- America has had a math problem for at least 50 years – since the Soviets launched Sputnik, if not before.
- The tragedy of American mathematics can be told through the history of a single course: algebra.
- The misguided transformation of algebra into a course for the masses has proven to be a cure worse than the disease.
- “Equality is not a goal worth pursuing if one must make all students worse off to achieve it.” –Jacob Vigdor
America has a math problem. We've had a math problem for at least 50 years — since the Soviets launched Sputnik, if not before. Our high school students have trouble competing with those raised in considerably poorer nations, and we aren't producing enough talented scientists and engineers to ensure our nation a leadership position in the 21st century knowledge economy.
If you think about it the right way, that's not just one math problem — it's two. You might think of improving math skills of both "average" students and the nation's top students as two birds that could be killed with one stone. But they aren't. In fact, some of the easiest ways to solve one problem make the other one worse. Our failure to recognize the distinction between these two problems helps explain why we've managed to spend so much time worrying about math in this country without ever improving the situation.
"The tragedy of American mathematics can be told through the history of a single course: algebra." The tragedy of American mathematics can be told through the history of a single course: algebra. Two generations ago, algebra was a course reserved for elite students — perhaps the top 10 percent. It was taught exclusively in high school. The educators who designed the curriculum saw little point in teaching the abstract subject to students destined for careers in manual labor. A large proportion of those students who took the course would go on to use math in their careers: among male college students who graduated in the 1940s, for example, about 3 in 10 majored in a mathematically intense subject.
The pragmatic attitude towards mathematics for the masses gave way in the post-World War II era. Successive waves of curricular reforms sought to improve the mathematical skills of ordinary students. The "New Math" movement of the 1950s and early ‘60s tried to beef up the curriculum for all students, with disastrous results. By steering the curriculum away from practical application to a focus on fundamentals, new math managed to turn a generation of students off from math. Male college graduates raised in the new math era chose math-intensive majors at a rate of 20 percent — down a third relative to the prior generation.
The new math movement waned, but an intense interest in improving the math performance of ordinary students persisted for more than a generation, culminating in the "No Child Left Behind" movement of the past decade. We now instruct our schools to prioritize the performance of the worst students, and impose no penalty if they neglect their top achievers in the process. Recent studies have confirmed that schools respond to these incentives.
Today, algebra is considered a "gateway" course seen as the most critical step toward college readiness, rather than an abstract course useful only to a select few. About one-third of American students take algebra as eighth graders. In some states, more than half of all students take algebra in middle school. A few years ago, the California State Board of Education attempted to mandate that all students take algebra in eighth grade. Proponents of early algebra point out that students who complete the course at an earlier age are more likely to do all sorts of wonderful things later in their lives. While this observation is true, it best serves to illustrate the difference between correlations and cause-and-effect relationships. Presumably, the students who take algebra at a young age were precocious even before they took the course — that's how they ended up there in the first place.
Unfortunately, the misguided transformation of algebra into a course for the masses has proven to be a cure worse than the disease. The transformation has resulted in a less rigorous course. Introductory textbooks have slimmed down considerably over the past century, omitting some subjects entirely. The primary victims of this dumbing-down are the elite students themselves. Among the most recent cohorts of college graduates, the proportion of male students majoring in math-intensive subjects has continued to hover in the 20 percent range. If we compare this to the historical 30 percent rate of two generations ago, we lose about 100,000 mathematicians, scientists and engineers every year — enough to replace every American employee of both Microsoft and Google and still have tens of thousands to spare.
Algebra remains a course that is simply too difficult for many students. With Duke colleagues Charles Clotfelter and Helen Ladd, I've recently conducted an evaluation of an algebra acceleration initiative that occurred about 10 years ago in the Charlotte-Mecklenburg school system. Students placed into algebra a year early ended up significantly less likely to complete a three-course college prep math curriculum — Algebra I, Geometry, and Algebra II by the time they completed high school.
So, in a nutshell, we have the story of Americas' twin mathematics problems. Begin with a focus on inequality and a mistaken premise that everyone could be another Einstein if they just have access to the right courses at the right time. You'll soon be patting yourself on the back for closing the gap between the best and the worst, only occasionally reminded that neither your best nor worst students are doing all that well in absolute terms. You've fallen into what might be termed the "achievement gap trap."
The silver lining around this cloud is that the path to better absolute performance is clear. The key is to realize that equality is not a goal worth pursuing if one must make all students worse off to achieve it. Mounting empirical evidence points to the benefits of curricular specialization — tailoring coursework to students' abilities, rather than adopting a simplistic "one-size-fits-all" strategy. Math is not a subject that comes equally easily to all students, and the sooner we stop pretending that it is, the sooner we'll be able to simultaneously seed our economy with mathematicians, scientists and engineers who create jobs and workers who possess the skills required to fill them.
Jacob Vigdor is an adjunct scholar at the American Enterprise Institute and a professor of public policy and economics at Duke University.