The Misplaced Math Student

Monday, September 22, 2008
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Algebra in eighth grade was once reserved for the mathematically gifted students. In 1990, very few eighth graders, about one out of six, were enrolled in an algebra course. As the decade unfolded, leaders began urging schools to increase that number. President Clinton lamented, “Around the world, middle students are learning algebra and geometry. Here at home, just a quarter of all students take algebra before high school.”

The Clinton administration made enrolling all children in an algebra course by eighth grade a national goal. In a handbook offering advice to middle school students on how to plan for college, U.S. secretary of education Richard Riley urged, “Take algebra beginning in the eighth grade and build from there.” Educator and civil rights activist Robert Moses ratcheted up the significance of the issue by labeling algebra the “New Civil Right,” thereby highlighting the social consequences of so many poor and minority students taking remedial and general math courses instead of algebra.

The campaign was incredibly successful. Several urban school districts declared a goal of algebra for all eighth graders. In 1996, the District of Columbia led the nation with 53 percent of eighth graders enrolled in algebra. From 1990 to 2000, national enrollment in algebra courses soared from 16 percent to 24 percent of all eighth graders.

The surge continued into the next decade. Eighth-grade enrollment in algebra hit 31 percent nationally in 2007, a near doubling of the 1990 proportion. Today, more U.S. eighth graders take algebra than any other math course. In July 2008, the state of California decided to adopt an algebra test as its eighth-grade assessment of student proficiency. The policy in effect mandates that all eighth graders will be enrolled in algebra by 2011.

At first glance, this appears to be good news. Transcript studies indicate that 83 percent of students who take geometry in ninth grade, most of whom completed algebra in eighth grade, complete calculus or another advanced math course during high school. Research also suggests that students who take algebra earlier rather than later subsequently have higher math skills. These findings, however, are clouded by selection effects—by the presence of unmeasured factors influencing who takes algebra early and who takes it late. Schools routinely assign incoming eighth graders to math courses based on how much math students already know. Moreover, it is no surprise that excellent math students want to take the most challenging math courses available to them and that low-achieving students avoid these courses as long as possible. Whether algebra for eighth graders is a good idea, especially for those who have not learned basic arithmetic, cannot be concluded from existing evidence. Studies that test for causality, such as experiments with random assignment of students to treatment and control groups, have not been conducted.

The misplaced eighth graders waste a year of mathematics, lost in a curriculum of advanced math.

The push for universal eighth-grade algebra is based on an argument for equity, not on empirical evidence. General or remedial math courses tend to be curricular dead ends, leading to more courses with the same title (for example, General Math 9, General Math 10) and no real progression in mathematical content. By completing algebra in eighth grade—and then completing a sequence of geometry as freshmen, advanced algebra as sophomores, and trigonometry, math analysis, or precalculus as juniors—students are able to take calculus in their senior year of high school. Waiting until ninth grade to take algebra makes taking calculus in high school more difficult. From this point of view, expanding eighth-grade algebra to include all students opens up opportunities for advancement to students who previously had not been afforded them, especially students of color and those from poor families. Democratizing eighthgrade algebra promotes social justice.

There’s one catch. Course taking is a means to an end, not an end in itself. Students take math courses to learn mathematics. Will policies mandating algebra for all eighth graders mean that the nation’s students learn more math? Not necessarily. Although cross-sectional state test data cannot answer such a question, they can answer a different question: Do states that enroll more students in advanced math courses score higher than states enrolling fewer students in advanced courses?

The 2007 eighth-grade National Assessment of Educational Progress (NAEP) scores for states and jurisdictions and the percentage of eighth graders enrolled in advanced math classes (Algebra I, Geometry, and Algebra II) were as follows: Massachusetts scores at the top (298) and has 45 percent of eighth graders enrolled in advanced math, more than the national average of 38 percent. But several high-scoring states enroll fewer students in advanced classes. North Dakota and Vermont, for example, are ranked third and fourth in math achievement but enroll a relatively low percentage of eighth graders in advanced math (21 percent and 26 percent, respectively). On the other end of the spectrum, the District of Columbia scores last on NAEP but continues to be one of the leaders in the percentage of students taking advanced math. The Pearson correlation coefficient, a measure of the statistical relationship between two variables, for NAEP score and advanced math enrollment is -0.09, indicating no correlation.

Another intriguing pattern in eighth-grade NAEP scores emerges from examining the scores of eighth graders taking advanced math courses. The national average in eighth-grade math has been rising steadily, increasing by 8 points from 2000 to 2007, from 273 to 281. But one group stands out for not participating in the score increase—eighth graders in advanced classes. Their NAEP scores have declined from 299 in 2000 to 295 in 2007, a loss of four scale score points. The typical eighth grader knows more math today than in 2000. But the typical eighth grader in an advanced math course knows less. How can that happen?

It happens because 120,000 students are misplaced in their eighth-grade math classes. They have not been prepared to learn the mathematics that they are expected to learn. This unfortunate situation arose from good intentions and the worthy objective of raising expectations for all American students.

Two groups of students pay a price. The misplaced eighth graders waste a year of mathematics, lost in a curriculum of advanced math when they have not yet learned elementary arithmetic. They should be taught whole number and fraction arithmetic so that they can then move on to advanced mathematics.

Will policies mandating algebra for all eighth graders mean that the nation’s students learn more math? Not necessarily.

Their classmates also lose—students who are good at math and ready for algebra. These well-prepared but ill-served students also tend to be black and Hispanic and to come from low socioeconomic backgrounds. Teachers report that classes of students with widely diverse mathematics preparation impede effective teaching, that too many students arrive in algebra classes unmotivated to learn, and that they wish elementary schools gave greater emphasis to basic skills and concepts in math. When algebra teachers have to depart from the curriculum to teach arithmetic, the students who already know arithmetic and are ready for algebra are the losers.

This is not a call to lower expectations. Nor is it a call for cynicism. But we must establish the right goals and pursue sound strategies for achieving them. The goal must not be for students to take an algebra course by eighth grade; it must be for more students to learn algebra. The strategy must not be to designate an arbitrary grade—unsupported by research or policy experience—in which all students are swept into an algebra course. Universal eighthgrade algebra is creating more problems than it solves, with 120,000 students not learning the mathematics that they need to know and hundreds of thousands of their classmates paying an educational price along with them.