Jacob Vigdor, a professor of public policy and economics at Duke University, wrote an interesting essay earlier this year challenging the conventional wisdom about school discipline. It led to a lot of discussion here on the blog
I suspect we will see a lot discussion around his latest report about U.S. math instruction. In a report for the American Enterprise Institute, Vigdor explains what has gone amiss with American math education.
In a recent essay based on his research — “Does Your Job Really Require Algebra ?“ — Vigdor writes:
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.
Among the questions in his report: Can we really think of an algebra course offered to every eighth grade student as the intellectual equivalent of a course that was offered only to the top quarter of students, typically in tenth grade or later, sixty years ago? (His answer is “no.”)
A highlight from the report:
The new-math movement may have succeeded in raising the bar, but students reacted by giving up rather than attempting to clear it. The implementation of new math in the 1950s associates with the marked decline in math-intensive majors: the birth cohorts of the late 1940s and early 1950s would have been exposed to this curriculum during their primary or secondary years.
Given that the substitution of rigor for practicality appears to have turned students off to math, it stands to reason that substitution in the reverse direction would undo the effect. And indeed, the wane of the new-math movement in the late 1960s and early 1970s helps to explain the resurgence of interest in math-intensive majors — the only such episode observed over a period of seventy-five years — among cohorts born in the late 1950s to early 1960s.
The resurgence was short-lived. From the 1962 birth cohort onward, the proportion of college graduates completing math-intensive majors dropped steadily. As we move forward from the 1962 birth cohort, we encounter students who spent a more significant proportion of their primary and secondary years in the 1980s, a decade when American policymakers focused increasingly on improving the performance of average students while not worrying much about those at the top.
Too Much Too Soon for Too Many: Accelerating students in algebra and other advanced math courses does not always improve their math performance. In the Charlotte-Mecklenburg Schools, students who took algebra early scored thirteen percentile points lower on a standardized end-of-course test than students who took algebra on a regular schedule, and accelerated students were less likely to pass an end-of-course test in geometry.
Dumbing Down Classes Hurts Strong Students: Attempts to close the achievement gap by reducing the rigor of math education have meant fewer top performers are equipped to pursue math careers; the past thirty years have witnessed a twenty-point increase in aveage math SAT scores but a 25 percent drop in the proportion of college students who major in math-intensive subjects.
Different Students Need Different Courses: American students are not all the same, and a rational strategy to improve math performance must begin with a willingness to meet different students’ needs rather than a single-minded focus on having all students taking the same classes.
The report’s conclusions include:
For several decades, the United States has counteracted its decline in math in part by importing highly talented immigrants. American immigration policy prioritizes family reunification over skills, in direct contrast with peer nations such as Australia and Canada. Any attempt at immigration reform should address this issue.
Curricular fads such as Singapore math hold promise in many circles but may not be readily adaptable to American cultural and educational settings. Experimentation is warranted, but we must be mindful that the net effect of our past curricular tinkering has been negative.
Pursuing equity in curriculum must harm some students, and evidence suggests that some past reforms have managed to harm all of them. American students are heterogeneous, and a rational strategy to improve math performance must begin with that premise.