Tom Loveless, speaking before the Secretary of Education’s Mathematics Summit in Washington, D.C., on February 6, 2003, at the Department of Education’s launch of its Mathematics and Science Initiative (PowerPoint Presentation; video )
Today I will attempt to
answer two questions. The first is: how are American students doing in mathematics?
To answer this question, I will review trends on the two math tests of the National
Assessment of Educational Progress (NAEP). We will see that although students
have made progress in some areas of math, when it comes to basic arithmetic—in
particular, the ability to compute—growth has been disappointing. In recent
years, progress has ground to a halt. That leads to the second question. Why
should we care? Some people argue that students no longer need to learn how
to compute now that calculators are widely available. Are basic math skills
still important? I will argue that they are. Unless every student receives a
thorough grounding in arithmetic, the nation has little chance of achieving
ambitious goals in mathematics.
Let’s look at some data.
Main and Trend
The NAEP administers two
math tests, the main and the long-term trend. The main NAEP test has been given
since 1990. As shown in Figure 1, main NAEP scores have increased significantly—scores
for 12th, 8th, and 4th grades are all up.
Figure 2 shows scores on
the trend NAEP. Since 1990, scores are up, but not as much as on the main NAEP.
One can see this better by converting the two tests’ gains to comparable units.
Table 1 does that, displaying gains in standard deviations, a unit of measure
used by statisticians. Gains on the main NAEP are at least twice as large as
those registered on the trend. The difference between the two tests is most
apparent with the youngest students, nine year olds and fourth graders. They
accomplished a huge gain on the main NAEP, .29 standard deviations, approximately
equal to one year’s worth of mathematics. But on the trend NAEP, the gain was
miniscule, equal to about one month of learning.
Why are the two tests telling
completely different stories? The most likely reason is that they assess different
skills. The main NAEP devotes more items to measuring students’ skills in areas
such as geometry, problem solving, and data analysis. For assessing basic skills,
and especially for measuring computation skills, the trend NAEP is the better
test. As the NAEP framework states, the trend test is the one that can “provide
insight into students’ computational abilities.” (Quotation from page 9,
2005 NAEP Mathematics Framework).
With that in mind, some
Brookings colleagues and I identified computation items on the long term NAEP,
grouped them by topic, and calculated gains for both the 1980s and 1990s. It
is important to note that the findings are not conclusive. The analyses are
based on a small number of NAEP items, and though this is the best available
evidence on computation skills at the national level, the findings are merely
suggestive. That said, the findings pinpoint important areas where problems
may be developing.
Table 2 breaks down computation
scores into ten separate areas of skill. The percentage of students answering
items correctly is presented for 1982, 1990, and 1999. The last two columns
compare gains or losses in the 1980s and 1990s. The better performing decade
is shaded in yellow. You can see that, overall, students gained more in computation
in the 1980s than in the 1990s. Eight of the ten clusters favor the 1980s. Two
of the clusters favor the 1990s. Scanning down the 1990s column and examining
the sign of each cell, you will notice that most cells are negative. Students
lost ground in most computation skills during the 1990s. Only in computing percentages
at ages 13 and 17 did students register gains.
Take a closer look at the
scores for nine year olds. These skills comprise the basic arithmetic that all
fourth graders are expected to master—addition, subtraction, multiplication,
and division of whole numbers. All four areas reversed direction in the 1990s,
turning solid gains that were made in the 1980s into losses. Not only that,
but the declines came from levels that weren’t very high at the beginning of
the 1990s—certainly not at a level that is acceptable for such fundamental material.
I taught sixth grade for
several years in California. My grading scale for tests and quizzes was pretty
straightforward: 90’s were “A’s,” 80’s were “B’s,” 70’s
were “C’s,” 60’s were “D’s,” and below 60% was an “F.”.
The 1999 NAEP scores for nine year olds would have received the following letter
grades in my class: in addition, a “C,” in subtraction, a”D,”
(with the benefit of rounding), in multiplication, an “F,” and in
division, an “F.” Those are not good grades. Think of it this way.
Youngsters who have not mastered whole number arithmetic by the end of 4th
grade are at risk of later becoming remedial students in mathematics. Half of
the nation’s nine year olds missed the multiplication and division items on
the trend NAEP the last time the test was given.
A similar concern can be
raised about the performance of thirteen and seventeen year olds. Their level
of proficiency on computation skills remains unacceptably low. Look closely
at fractions. Proficiency with fractions is critical in preparation for algebra.
In 1999, only about half of thirteen and seventeen year olds could compute accurately
with fractions on the NAEP. Students who leave eighth grade not knowing how
to compute with fractions enter high school as remedial math students. Students
who leave high school lacking proficiency with fractions are inadequately prepared
for college mathematics. On the most recent trend NAEP, both age groups were
less proficient at computing with fractions than in 1982, twenty years ago.
Should we be worried if
the evidence suggests that students are not learning how to compute?
We should—for the following
- Basic skills serve equity
As shown in Table 3, the lack of progress in computation skills has disproportionately
affected African-American students. The black-white achievement gap expanded
in every computation skill area in the 1990s. This is typical of what happens
when basic skills are shortchanged. The students who pay the biggest price
are those with the least to lose, those for whom the educational system has
never worked very well. When basic skills are not taught, the least privileged
in our society—those who cannot afford tutors, fancy computer programs, or
academic summer camps—suffer the biggest losses.
- Basic skills are necessary
to advance in math.Insisting that students master computation skills is not
to advocate that they stop at the basics. Basic skills are a floor, not a
ceiling. Students must learn arithmetic so that they can move on to more demanding
mathematics—algebra, geometry, calculus. An emphasis on the basics should
never be used as an excuse to straightjacket students or to slow their progress
in the math curriculum.
- Basic skills predict
adult earnings.In recent years, a growing body of research has documented
that the skills and knowledge students learn in school is correlated with
success later in life. In their landmark study showing the impact of basic
skills on adult earnings, Richard Murnane and Frank Levy conclude, “mastery
of skills taught in American schools no later than the eighth grade is an
increasingly important determinant of subsequent wages.”
A final word on the controversy
surrounding basic skills. I am mystified when some analysts refer to a concern
for arithmetic and computation skills as advocating “back to basics.”
Well, as an old elementary teacher, I am very concerned about American fourth
graders learning arithmetic. A 50% proficiency rate is unacceptable. But I don’t
want to go back to anything. I want to go forward on the basics. Back
to basics implies there was a golden age when everyone learned essential skills.
That age has never existed. To ensure that every fourth grader is proficient
at whole number arithmetic means that we must go forward, not backward. We must
go forward on basic skills if a more equitable school system is a national goal;
we must go forward if American students are to be prepared for higher level
mathematics; we must go forward if young people are to master the skills correlated
with middle class employment as adults. Back to basics is a bad idea. There
is nothing to go back to but mediocrity and failure. It is time to go forward
as a nation on basic skills.