Trends in Math Achievement: The Importance of Basic Skills

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 12^th, 8^th, and 4^th 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.

Computation

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 4^th 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 reasons.

Why Important?

1. 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.
2. 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.
3. 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.