking rigorous
mathematics courses. While only 8 percent of those students who said that they did not discuss
programs at school with their parents took algebra I by the 8th grade, 17 percent of those who
said that they discussed school programs three or more times during the previous semester took
algebra I by the 8th grade. Students whose parents or teachers indicated greater levels of parental
involvement were also more likely to take advanced courses. Thirty-seven percent of students
whose parents said that they rarely talked to their child about high school plans took geometry by
the 10th grade, while 48 percent of those students whose parents said they regularly spoke to the
child about high school plans took geometry by the 10th grade. While 27 percent of students
whose teachers said their parents were not involved took geometry by the 10th grade, a full 63
percent of the students whose teachers said that their parents were very involved took geometry
by the 10th grade.
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Mathematics in the U.S. Today
International Comparisons of
Middle School Mathematics and
Science Proficiency
U.S. Performance on TIMSS,
Relative to International Average
Recent findings from the Third International
Fourth grade
Eighth Grade
Mathematics and Science Study (TIMSS),
indicate that the mathematics curriculum
Mathematics
from grades five through eight may be a weak
link in the U. S. educational system. Newly
available data from TIMSS (the most
Above average
Below average
comprehensive international comparison of
schools and students ever undertaken) reveal
Science
that U.S. 4th graders scored above the
international average in both mathematics and
Above average
Above average
science. Among 25 other participating nations,
only Korea performed better than the U.S. in
4th grade science, and only 7 of the 25 other
countries did better than the U.S. in 4th grade mathematics. These findings are in contrast to
earlier findings from TIMSS that indicate that U.S. 8th graders perform slightly below the
international average in mathematics, and only slightly above the international average in
science. In fact, only one country--the U.S. in mathematics--falls from above the international
average at 4th grade to below the international average at 8th grade.
The U.S. expects less of its middle school students compared to high performing nations.
TIMSS data suggest that one reason U.S. students do less well at 8th grade is that the middle
school mathematics curriculum in the U.S. is significantly less challenging than curricula in other
countries. In Germany and Japan, virtually all students in grades 5 through 8 move beyond
arithmetic to the foundations of algebra and geometry. By 8th grade, mathematics courses in
virtually all other countries participating in TIMSS include significant algebra and geometry,
while in the U.S., only students in college-preparatory classes receive significant exposure to
algebra, and very few students study geometry. As a result, the content taught in U.S. 8th grade
mathematics classrooms is usually at a 7th-grade level compared to the 40 other nations in the
TIMSS study.
TIMSS also found that U.S. mathematics classes require students to engage in less high-level
mathematical thought and solve fewer multi-step problems than classes in Germany and
Japan. A U.S. mathematics teacher's typical goal is to teach students the mechanics of solving a
problem versus understanding the concepts behind it, while a Japanese teacher's goal is to help
them learn the basics as well as understand the relevant mathematical concepts. In a typical U.S.
classroom, students follow the teacher as he or she leads them through solutions to mathematics
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problems. In Japan, students are asked to solve problems, present them to the class, and describe
how they approached the problem to increase their own understanding.
How Does Our Curriculum Compare Internationally?
The 8th grade mathematics curricula in both Germany and Japan are more advanced than
in the United States. The TIMSS analysis of U.S. curricula examined both the content of
textbooks and how it is implemented in classrooms.
An analysis of curricula in the U.S. and other countries found that algebra and
gcometry occupy more space' in German and Japanese textbooks than they de
in the textbooks used by a majority of U.S. 8th graders (Figure 6).
Analyses of curriculum implementation make clear that in the middle school years, the
U.S. still focuses on arithmetic. For example, 40 percent of U.S. 8th grade
mathematics lessons included arithmotic topics, whereas only 13 percent of Germany's
and none of Japan's lessons at the 8th grade level included these topics. The major
focus of curriculum taught in these countries is on algebra and geometry.
Figure 6
Algebra in 8th Grade Textbooks
% of space devoted to algebra In 8th grade mathematics textbooks
50%
40%
40%
30%
26%
20%
10%
10%
0%
Space is defined in terms of the percentage of a textbook OF guidebook that is devoted to particular topics/blocks
Topics include such items as formulas, geometry, numbers, and estimation. Blocks OFC sub-units of topics that are
parts of a textbook and which might include individual pedagogical suggestions, individual examples, individual
testing narrative blocks, graphic blocks, suggested activities, and mathematical problems.
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Promising Practices
Across the country, there are many promising mathematics and science practices underway.
Many of these are responsible for increases in the numbers of students taking rigorous courses in
mathematics and science. Just as important, many students arc finding that they do quite well in
these more advanced courses. There is, of course, no one formula to success. Highlighted here
are a number of places that demonstrate effective strategies.
Getting Set for Success. The Algebra Project, supported by the National Science Foundation
(NSF) and directed by Robert Moses, addresses equity of opportunity by helping 6th, 7th, and 8th
graders in inner city and rural areas understand challenging mathematics. Based on the
conviction that all students can learn algebra given the proper context, the Algebra Project scrves
over 40,000 low-income and minority middle school students in 22 urban and rural sites in 13
states. Part of what makes the Algebra Project successful is that students study algebra as early
as possible. This ensures their access to a college preparatory high school curriculum.
The project introduces rigorous mathematics concepts in 6th grade, creating a foundation to build
upon throughout the middle school years. Using a variety of strategies, it has been successful in
helping traditionally underserved students complete algebra I by the 8th or 9th grades, and either
pre-calculus or calculus by the 12th grade. For example, one strategy is to place young
college-age students in schools to provide extra assistance. In addition, the project provides
after-school activities for students, and professional development for teachers. Teacher
professional development highlights beliefs about the curriculum and how it should be taught.
The Algebra Project has produced positive effects in the Mississippi Delta and in Jackson,
Mississippi. Additionally, an evaluation team of education experts from across the country found
evidence of positive outcomes in teaching, student attitudes about and engagement in
mathematical ideas, and community involvement.
Contact:
Robert Moses
The Algebra Project, Inc.
99 Bishop Richard Allen Dr.
Cambridge, MA 02139
(617) 491-0200
Taking the Right Courses. In 1990, the College Board launched EQUITY 2000 to increase
minority enrollment in college preparatory mathematics courses. Originally piloted in six
communities, EQUITY 2000 requires participating school districts to phase out lower-level
mathematics in favor of all students taking college preparatory curriculum-beginning with
algebra and geometry. EQUITY 2000 influences policies, curricula and student academic
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development at all grade levels, but particularly grades six through nine. These are critical years
for mathematics education. During this period, parents, students, and educators make key
decisions about which courses students should take and how they should begin planning for
education and careers after high school. Equity 2000 provides on-going professional
development to help teachers work with mixed-ability classes. It also trains administrators and
teachers to use student enrollment and achievement data to drive school-based decision-making,
helps schools establish support services for students who need extra time and effort to learn
challenging content, and encourages and supports parents to become advocates on behalf of their
children.
Increased parental involvement is a priority in Equity 2000. It recognizes the important role that
parents play in nurturing and reinforcing their children's desire to attend college. Equity 2000
has sponsored Saturday and summer academies on college campuses for entire families. It also
sponsors Family Math nights in which parents and students learn mathematics concepts together.
Results at the six pilot sites indicate that:
All sites dramatically increased the percentage of students enrolled in algebra I
by the 9th grade, and in three pilot districts, all 9th graders enrolled in
algebra I.
The percentage of students passing algebra I did not decline significantly, and
in some cases rose, as more students from the discontinued lower tracks began
enrolling in algebra classes.
Contact:
Vinetta Jones
Equity 2000
The College Board
1717 Massachusetts Avc., NW
Washington, DC 20036
(202) 822-5900
www.collegeboard.org/equity/html/indx001.html
Advanced Placement Participation and Scores on the Rise. The College Board's Advanced
Placement (AP) Program was started nearly four decades ago to enable students to complete college-
level studies while still in high school and to obtain college credit or placement. AP courses are
widely recognized as setting the standard for high levcls of academic achicvement in high school.
Today more than 500,000 students in about half of the nation's high schools take at least one AP
course. Dramatically increased participation in AP courses in Texas and South Carolina illustrate
the success of AP-based reform initiatives in two states.
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Texas: The Advanced Placement Incentives program was developed in the Dallas, Texas area by
O'Donnell Foundation in reaction to low rates of college attendance and poor college preparation.
The Advanced Placement Incentives program reward results in AP courses in mathematics,
science, English, and the arts by providing performancc-based financial incentives to teachers,
school and students. Teachers are given financial incentives as well as registration and fees for
attending College Board AP teacher training during the summer, and to teach AP courses.
Students who complete the Advanced Placement course may take the AP exam at half-cost (the
total cost for an AP exam is about $73). Those who score a three or better (on a five point scale)
are given financial incentive and reimbursed for the cost of the exam.
In five years of operation in nine Texas public schools, the O'Donnell foundation reports that:
The year before the program began in nine typical public high schools, 48 students took
AP exams in mathematics, science, and English, and received a three or better. In the fifth
year of operation, 1,099 students took AP exams and 521 received a score of three or
better.
In nine high schools in the Dallas Independent School District, the eighth largest inner-city
school district in the country, with 85 percent minority enrollment, growth in AP
participation has been outstanding. Students took 312 AP in mathematics, science, and
English in May 1995, the year before the program started in the Dallas schools. In May
1997, the second year of the Dallas program, this number has grown to 1,750. The
number of students scoring three or higher during that time period grew from 139 to 559.
The Dallas school program has experienced proportional growth among female and
minority students. The year before the program started, 94 females took exams in
mathematics, computer science, and the sciences. In the program's second year, 452
female students took these exams.
Minority participation has also grown in Dallas, from 64 7 African-American and Hispanic
students taking AP mathematics, science, and English exams the year before the program
began, to 734 in the program's second year.
South Carolina: With former Governor Riley's school reform package of 1984, South Carolina
became one of the first states to legislate funding and other actions to boost student participation
in AP classes. The state appropriated funds to train AP teachers and to help pay for AP exams, as
well as required that public colleges accept AP courses if the student scored 3 or higher on the
exam. As a result, from 1984 to 1997 South Carolina experienced:
An increase in the number of students taking AP exams from 2,799 to 9,748.
An increase in the number of AP exams from 3,461 to 14,890, with the mean grade
remaining stable at approximately 2.7 - 2.8.
An increase in the number of AP science exams (Biology, Chemistry, Physics) from
27 to 2,414.
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An increase in the number of AP math exams (Calculus AB and BC) from 46 to
2,767.
Ninety-three percent of all the public high schools in the state participating in AP
(184 of 197 public high schools).
AP participation rates above the national average.
AP Exams Taken
(Eleventh and Twelfth Graders)
1984
1997
Percent increase
South Carolina
3,461
14,890
77 percent
National
223,888
843,399
73 percent
Sources: College Board. Advanced Placement Program, National and South Carolina Summary Reports, 1984 -
1997.
Contacts:
Macarthur Goodwin
South Carolina Department of Education 1429 Senate St.
Columbia, SC 29201
(803) 734-8382
www.state.sc.us/sde
Patrick Moore
O'Donnell Foundation
100 Crescent Ct.
Suite 1660
Dallas, TX 75201
(214) 871-5800
Strengthening Curriculum and Instruction. Sponsored by the University of Pittsburgh's
Learning Research and Development Center, the Quantitative Understanding: Amplifying
Student Achievement and Reasoning (QUASAR) Project aims to raisc low levels of student
participation and performance in mathematics. QUASAR is an urban middle school
demonstration project that fosters the development and implementation of improved mathematics
instructional programs in economically disadvantaged communities. The program revolves
around three key principles: (1) all students are able to learn a broad range of mathematical
content; (2) all students can acquire a deeper and more meaningful understanding of
mathematical ideas; and (3) all students can demonstrate proficiency in mathematical reasoning
and complex problem solving.
In QUASAR schools, teams of mathematics teachers, school administrators and "resource
partners"-- generally mathematics educators from local universities -- collaborate to develop,
implement, and refine mathematics instruction. All project schools have eliminated most forms
of academic tracking, replacing it with the development of deeper student understanding and
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022
high-level thinking and reasoning for all students. While curricula, teaching strategies, and
approaches to professional development vary, all QUASAR sites include extensive attention to
professional development and teacher support. Additionally, the University of Pittsburgh's
Learning Research and Development Center provides schools with ongoing support and updated
information on their progress.
Data indicate that QUASAR schools build teachers' capacity to improve the quality of their
mathematics instruction. Students increase their capacity to think, reason, solve complex
problems, and communicate mathematically and they do SO while continuing to learn basic skills.
QUASAR school students, particularly those who are from minority groups and whose English
proficiency is limited, have increased their understandings across a range of important
mathematical ideas. Additionally, QUASAR students in grade 8 performed as well as other
students on basic and traditional items of the 1992 NAEP Mathematics Assessment. They
performed better than their peers on less traditional middle school mathematics content.
Contact:
Edward Silver
QUASAR
Learning Research Development Center 3939 O'Hara St.
Pittsburgh, PA 15260
(412) 624-3231
www.lrdc.pitt.cdu/quasar/quasar.htmil
Raising the Standard. The New York Regents Exam has spurred thousands more high school
students to take and pass college-preparatory mathematics courses. In 1993 then New York
Chancellor Ramon Cortines required all students to take tougher Regents-level mathematics and
science courses traditionally reserved for college-bound students. Beginning in 1995, the state
required that all students take Regents-level classes. The number of Hispanic and black students
who passed the science portion of the Regents Exam more than doubled over the previous year.
The state is now requiring all students take and pass Regents Exams. In addition, Commissioner
of Education Richard Mills recently called for an increase in the rigor of the state's requirements
for graduation from high school, including adding another year of both mathematics and science
to the current two years required in each.
Contact:
Edward Lalor
New York State Department of Education
Education Building
111 Washington Ave.
Room 675
Albany, NY 12234
(518) 473-7880
www.nysed.gov
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023
Living Up to Potential. Twenty school districts from Chicago's North Shore joined forces in
1995 to provide their students with a world class education in mathematics and science. Calling
themselves the First in the World Consortium, their first challenge was to determine what a
"world class" education looked like. They then measured their current performance against that
benchmark and developed an improvement strategy.
The Consortium's directed its efforts toward three objectives: (1) benchmarking performance
against international standards in mathematics and science, using the Third International
Mathematics and Science Study as a guide; (2) creating a forum to clarify world-class education
standards for business leaders, policy makers, educators, and community members; and (3)
establishing a network of learning communities for educators, parents, and community leaders
within the Consortium school districts and beyond.
Students in grades 4. 8, and 12 in First in the World Consortium districts took the TIMSS
assessment in Spring 1996. Fourth and eighth graders' results placed them among the top
performers in the world, well exceeding U.S. performance generally.
The Consortium attributes its success to the fact that:
Fifty percent of its 8th grade students took algebra or geometry compared to 25 percent of
students nationally who take algebra;
it had high expectations for students and teachers; and
it had gained broad-based community support for improved student performance.
The First in the World Consortium is not resting on its success. Its "community of lcarners"
approach continues to promote teacher participation and provide a context for long-term
commitment to the consortium's goals and to growth in student learning. To this end, it has
created teacher learning networks to strengthen curriculum standards, models of instruction,
assessment, and use of technology.
The resources of the First in the World Consortium place it at an advantage. Yet, what truly
distinguishes it is its willingness to identify its weaknesses and address them. The consortium
credits both state and federal support for helping it focus on its goals. Its experiences
demonstrate that, when given the opportunity, U.S. students can perform as well as, or better
than, students anywhere.
Contact:
Paul Kimmelman
West Northfield School District 31, First in the World Consortium
3131 Techny Rd.
Northbrook, IL 60062
(847) 272-6880
www.ncrel.org/sdrs/firstwor.htm
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024
Next Steps
Six things educators, policymakers and community members can do:
1. Provide all students the opportunity to take algebra I or a similarly demanding course that
includes fundamental algebraic concepts in the 8th grade and more advanced math and science
courses in all four years of high school.
2. Build the groundwork for success in algebra by providing a rigorous curriculum in grades K-7
that moves beyond arithmetic and prepares students for the transition to algebra.
3. Ensure that all students, parents, teachers, and counselors understand the importance of
students' early study of algebra as well as continued study of rigorous mathematics and science in
high school.
4. Provide teacher preparation and professional development to teachers of mathematics to
increase their knowledge and skills in mathematics and the teaching of mathematics.
5. Support mathematics achievement outside the classroom through math clubs, tutoring, and job
shadowing for students who may need extra help.
6. Support parent involvement in their children's mathematics education.
Six things parents can do:
1. Discuss your children's mathematics homework with them.
2. Visit your children's mathematics teacher to find out what your children are learning and how
you can help.
3. Insist that your children enroll in algebra I or a similarly demanding course that includes
fundamental algebraic concepts in the 8th grade and more advanced math and science courses in
high school SO they can keep all of their future options open.
4. Ensure that your children are gaining the groundwork for success in algebra through a rigorous
curriculum in grades K-7 that moves beyond arithmetic and prepares them for the transition to
algebra.
5. Help your children understand the importance of taking challenging mathematics and science
courses to their future by visiting colleges, familiarizing them with college requirements, and
exploring financial aid options available to students.
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025
6. Show the importance of mathematics for career choices by talking with your children about the
use of mathematics in your work or the work of adults they know.
I
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Resources
Everson, Howard T. and Marlcne Dunham "Signs of Success-EQUITY 2000, Preliminary
Evidence of Effectiveness. New York, NY: The College Board, 1996.
Hawcs, Mark, Kimmclman, Paul, and Kroeze, David. "Becoming 'First in the World' in Math
and Science: Moving High Expectations and Promising Practices to Scale." Phi Delta
Kappan, Volume 79, Number 1, September 1997.
Jones, Vinetta C. "What A Difference A Standard Makes." In D. Bartels & J. Opert Sandler
(Eds.), This Year in Science: Implementing Science Education Reform." Washington, DC:
American Association for the Advancement of Science, in press.
Levy, Frank and Richard Murnane. Teaching the New Basic Skills: Principles for Educating
Children to Thrive in a Changing Economy, New York: The Free Press, 1996.
National Action Council for Minorities in Engineering. Uninformed Decisions: 1 Survey of
Children and Parents about Math and Science, Conducted for National Action Council for
Minorities in Engineering, By Louis Harris and Associates, 1995.
The National Commission on Teaching and America's Future. What Matters Most: Teaching for
America's Future, September, 1996. http://www.tc.columbia.edu/-teachcomm/index2.htm
Porter, Andrew. "The Effects of Upgrading Policies on High School Mathematics and Science."
Consortium for Policy Research in Education, 1997, and in Brookings Papers on Education
Policy, 1997.
Schmidt, William H., McNight, Curtis C., and Raizen, Senta A. A Splintered Vision: An
Investigation of U.S. Science and Mathematics Education, East Lansing, MI; U.S. National
Center for the Third International Mathematics and Science Study, Michigan State
University, 1996. ttp://kapiswww.wkap.nl/kapis/CIG-BIN/WORLD/bovK.htm?0-7923-
4441-3
U.S. Department of Education. National Center for Education Statistics. Education and the
Economy: An Indicators Report, Washington, D.C.: U.S. Government Printing Office, 1997.
http://nces.ed.gov/pubsearch/infopage.idc?cil=97269XXXXX
U.S. Department of Education. National Center for Education Statistics. NAEP Facts: Eighth-
Grade Algebra Course-Taking and Mathematics Proficiency, Washington, D.C.: U.S.
Government Printing Office, 1996. http://nces.ed.gov/pubs/96815.html
U.S. Department of Education. National Center for Education Statistics. Pursuing Excellence: A
Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum, and
26
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Achievement in International Context, Washington, D.C.: U.S. Government Printing Office,
1996. http://nces.cd.gov/timss/
U.S. Department of Education. National Center for Education Statistics. Pursuing Excellence: A
Study of U.S. Fourth-Grade Mathematics and Science Achievement in International Context,
Washington, D.C.: U.S. Government Printing Office, 1997. http://nces.ed.gov/timss/
U.S. Department of Education. National Center for Education Statistics. Statistics in Brief:
Changes in Math Proficiency Between Sih and 10th Grades, Washington, D.C.: U.S.
Government Printing Office, 1996.
http://nces.ed.gov/pubsearch/infopagc.idc7cid=93455XXXXX
U.S. Department of Education. Planning and Evaluation Service. Analysis of NELS:88
Follow-Up Data: Factors That Affect College Enrollment, Forthcoming.
U.S. Department of Labor, Bureau of Labor Statistics. Occupational Outlook Handbook,
Washington, D.C.: U.S. Government Printing Office, 1997.
http://stats.bls.gov:80/ocohome.htm
27
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Appendix
The NELS:88 data. The National Education Longitudinal Study of 1988 (NELS:88) initially
surveyed a nationally representative sample of 26,000 public and private school 8th grade
students in 1988. The data collected include responses to student questionnaires, scores on
standardized achievement tests, high school transcripts, and interviews with parents and teachers.
Since the initial survey in 1988, the students have been resurveyed every two years, with the most
recent data available gathered two years after their scheduled high school graduation in 1994.
The analyses in this report are based on a sub-sample of over 13,000 individuals from whom data
were collected in all three follow-up surveys. Analysis of course-taking patterns is based on
student reports of 8th-grade course-taking and high school transcript data. The actual titles of
mathematics courses as they appcar on the transcripts may vary, despite covering similar content
(for example, geometric concepts); accordingly, we have attempted to include all courses under
the traditional course names (i.e. "geomctry," "algebra II") reflective of their content.
28
A Letter from the Secretary of Education
Many parents, students, and educators do not realize that within the United States today,
mastering mathematics has become a gateway to the road to college--and taking algebra or
courses covering algebraic concepts by the end of the 8th grade is a key to the "gate." Although
almost all parents want their children to go on to college or some advanced training, many 8th
and 9th graders may be behind in their course taking to get on the road to college, and not realize
it.
Recent analyses conducted by the U.S. Department of Education indicate that students with
strong mathematics backgrounds-those who take algebra and geometry and more rigorous
mathematics courses during high school--are more likely to go on to college. This is true
regardless of their family's level of income. In fact, the positive impact of taking rigorous
courses is most dramatic for students from low-income families. In addition, students who took
chemistry, a subject which requires a strong background in mathematics, were also more likely to
go to college. Other research tells us that the benefits of a strong background in mathematics are
not limited to college-going, and workers with high levels of mathematics achievement carn
more and are less likely to be unemployed than workers who are less proficient in mathematics.
However, not all students have access to rigorous mathematics courses--either because their
school may not offer a full selection of challenging courses to all students, or because students
are not prepared for and encouraged to take them. The results of the recently completed Third
International Mathematics and Science Study (TIMSS) confirm that many students enter high
school without a solid grounding in mathematics, closing doors very early to opportunities for
further education and better career opportunities.
The implications are clear: The 8th grade is a critical point in mathematics education
Achievement at that stage opens opportunities for students to take rigorous high school
mathematics and science courses important for later success. As a nation, we must ensure that all
our students develop the necessary mathematics background by the end of the 8th grade--and
build on that foundation throughout high school. We challenge parents, schools, community
groups, colleges, universities, and employers to ensure that all children have access to rigorous
mathematics courses and encourage them to go to college. To assist in that effort, the U.S.
Department of Education stands ready to assist states, local communities, and individual students
by providing federal student financial aid for college, by supplementing Advanced Placement
Exam fees for students' who demonstrate need by providing funding through Title I of the
Elementary and Secondary Education Act (ESEA) and other programs to assist schools in
upgrading mathematics teaching and learning, and by providing a voluntary national test in 8th
grade in mathematics to help ensure that all students are given the opportunity to excel.
Sincerely,
Richard Rilcy
Executive Summary
Within the United States today, mastering mathematics has become more important than ever.
Students with strong mathematics backgrounds have advantages in academics and in the job
market. The 8th grade is a critical point in mathematics education, and achicvement at that stage
opens opportunities for students to take rigorous high school mathematics and science courses
that are keys to college entrance and success in the labor force. However, although most parents
want their children to go on to college or some advanced training, most 8th and 9th graders are
behind in their course taking to get on the road to college. Findings highlighted in this report
include:
Students who take rigorous mathematics and science courses arc much more likely to
go to college than those who do not. Data from the National Educational Longitudinal
Study (NELS) reveal that 83 percent of students who took algebra I and geometry went on to
attend a two or four year college within two years of their scheduled high school graduation,
compared to a college attendance rate of only 36 percent among students not taking algebra I
and geometry; while nearly 89 percent of students who took chemistry went to college, only
43 percent of students who did not take chemistry in high school went to college.
Algebra is the "gateway" to advanced mathematics and science in high school-yet
most students currently do not take algebra during middle school. Students who plan to
take advanced mathematics and science courses during high school and study algebra during
middle school are at an advantage: Forty-six percent of students who took algebra I in the
8th grade took calculus in high school, compared to only eight percent of students who took
algebra I in the 9th grade. However, 1996 NAEP data reveal that only 25 percent of 8th
graders in the U.S. were enrolled in algebra, and that low-income and minority students are
even less likely to be enrolled in algebra during the 8th grade.
Taking rigorous mathematics and science courses in high schools appears to be
especially important for low-income students. Low-income students who took algebra I
and geomctry were almost three times as likely to attend college as those who did not: While
71 percent of those who took algebra I and geometry went to college, only 27 percent who
did not went on to college. By way of comparison, 94 percent of students from high income
families, and 84 percent of students from middle income families who took algebra I and
geometry in high school went on to college, while 60 percent of students from high income
families and 44 percent of students from middle income families who did not take algebra I
and geometry still did go on to college.
Despite the importance of taking rigorous mathematics and science courses for low-
income students, they are less likely to take these courses. Students from higher income
families arc almost twice as likely to take algebra in middle school and geometry in high
school and more than twice as likely to take chemistry than lower income students.
2
Other important findings include:
Mathematics achievement depcnds on course-taking, not the type of school a student
attends. Students at public and private school who had taken the same rigorous
mathematics courses were equally likely to score at the highest level on the NELS 12th
grade mathematics achievement test.
Students who have parents who are involved in their school work are more likely to
take challenging mathematics courses early. Students whose parents were involved in
their educations were more likely to take courses like algebra and geometry in the 8th and
9th grade, than students' whose parents were not involved.
The results of the Third International Mathematics and Science Study (TIMSS) reveal
that the U.S. middlc school mathematics curriculum may be a weak link in the U.S.
cducational system. While U.S. 4th graders score above the international average in
mathematics and science, U.S. 8th graders score below average in 8th grade mathematics,
and only slightly above the international average in science. Initial analysis of the TIMSS
data also shows that the U.S. middle school mathematics curriculum is not as challenging as
that of other countries. The curriculum of average 8th-grade mathematics classrooms in the
U.S. resembles 7th grade mathematics elsewhere. Although algebra and geometry are
important elements in the middle school curriculum taught in other countries, only a small
fraction of U.S. middle school students are exposed to these topics.
Algebra in the Curriculum
Making a successful transition from arithmetic to more arivanced topics, meluding algebra and
geometry, has often been difficult for students As a result many mathematic programs in the
U.S. are now stematically incorporating some of the fundamental ideas from algehra and
geometry into the upper elementary grades In these programs, 5th, 6th and 7th grade students
are learning about representing and solving equations. characterizing patterns and rates of
change among variables and other fundamental algebraic concepts
In addition, the approach middle and high schools take to-presenting-adv anced topics differs
Many schools offerthe traditional model of pre-Algebra A leebra 1, Genmetry Algebra II
1 rigonometry, pre Calculus and Calculus However, an increasing number of schools offer
courses in which algebra genmetry and other ad vanced topics are more integrated This
approach is consistent with the practice in other industrialized nations which integrate algebra,
geometry and other topics.through out the elementary, middle and high school years and offer
a significant component of algebra in the 8th grade Building 1 firm foundation in algebra in
the elementary and middle school years-makes the shift from erithmeno to advanced topics
more successful, regardless of the format of the middle and highschool curriculum NELS
and NAEP, the two sources of national course-taking data which are analyzed in this brief,
employ traditional correstitities, such as algebra I" and geometty for mathematics courses
Thus, these traditional litles are used throughout the brief.
3
Table of Contents
Page
Mathematics and Future Opportunities
The Importance of Mathematics for College Entrance
Mathematics in College the Workplace, and the 21st Century
Middle School: Getting on the Road to Challenging Mathematics and Science Courses
Laying the Foundation
Coursc-Taking Patterns in Middle School
Parent and student Attitudes about Mathematics and Science
Mathematics in the U.S. Today
International Comparisons of Middle School Mathematics and Science Proficiency
Promising Practices
Next Steps
Six things educators, policymakers and community members can do
Six things parents can do
Resources
Appendix
4
Mathematics and Future Opportunities
The Importance of Mathematics for College Entrance
Students who take rigorous
mathematics and science courses
Figure 1
are much more likely to go to
college than those who do not.
College Attendance by Course-Taking
Data from a longitudinal survey of
% attending college
students who were in the 8th grade
100%
in 1988 (National Educational
83%
Longitudinal Study or NELS)
80%
reveal that 83 percent of students
who took algebra I and geometry
60%
went on to attend college' within
two years of their scheduled high
40%
36%
school graduation. By way of
comparison, only 36 percent of
20%
students not taking algebra I and
geometry went to college (Figure
0%
Took Algebra I
Did Not Take
1). Similarly, students who take
and Geornetry
Algebra I and
rigorous science courses in high
Geometry
school are also much more likely
Source: Analysis of NELS data
to go to college: While nearly 89
percent of students who took
chemistry went to college, only 43 percent of students who did not take chemistry in high school
went to college. Students who take more rigorous mathematics courses also have higher gains in
mathematics achievement (measured by the mathematics achievement test given as part of
NELS) than students who take less challenging courses, even when controlling for achievement.
For example, among students who initially began at the same level of mathematics proficiency in
the 8th grade, those students who had taken algebra II or geometry by the 10th grade experienced
greater gains, on average, than those students who had taken no algebra or only algebra I during
the same period.
Students of all income levels who take rigorous mathematics and science courses in high
school are more likely to go to college, and among low-income students (students in the
bottom third of the income distribution)2, the difference is particularly dramatic. Students
¹Throughout this report, the term "college" is used to refer to any postsecondary education taken at a public,
private not-for-profit, or private for-profit institution.
²Income data are based on total family income reported by parents. Low, middle, and high income groups cach
contain approximately one-third of the sample. The "all" category includes additional observations with
5
/R/CT/OT
from low-income families who took algebra
I and gcometry were almost three times as
Figure 2
likely to attend college as those who did not:
College Attendance by Income and
While 71 percent of low-income students
Course-Taking
who took algebra I and geometry went to
%attending ooflege
college, only 27 percent of low-income
students who did not take algebra I and
geometry went on to college. The
100
differences are also dramatic among
80
students from middle- and high-income
60
families: 94 percent of students from high-
40
income families, and 84 percent of students
20
Yes Took
2
Algebral
from middle-incomc families who took
0
and
Low
Moble
Hgh
Georretry
algebra I and geometry went on to college,
Income
while 60 percent of students from high-
SOURCE Analysis of NELSdate
income families and 44 percent of students from
middle-income families who did not take
geometry still did go on to college (Figure
2).
Unfortunately, many students, in particular low-income students, do not take these rigorous
mathematics and science courses. According to NELS, 63 percent of all students took algebra 1
2
and geometry and 50 percent took chemistry. Students from low-income families, however, were
and hu
far less likely than their peers to take these rigorous courses. Among students in the bottom third
of the income distribution, 46 percent took algebra I and geometry and only 33 percent took
chemistry. By way of comparison, fully 81 percent of students in the top third of the income
distribution took algebra I and geometry, and 72 percent took chemistry. The differences are
similar for other rigorous mathematics courses (Table 1).
missing income data.
6
10/15/97
0202 4V1
Table 1: Course-Taking Patterns of NELS Students
Percont of Students Taking Course
All
Bottom Income
Middle:Income
Top-Income
Algebra Iand
63
46
68
81
Geometry
Trigonometry
8
10
19
30
Chemistry
50
33
52
72
When course-taking patterns are accounted for, the difference in the rate of college-going
between low and high income students is dramatically reduced. When course taking patterns
are not accounted for, students from high-income families are almost twice as likely to attend
college as students from low-income families (86 percent compared to 44 percent). However,
when only students who have taken rigorous courses are compared to one another, students from
low-income families go to college at rates much more similar to students from middle- and high-
income families (Table 2). For example, among students who took chemistry in high school, 95
percent of high-income students; 89 percent of middle-income students; and 79 percent of
low-income students went on to college. When low-income students take rigorous courses,
income effects on college-going rates diminish greatly, although they do not disappear.
Table 2: College Attendance by High School Course-Taking Patterns of NELS Students
Percent of Students Alteriding Postaccondary Education
All
Bottom Income
Middle Incone
Top. Income
All
63
or
00
86
Algebra I and
Yes
83
71
84
94
Georgetry
No
36
27
44
60
Trigonometry
Yes
94
90
92
98
No
59
42
66
83
Chemistry
Yes
89
79
89
95
No
43
SD
68
7
Public Versus Private
Achievement Depends on Course- Laking, Not the ype of School
In general, the mathematics courses students take in Righ school are more important for
achievement than the type of school attended While recognizing that a great deal of
diversity exists among public and private schools, it is uscful to note that when edurse-taking
patterns are accounted for the mathematics achievement of students in both categories of
school is very similar, Public and private, school students who had taken the same
mathematic: courses were almost equally likely to score at the highest achievement le vel on
the NELS 12th grade mathematics achievement test. This was also true for lo waincome
public and private school students. Additionally, among.both public and private school
students ofall incomes students who had taken more rigorous mathematics courses were
much more likely to score at the highest achievement level igurc 3)
Figure 3
Mathematics Achievement by
Highest Mathematics Course Taken
All Students
Public
Algebra II
Private
Trigonometry
or Higher
Low Income
Students
Algebra II
Trigonometry
or Higher
0%
20%
40%
60%
80%
100%
Percent of Students Scoring at the Highest Level of the
NELS 12th Grade Mathematics Achievement Test
Achievement divided into thirds; Students in highest level scored in the top third
Source: Analysis of NELS data
Private schools include non-retigious, Catholic, and/other private.schools
1
8
Mathematics in College, the Workplace, and the 21st Century
The benefits of taking rigorous mathematics and science courses extend to both two- and four-
year colleges, and to the job market. As the prevalence of technology in the workplace steadily
increases, workers in more and more jobs will be required to have strong backgrounds in
mathematics and science--backgrounds which begin to be formed during high school. Rigorous
mathematics and science preparation is also important to students intending to go to a two or four
year college or university. The level and number of mathematics courses that a student needs to
take before and during college depend on the type of college and the major that the student wants
to pursue, and while students who plan to major in mathematics- and science-related disciplincs
typically need to take a more rigorous mathematics program, many other popular courses of
study also require strong mathematics backgrounds.
Two-year colleges often require all students to gain an understanding of intermediate algebra
prior to graduation, regardless of their course of study. In many two-year colleges, all entering
degree-sceking students are required to take mathematics placement exams prior to enrollment.
Students who score high enough may bc exempted from taking certain mathematics courses,
while students with low scores may be required to enroll in remedial mathematics courses. Many
of the most popular majors at typical two-year colleges--including Business, Nursing, and
Computer Science-require more rigorous mathematics course work, such as statistics.
Four-year colleges and universities typically require more high school mathematics
preparation for admission. Typical state four-year colleges and universities recommend, and in
some cases, require, that all students take at least three, and sometimes four, years of
mathematics in high school. Data collected by the College Board reveal that in 1997, 68 percent
of incoming freshmen at four-year colleges and universities had taken four years of mathematics
in high school. Furthermore, almost all of these students had taken algebra and geometry, and
more than half had taken trigonometry. Upon enrollment, most state colleges require students to
take mathematics placement exams. Advanced Placement courses are looked at favorably by
colleges and can result in placement out of introductory mathematics courses. While graduation
requirements differ depending on the student's major, many popular majors, such as Business and
Psychology, require students to take several more rigorous courses in mathematics or science.
In the job market, workers who have a strong background in mathematics and science are
more likely to be employed and generally earn more than workers with lower achievement,
even if they have not gone on to college. A national survey found that by age 30, high school
graduates who had not gone on to further education and had previously scored in the top quartile
on the mathematics portion of the Armed Services Vocational Aptitude Battery
(ASVAB--administered to civilians for study purposes) earned, on average, 38 percent more per
hour than high school graduates who had not gone to college and had scored in the bottom
quartile of the mathematic portion of the ASVAB. Similarly, the unemployment rate among high
school graduates who scored in the top quartile of the mathematics test was only 4.4 percent,
compared to an unemployment rate of 10.3 percent among high school graduates who scored in
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the lowest quartile. Workers who scored in the top quartile of the science section of the ASVAB
also earned more, on average, and wcre less likely to be unemployed.
In the future, ability in mathematics will be even more important for good-paying jobs. Today,
some major firms now require that all job applicants pass standardized mathematics and reading
tests, so that they may hire only individuals with solid backgrounds in these areas. For example,
at Diamond-Star Motors, a joint venture of Chrysler and Mitsubishi, all applicants for
production and maintenance positions must pass a standardized tcst that assesses their ability to
do mathematics at a high school level. Authors Richard Murnane and Frank Levy have identified
a set of "New Basic Skills," in their book of the same name, that, though fundamental for good-
paying jobs in the modern labor market, are often not mastered by non-college-bound high
school graduates. The "New Basic Skills" that workers will need to eam a good wage include the
ability to use mathematics skills and concepts at least at the 9th grade level, yet currently many
non-college bound students looking for work do not possess a sufficient mathematics background
to do SO.
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Mathematics and Science in the Modern J Market
Many jobs in today labor market require a mathematics or science background. A number
of these are among the fastest growing occupations national and are not ones ordinarily
thought of as "technical. Projections from the Bireau of abor Statistics' (BLS)
Occupational Outlook Handbook indicate that during the 1994 to 2005 period, jobs requiring
the most education and training will be the fastest growing and highest paying. BLS predicts
that occupations requiring a bachelor's degree or higher will average 23 percent growth,
almost double the 12 percent growth rate projected for occupations that require loss education
and training
Many jobsthat once required little background in mathematics now call for specific skills in
algebra, geometry, measurement, probability, and statistics According to an industry-wide
standard, an entry level automobile worker needs to be able to apply formulas from algebra
and physics to properly wire the electrical circuits of any car The National Coalition for
Advanced Manufacturing has defined 25 specific standards of mathematics and measurcment
among their national skill standards for whata good compelent worker should know and be
able to do.
Several of the fastest growing areas will reflect growth in computer technology and health
services-fields that can require substantial mathematics.and science preparation. Generally
speaking, fields requiring a strong science base also require substantial mathematics
preparation, as most academic science programs build upon astrong background in
mathematics. Below are some of the jobs which BLS indicates require a-mathematics or
science background, while mai fthese jobs require mathematics or science course work
beyond the Ingh school level all require at least a high school level background The
nccupations that BL Sprojects will be arhong the fastest growing during the period from 1994
to 2005 are noted with a star ()
Computer Scientists (*)
Surgical Technologists
Systems Analysis (*)
Dieticums and Nutritionists
Occupational Therapy Assistants and Aides (*)
Optometrists
Chemical Engineers
Physical Therapists (*)
Civil Engin
Roofers
Aerospace Engineers
Tool and-Die Makers
Medical Assistants (4)
Photographers
Dentists and Dental Hygienists
Financial Managers
Surveyors
Budget Analysts
11
Middle School:
Getting on the Road to Challenging Mathematics
and Science Courses
Laying the Foundation
"Mathematics is the language of science, and
Algebra is the "gateway" to rigorous
afgebra is the minimum Vocabulary that
mathematics courses. Rigorous mathematics
scientists of every discipline use to describe
courses build upon the skills and concepts
their work
that students learn in earlier mathematics
Dr George Castro, Associate Dean of the
courses. Traditionally, students cannot take a
College of Science at San Jose State
rigorous mathematics course in high school
University
until they have successfully completed one or
more prerequisite courses that provide the
foundation for the next course. Algebra I, or another course that covers basic algebraic concepts,
is the prerequisite for more rigorous mathematics classes in high school.
Students who plan to take advanced mathematics and science courses during high school and
begin to study algebra during middle school are at a clear advantage. A rigorous sequence of
mathematics courses spans several years. The traditional scquence of recommended mathematics
courses involves one year courses in algebra I, geometry, and algebra п, followed by a half-year
course in trigonometry, a full- or half-year course in pre-calculus then calculus, or an Advanced
Placement course. In addition, an increasing number of schools use curricula that cover these
rigorous content areas, but integrate algebra, geometry and other areas of mathematics such as
statistics and probability, rather than teaching each in a separate course. According to NELS,
forty-six percent of students who took algebra I in the 8th grade took calculus in high school,
compared to only eight percent of students who took algebra I in the 9th grade. The typical high
school sequence of rigorous science courses (biology, chemistry, and physics) also necessitates
an early background in algebra and geometry. Although not all students need to take all of the
most rigorous mathematics or science courses that their school offers, most colleges encourage
students to take four years of challenging mathematics and science courses during high school.
Students who do not take courses covering algebraic concepts early in their educational career
risk closing the door on many important opportunities, including opportunities to take courses
outside of mathematics and science. Some high schools require students to complete a specific
package of courses, including mathematics and science, in order to graduate. By the junior and
senior year, students who have not planned ahead to complete the courses that their school
requires have fewer options in choosing which courses they take. Students who do not complete
prerequisite and required courses early enough not only risk being unable to take more rigorous
courses in those disciplines later, but also may not have time in their schedules to take other
courses that can help prepare them for college or a carcer, including foreign language, art,
12
/R/CT/OT
Advanced Placement, and "tech prep" courses.
Course-Taking Patterns in Middle
School
Figure 4
Proportion of Eighth-Graders Enrolled in Algebra, 1996
Despite recent increases in the proportion
of students taking algebra I in the 8th grade,
All
25%
in 1996, most students were not enrolled in
this course. The proportion of 8th-graders
White
27%
taking the National Assessment of
Educational Progress (NAEP) mathematics
assessment who reported taking algebra has
Black
20%
increased in recent years. In 1992, only 20
percent of students reported taking algebra.
In 1996, the next year the NAEP mathematics
Hispanic
20%
assessment was administered, 25 percent
reported taking algebra. This increase may be
0%
20%
40%
60%
80%
100%
due to a number of factors, including the
Source: 1996 NAEP Mathematics Assessment background questions
National Council of Teachers of
Mathematics' (NCTM) call for the inclusion
of algebraic topics in the middle school curriculum. However, most students still werc not
enrolled in courses that include significant amounts of algebra in the 8th grade.
Minority and low-income students continue to be less likely to take challenging mathematics
courses in middle school than other students. The 1996 NAEP data reveal that minority
students are less likely to report being enrolled in algebra in the 8th-grade (Figure 4). The data
also provide some indication that students from disadvantaged backgrounds are less likely to be
enrolled in algebra during the 8th grade: While 29 percent of students who were not eligible for
the national school lunch program reported being enrolled in algebra during the 8th grade, only
15 percent of students who werc eligible for the national school lunch program were enrolled in
algebra.
While the number of students taking algebra courses has increased, recent evidence suggests
that the content of these courses has remained rigorous. Many states have recently increased
mathematics requirements for high school graduation, often requiring that students take more
years of mathematics than were required in the past, or mandating that students complete certain
courses. A recent study supported by the National Science Foundation (NSF) examined the
content of mathematics courses in schools in several of the states making the most substantial
changes in mathematics requirements. The study focused on basic courses, such as algebra I,
which had experienced large enrollment increases because of the more stringent graduation
requirements. Despite the larger numbers of students enrolling in the courses, the study found
that the content of these courses was essentially unchanged, indicating that more students were in
fact being exposed to rigorous mathematics.
13
Parent and Student Attitudes about Mathematics and Science
Large proportions of middle school
students indicate that they do not plan to
take mathematics and science courses
Figure 5
beyond what their schools require. A
Students Plan to Drop Mathematics, But Want to Go to College
nationally representative survey of public
school students and parents conducted by
All B Black Hispenic
Louis Harris Associates for the National
100%
Action Council for Minorities in
90%
91%
92%
93%
86%
83%
Engineering (NACME), Inc. found that
80%
large proportions of students would like to
63%
stop taking mathematics and science
60%
60%
courses as soon as they are able to: 51
51%
percent of the 5th through 11th grade
40%
students surveyed indicated that they would
take mathematics classes only as long as
20%
required, while 47 percent reported they
would study science only as long as it is
required. Distressingly, young minority
0%
students--5th through 8th grade students
Child plans to drop
Child wants to
Parent expects child
matherretics
goto college
to go goto college
who will soon be facing major decisions
Source: NAOME Survey
about which courses to take--were more
likely to indicate that they planned to drop
mathematics and science as soon as they were able to (61 percent planned to drop mathematics,
and 58 percent planned to drop science). Minority students of all ages were more likely than
other students to indicate that they would like to stop taking mathematics and science as soon as
they were able to (Figure 5).
However, the same group of students indicate that they would be interested in going to college,
and taking college-level mathematics courses. Eighty-six percent of all students surveyed said
that they would like to go to college. Although less than half of the 9th- to 11th-grade students
said that they planned to take trigonometry or algebra II in high school, nearly two-thirds said
that they were interested in taking Advanced Placement courses. These contrasts signal that
many students do not understand the importance of, and requirements for, taking rigorous
mathematics and science courses in high school, including the need to take algebra by the 8th
grade. In fact, only 25 percent of minority and 42 percent of non-minority 5th- through 8th-grade
students recognized that if they did not take algebra they would not be able to take other
mathematics classes in the future.
Parent and teacher involvement may make a large difference in students' decisions about
mathematics and science. According to the NACME survey, ninety-four percent of students
indicated that their parent's or guardian's advice was important to them in deciding what they
14
would study in school, and 88 percent indicated their teachers' advice was important. Ninety-one
percent of parents want their children to continue their education beyond high school. However,
when 9th- through eleventh-graders were asked who decided which mathematics classes they
would take, seventy-nine percent indicate that they had made the decision by themselves.
Analysis of the NELS data indicates that students with greater levels of parental involvement
are more likely to take advanced mathematics courses. Analysis of the course-taking patterns
of the NELS students who wcre in 8th-grade in 1988 reveals that regardless of whether the level
of parent involvement was reported by the student, the parent, or the teacher, higher levels of
parental involvement were consistently associated with higher likelihoods of taking rigorous
mathematics courses. While only 8 percent of those students who said that they did not discuss
programs at school with their parents took algebra I by the 8th grade, 17 percent of those who
said that they discussed school programs three or more times during the previous semester took
algebra I by the 8th grade. Students who had parents or teachers who said that there were greater
levels of parental involvement were also more likely to take advanced courses. Thirty-seven
percent of those students whose parents said that they rarely talked to their child about high
school plans took geometry by the 10th grade, while 48 percent of those students whose parents
said they regularly spoke to the child about high school plans took geomctry by the 10th grade.
While 27 percent of students whose teachers said their parents were not involved took geometry
by the 10th grade, a full 63 percent of the students whose teachers said that their parents were
very involved took geometry by the 10th grade.
15
Mathematics in the U.S. Today
International Comparisons of
Middle School Mathematics and
Science Proficiency
U.S. Performance on TIMSS,
Relative to International Average
Recent findings from the Third International
Fourth grade Eighth Grade
Mathematics and Science Study (TIMSS),
indicate that the mathematics curriculum
Mathematics
from grades five through eight may be a weak
link in the U. S. educational system. Newly
available data from TIMSS (the most
Above average
Below average
comprehensive international comparison of
schools and students ever undertaken) reveal
Science
that U.S. 4th graders score above the
international average in both mathematics and
Above average
Above average
science. Among 25 other participating nations,
only Korea performed better than the U.S. in
4th grade science, and only 7 of the 25 other
countries did better than the U.S. in 4th grade mathematics. These findings are in contrast to
earlier findings from TIMSS that indicate that U.S. 8th graders perform slightly below the
international average in mathematics, and only slightly above the international average in
science. In fact, only one country--the U.S. in mathematics--falls from above the international
average at 4th grade to below the international average at 8th grade.
The U.S. expects less of its middle school and junior high students compared to high
performing nations. TIMSS data suggest that one reason U.S. students do less well at 8th grade
is that the middle school mathematics curriculum in the U.S. is significantly less challenging than
the curricula used in other countries. In Germany and Japan, virtually all students in grades 5
through 8 move beyond arithmetic to the foundations of algebra and geornetry. By 8th grade,
mathematics courses in virtually all other countries participating in TIMSS include significant
algebra and geometry, while in the U.S., only students in college-preparatory classes receive
significant exposure to algebra, and very few students study geometry. As a result, the content
taught in U.S. 8th grade mathematics classrooms is usually at a 7th-grade level compared to the
40 other nations in the TIMSS study.
TIMSS also found that U.S. mathematics classes require students to engage in less high-level
mathematical thought and solve fewer multi-step problems than classes in Germany and
Japan. A U.S. mathematics teacher's typical goal is to teach students the mechanics of solving a
problem versus understanding the concepts behind it, while a Japanese teacher's goal is to help
them learn the basics as well as understand the relevant mathematical concepts. In a typical U.S.
classroom, students follow the teacher as he or she leads them through solutions to mathematics
16
problems. In Japan, students are asked to solve problems, present them to the class, and describe
how they approached the problem to increase their own understanding.
How Does Our Cm riculum Compare Internationally?
The 8th grade mathematics curriculum in both Germany and Japan is more advanced than
in the United States. The TIMSS analysis 6PUS curricula examined both what is in
textbooks and how it is implemented in classrooms
Ananalysis of curriculum in the U and other countries, found that algehra
and geometry occipy more space in German and Japanese textbooks than do
the textbooks used by a majority of U.S 8th graders (Figure 6).
Analyses BI implementation of currioulum make clear that in the middle school years,
the U.S. facused on arthmetic For example, 40 percent ofUS Sth grade
mathematics lessons included mithmetic.topics. whereas only:13 percent of Germany'
and 0 percent of of Japan's lessons at the 8th-grade level included these topics. lic major
focus of curriculum taught in these countries is on algebra and geornetry
Figure 6
Algebra-in 8th Grade extbooks
% of space of devoted to algobra (n Bth grade mathematics textbooks
50%
40%
30%
20%
10%
-109
0%
Germany
Japan
D.s.
course: The This International Membmatics and Relance
Space is defined In terms of the percentage of textbook or guidehook that is devoted to particular topies/blocks
Topics include such items as formulas Leometry, numbers estimation Blocks are sub-units of topics that are
parts of attex/book and which.might include individual pedagogical suggestions, individual examples, Individual
testing marrative blacks. graphic. blocks,ruggested activities and mathematical problems:
17
Promising Practices
and
In many places across the country, there are promising programs underway that focus on
improving student achievement in mathematics in science. Many of these are greatly expanding
the numbers of students taking rigorous courses in mathematics and science, and are finding that
students are doing quite well. While recognizing that there is no one formula to success, we have
highlighted a number of places that demonstrate effective strategies. We hope that these
examples will bc useful to you as you plan efforts to improve mathematics and science education
?
for students in your community and across the nation.
Preparing for success: The Algebra Project, supported by the National Science Foundation
(NSF) and directed by Robert Moses, addresses equity of opportunity by helping 6th, 7th, and
8th graders in inner city and rural areas gain an understanding of challenging mathematics.
Serving over 40,000 traditionally low-income and minority middle school students, the Algebra
Project is based on the conviction that all students can learn algebra given the proper context. An
essential first step is that all students study algebra as early as possible to ensure their access to a
college preparatory high school curriculum.
The project assists students in 22 urban and rural sites in 13 states to succeed in challenging high
school mathematics courses by introducing rigorous mathematics concepts in the 6th grade,
creating a foundation to build upon throughout the middle school years. The project has been
successful in helping traditionally underserved students complete algebra I by the 8th or 9th
grades, and either pre-calculus or calculus by the 12th grade utilizing a variety of strategies. The
project places young college-age students in schools to provide extra assistance. In addition, the
project provides after-school activities; and provides teacher professional development in
examining the curriculum and beliefs about how it should be taught.
The Algebra Project has had important effects for communities. For instance, in the Mississippi
Delta and in Jackson, Mississippi, the project showed positive short term effects. Additionally,
an evaluation team, comprised of education experts from across the country, found evidence of
positive outcomes in teaching, student attitudes about and engagement in mathematical ideas,
and community involvement.
Taking the right courses: In 1990, the College Board launched EQUITY 2000 to increase
minority enrollment in college preparatory mathematics courses. Originally piloted in six
communities, EQUITY 2000 requires participating school districts to phase out lower-level
mathematics and require all students to take a college preparatory curriculum-beginning with
algebra and gcometry. EQUITY 2000 influences policies, curricula and student academic
development at all grade levels, with a particular focus on grades six through ninc--critical years
for mathematics education during which key decisions are made about which courses students
should take and how they should begin planning for education and careers beyond high school.
18
The project provides on-going professional development to help teachers work with
heterogcneous ability classes, encourages and supports parents to become advocates on behalf of
their children, helps schools establish support services for students who need extra time and
effort to learn challenging content, and trains administrators and teachers to use student
enrollment and achievement data to drive school-based decision-making.
Finally, EQUITY 2000 has made increased parental involvement a priority because it recognizes
the important role that parents play in nurturing and reinforcing their children's desire to attend
college. It has sponsored Saturday and summer academics on college campuses for entire
families. The program also sponsors Family Math nights in which parents and students learn
mathematics concepts together.
An analysis of results at the six pilot sites found that:
All sites dramatically increased the percentage of students enrolled in algebra
I by the 9th grade, and in three pilot districts, all 9th graders enrolled in
algebra I.
The percentage of students passing algebra I did not decline significantly, and
in some cases rose, as more students from the discontinued lower tracks
began enrolling in algebra classes.
Advanced Placement Participation Rising in South Carolina and Texas. The College Board's
Advanced Placement (AP) Program was started nearly four decades ago to enable students to
complete college-level studies while still in high school and to obtain college credit or
placement. Today more than 500,000 students in about half of the nation's high schools take at
least one AP course, and those courses are widely recognized as setting the standard for high
Vague
levels of academic achievement in high school. Dramatically increased participation in
Advanced Placement courses in South Carolina and Texas illustrate the success of AP-based
reform initiatives in two states.
South Carolina: With former-Governor Riley's school reform package of 1984, South Carolina
became one of the first states to legislate funding and other actions to boost participation in AP.
Actions included state appropriations to train AP teachers and to help pay for AP exams, as well
as a requirement that public colleges accept AP courses if the student scored 3 or higher on the
exam. As a result, from 1984 to 1997 South Carolina experienced:
An increase in the number of students taking AP exams from 2,799 to 9,748...
An increase in the number of AP exams from 3,461 to 14,890, with the mean grade
remaining stable at approximately 2.7 - 2.8.
An increase in the number of AP science exams (Biology, Chemistry, Physics) from 27
to 2,414.
An increase in the number of AP math exams (Calculus AB and BC) from 46 to 2,767.
19
Ninety-three percent of all the public high schools in the state participating in AP(184 of
197 public high schools).
AP participation rates above the national average.
AP Exams Taken
(Eleventh and Twelfth Graders)
1984
1997
Percent increase
South Carolina
3,461
14,890
77 percent
National
223,888
843,399
73 percent
Sources: College Board. Advanced Placement Program, National and South Carolina Summary Reports, 1984 -
1997.
Texas: The Advanced Placement Incentives program was developed in the Dallas, Texas area by the
1st
O'Donnell Foundation in reaction to the low rates of college attendance and poor college preparation
of low-income and minority students. The Advanced Placcment Incentives program addresses
shortfalls in both the supply and demand for AP courses in math, science, and the arts, by providing
performance-based financial incentives to teachers, school and students. Teachers are given
financial incentives as well as registration and fees for attending College Board AP teacher training
during the summer, and to begin to teach AP courses. Students who complete the Advanced
Placement course may take the AP exam at half-cost (the total cost for an AP exam is about $73),
and those who score a three or better (on a five point scale) are given a financial incentive and
reimbursed for the cost of the exam.
In five years of operation in nine Texas public schools the O'Donnell foundation reports that:
In the first year of the program 97 students took AP exams, and 52 received a three or better.
In the fifth year of operation 1,099 students took AP exams, and 521 received a score of three
or better.
AP participation increased among female students in areas in which females are traditionally
under represented, with 19 female students taking AP exams in math, science, or computer
science during the program's first year, and 240 female students (compared to 272 male
students) doing SO in the program's fifth year.
Minority participation increased, from 7 African-American or Hispanic students taking AP
exams during the program's first year, to 116 in the program's fifth year.
Instructional Reform in Mathematics. Sponsored by the University of Pittsburgh's Learning
Research and Development Center, the Quantitative Understanding: Amplifying Student
Achievement and Reasoning (QUASAR) Project is designed to respond to low levels of student
participation and the inadequacy of student performance in mathematics. QUASAR is a
practical school demonstration project for urban middles schools that fosters the development and
implementation of enhanced mathematics instructional programs in cconomically disadvantaged
communities. The program's key principles are that all students are able to learn a broad range of
mathematical content, acquire a deeper and more meaningful understanding of mathematical ideas,
20
and demonstrate proficiency in mathematical reasoning and complex problem solving.
1N QUASAR schools, teams of mathematics teachers, school administrators and "resource
partners"- generally mathematics educators from local universities- collaborate to develop,
implement, and refine mathematics instructional programs. All project schools have eliminated
most forms of academic tracking, and have emphasized deeper student understanding and high-level
thinking and reasoning for all students. While there is variation across the sites in curricula,
teaching strategies, and approaches to professional development, all QUASAR sites included
extensive attention to professional development and teacher support. Additionally, the University
of Pittsburgh's Learning Research and Development Center provides the schools with ongoing
support and updated information on progress.
Program data indicate that QUASAR schools build the capacity of teachers to improve the quality
of their mathematics instruction and to increase the capacity of students to think, reason, solve
complex problems, and communicate mathematically. Students in QUASAR schools, particularly
those who are from minority groups and those with limited English proficiency, have increased
their understandings of important mathematical ideas across a range of content topic areas.
Additionally, QUASAR students in grade 8 performed as well as students on basic and traditional
items of the 1992 NAEP Mathematics Assessment, and above their peers on less traditional middle
school mathematics content.
Standards-based Reform. The New York Regents Exam has spurred thousands more high
school students to take and pass college-preparatory mathematics courses. In 1993 then-Ncw
York-Chancellor Ramon Cortines required all students to take tougher Regents-level mathematics
and science courses traditionally reserved for college-bound students. Beginning in 1995, the state
required that all students take Regents-level classes. The number of Hispanic and black students
who passed the science portion of the Regents Exam more than doubled from the previous year.
Since then, the state has decided to require that all students take and pass the Regents Exams In
addition, Commissioner of Education Richard Mills has recently called for an increase in the rigor
of the state's requirements for graduation from high school, including adding another year of both
mathematics and science to the current two years required in each.
Living Up to Our Potential: The First in the World Consortium, Chicago, Illinois. Twenty
school districts from Chicago's North Shore joined forces in 1995 to meet the challenge of
providing their students with a world class education in mathematics and science. Their first
challenge was to determine what a "world class" education looked like, measure their current
performance against that benchmark, and develop an improvement strategy.
The Consortium's efforts were directed toward three objectives: benchmarking performance against
international standards in mathematics and science, using the Third International Mathematics and
Science Study; creating a forum to clarify world-class education standards for business leaders,
policy makers, educators, and community membcrs; and establishing a network of learning
communities involving educators, parents, and community leaders within the Consortium school
21
districts and beyond.
The districts in the First in the World Consortium took the TIMSS assessment in Spring 1996 at the
4th, 8th, and 12th grade level. Their 8th grade results placed them among the top performing
countries in the world at the 4th and 8th grades, well exceeding the United States' performance. In
addition:
Fifty percent of their 8th grade students took algebra or geometry compared to 25 percent of
students nationally who take algebra;
The Consortium had high expectations for students and teachers; and
Gained broad-based community support for improved student performance.
However, the First in the World Consortium is not resting on their success; in fact they have created
teacher learning networks to strengthcn curriculum standards, models of instruction, assessment,
and use of technology. This "community of learners" approach promotes teacher participation and
provides a context for long-term commitment to the consortium's goals and to growth in student
learning.
Although the First in the World Consortium is at an advantage in terms of its resources, its
willingness to identify its weaknesses and address them has distinguished its efforts. The
consortium identifies both state and federal support as helping it focus on its goals. These
experiences emphasize that, when given the opportunity, U.S. students can perform as well as, or
better than, students in any part of the world.
22
Next Steps
Six things educators, policymakers and community members can do:
1. Provide all students the opportunity to take algebra I or a similarly demanding course that
includes fundamental algebraic concepts in the 8th grade and more advanced math and science
courses in all four years of high school.
2. Build the groundwork for success in algebra by providing a rigorous curriculum in grades K-7
that moves beyond arithmetic and prepares students for the transition to algebra.
3. Ensure that all students, parents, teachers, and counselors understand the importance of
students' early study of algebra as well as continued study of rigorous mathematics and science in
high school to their future college and career opportunities.
4. Prepare teachers of mathematics to teach rigorous mathematics by providing teacher
preparation and professional development opportunities that increases teachers knowledge and
skills in mathematics and the teaching of mathematics.
5. Support mathematics achievement outside the classroom such as math clubs, tutoring and job
shadowing for students who may need extra help to ensure that they can achieve at high levels.
6. Support parent involvement in their children's mathematics education.
Six things parents can do:
1. Discuss your children's mathematics homework with them.
2. Visit your children's mathematics teacher to find out what your children are learning and how
you can help.
3. Insist that your children be enrolled in algebra I or a similarly demanding course that includes
fundamental algebraic concepts in the 8th grade and more advanced math and science courses in
high school so they can keep all of their future options open.
4. Ensure that your children are gaining the groundwork for success in algebra through a rigorous
curriculum in grades K-7 that moves beyond arithmetic and prepares them for the transition to
algebra.
5. Help your children understand the importance of taking challenging mathematics and science
courses to their future by visiting colleges, familiarizing them with college requirements, and
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exploring financial aid options available to students.
6. Show the importance of mathematics to career choices by talking with your children about the
use of mathematics in your work or the work of adults they know.
24
Resources
Everson, Howard T. and Marlene Dunham "Signs of Success-EQUITY 2000, Preliminary
Evidence of Effectiveness." New York, NY: The College Board, 1966.
Hawes, Mark, Kimmelman, Paul, and Kroeze, David. "Becoming 'First in the World' in Math
and Science: Moving High Expectations and Promising Practices to Scale." Phi Delta
Kappan, Volume 79, Number 1, September 1997.
Jones, Vinetta C. "What A Difference A Standard Makes." In D. Bartels & J. Opert Sandler
(Eds.), This Year in Science: Implementing Science Education Reform." Washington, DC:
American Association for the Advancement of Science, in press.
Levy, Frank and Richard Murnane. Teaching the New Basic Skills: Principles for Educating
Children to Thrive in a Changing Economy, New York: The Free Press, 1996.
Lynn, Leon and Wheclock, Anne. "Making Detracking Work," The Harvard Education Letter,
Cambridge: Harvard Graduate School of Education, January/February 1997.
National Action Council for Minorities in Engineering. Uninformed Decisions: A Survey of
Children and Parents about Math and Science, Conducted for National Action Council for
Minorities in Engineering, By Louis Harris and Associates, 1995.
The National Commission on Teaching and America's Future. What Matters Most: Teaching for
America's Future, September, 1996.
National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School
Mathematics, Reston, VA: Author, 1989.
Porter, Andrew. "The Effects of Upgrading Policies on High School Mathematics and Science."
Consortium for Policy Research in Education, 1997, and in Brookings Papers on Education
Policy, 1997.
Schmidt, William H., McNight, Curtis C., and Raizen, Senta A. 1 Splintered Vision: An
Investigation of U.S. Science and Mathematics Education, East Lansing, MI: U.S. National
Center for the Third International Mathematics and Science Study, Michigan State
University, 1996.
U.S. Department of Education. National Center for Education Statistics. Education and the
Economy: An Indicators Report, Washington, D.C.: U.S. Government Printing Office, 1997.
U.S. Department of Education. National Center for Education Statistics. NAEP Facts: Eighth-
Grade Algebra course-Taking and Mathematics Proficiency, Washington, D.C.: U.S.
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Government Printing Office, 1996.
U.S. Department of Education. National Center for Education Statistics. Pursuing Excellence: A
Study of U.S. Eighih-Grade Mathematics and Science Teaching, Learning, Curriculum, and
Achievement in International Context, Washington, D.C.: U.S. Government Printing Office,
1996.
U.S. Department of Education. National Center for Education Statistics. Pursuing Excellence: A
Study of U.S. Fourth-Grade Mathematics and Science Achievement in International Context,
Washington, D.C.: U.S. Government Printing Office, 1997.
U.S. Department of Education. National Center for Education Statistics. Statistics in Brief:
Changes in Math Proficiency Between 8th and 10th Grades, Washington, D.C.: U.S.
Government Printing Office, 1996.
U.S. Department of Education. Planning and Evaluation Service. Analysis of
NELS:88
Follow-Up Data: Factors That Affect College Enrollment, Forthcoming.
U.S. Department of Labor, Bureau of Labor Statistics. Occupational Outlook Handbook,
Washington, D.C.: U.S. Government Printing Office, 1997.
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10/15/97
10.11
4V1
Appendix
The NELS:88 data. The National Education Longitudinal Study of 1988 (NELS:88) initially
surveyed a nationally representative sample of 26,000 public and private school 8th grade
students in 1988. The data collected include responses to student questionnaires, scores on
standardized achievement tests, high school transcripts, and interviews with parents and teachers.
Since the initial survey in 1988, the students have been resurveyed every two years, with the most
recent data available gathered two years after their scheduled high school graduation in 1994.
The analyses in this report are based on a sub-sample of over 13,000 individuals from whom data
were collected in all three follow-up surveys. Analysis of course-taking patterns is based on
student reports of 8th-grade course-taking and high school transcript data. The actual titles of
mathematics courses as they appear on the transcripts may vary, despite covering similar content
(for example, geometric concepts); accordingly, we have attempted to include all courses
covering similar content under traditional course names (i.e. "geometry," "algebra II") reflective
of their content.
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