How are American students doing in mathematics? Trends on the two math tests of the National Assessment of Educational Progress (NAEP) show that although students have made progress in some areas of math, improvement has been disappointing when it comes to basic arithmetic—in particular, the ability to compute. In recent years, in fact, progress has ground to a halt.
Is this new slowing of progress in basic math a matter for concern, especially if American youngsters are showing gains in more sophisticated areas of math? After all, some people argue that students no longer need to learn how to compute now that calculators are widely available. The truth is that, calculators or no calculators, basic math skills are still important. 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. Its questions may be changed slightly from test to test, but the test faithfully reflects the goals of the National Council of Teachers of Mathematics. As shown in figure 1, main NAEP scores have increased significantly—scores for twelfth, eighth, and fourth grades are all up.
Figure 2 shows scores on the trend NAEP, whose questions have remained the same throughout the life of NAEP. Since 1990, scores are up, but not as much as on the main NAEP. For ease of comparison, table 1 converts the two tests’ gains and displays them 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, 9-year-old fourth graders. They accomplished a huge gain on the main NAEP, 0.29 standard deviations, equal to about 1.2 year’s worth of mathematics. But on the trend NAEP, the gain was minuscule, 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.”
With that in mind, some Brookings colleagues and I identified computation items on the trend NAEP, grouped them by topic, and calculated gains for both the 1980s and the 1990s. It is important to note that the analyses are based on a small number of NAEP items. Though this is the best available evidence on computation skills at the national level, the findings are not conclusive but merely suggestive. That said, the findings pinpoint important areas where problems may be developing.
Table 2 breaks down computation scores into 10 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, with the better performing decade being shaded. Overall, students gained more in computation during the 1980s than during the 1990s, with eight of the ten clusters favoring the 1980s, two favoring the 1990s. In the 1990s column, most cells are negative, showing that 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 9-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 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: 90s were “A’s,” 80s were “B’s,” 70s were “C’s,” 60s were “D’s,” and below 60 percent was an “F.” The 1999 NAEP scores for 9-year-olds would have received the following letter grades in my class: a “C” in addition, a “D” in subtraction (with the benefit of rounding), an “F” in multiplication, and an “F” in division. Those are not good grades. Think of it this way. Youngsters who have not mastered whole-number arithmetic by the end of fourth grade are at risk of later becoming remedial students in mathematics. Half of the nation’s 9-year-olds missed the multiplication and division items on the trend NAEP the last time the test was given.
The proficiency of 13- and 17-year-olds on computation skills also remains unacceptably low. Although proficiency with fractions is critical in preparation for algebra, in 1999 only about half of 13- and 17-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 their peers were in 1982, more than 20 years ago.
Should we be worried if the evidence suggests that students are not learning how to compute? We should—for three reasons. First, 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. When basic skills are not taught, the least privileged in our society—those who cannot afford tutors, sophisticated computer programs, or academic summer camps—suffer the biggest losses. The students who pay the biggest price are those who can least afford it. Unfortunately, they are also students for whom the educational system has never worked well.
Second, 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 straitjacket students or to slow their progress in the math curriculum.
And finally, 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.”
Forward to Basics
About one-half of U.S. 9-year-olds cannot multiply or divide whole numbers accurately, and half of 13- and 17-year-olds cannot compute correctly with fractions. These deficiencies mean that large numbers of American elementary students are ill prepared to study algebra in middle school, large numbers of middle school students are inadequately prepared to take advanced mathematics courses in high school, and large numbers of high school students have not mastered the rudimentary skills required for entering college or gaining middle-class employment. A 50 percent proficiency rate is unacceptable. But it does not justify a call for “back to basics.” Back to basics implies some past golden age when everyone learned essential skills. That age never existed. To ensure that every American student is proficient at basic math skills mandates that the nation go forward, not backward. The goal of leaving no child behind is nothing but a pipe dream if children don’t learn arithmetic, the starting point in mathematics.