Andrew Hacker argues that, while quantitative skills are “critical for informed citizenship and personal finance,” making kids master algebra to graduate high school has disastrous consequences.
Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.
The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.
Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia.
Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee. Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.
California’s two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.
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Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.” A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.
Nor will just passing grades suffice. Many colleges seek to raise their status by setting a high mathematics bar. Hence, they look for 700 on the math section of the SAT, a height attained in 2009 by only 9 percent of men and 4 percent of women. And it’s not just Ivy League colleges that do this: at schools like Vanderbilt, Rice and Washington University in St. Louis, applicants had best be legacies or athletes if they have scored less than 700 on their math SATs.
This comports with my own experience. I excelled at math through my early years of school and was even on the math team as a high school sophomore. While my skills have eroded somewhat owing to technology, I’m still pretty good at the sort of math that’s useful in everyday life, including estimation and statistical interpretation.
In my own case, it wasn’t algebra that got me but calculus. I graduated high school in 1984, just before the Advanced Placement craze swept the country. (Indeed, it had probably already swept the country, as it hit my rural Alabama high school the next year.) No advanced mathematics classes were necessary to graduate but I nonetheless took two years of algebra, geometry, and something called “advanced math” (essentially, pre-calculus) as electives. While I’m not sure I learned much useful—in the sense that I actually used any of it outside school, much less still remember it–I was able to get through that sequence with good grades, although I did stumble a semester or two and wound up with a B+ rather than an A-. But it was mostly a matter of remembering formulas by rote and applying them in cookbook fashion; I never truly understood what I was doing in the way that I did arithmetic. That last year was at a level of abstraction that truly baffled me—such that I don’t even really remember what it was that I was exposed to.
When I got into West Point that summer, despite solid SAT and ACT scores in math, I did poorly enough on their post-acceptance placement exam that I was placed in a what was derisively called “rock math,” a remedial course in an institution that was still at heart an engineering school, rather than calculus. I never really recovered. I got through that and Calculus I, although the latter only because they were grading on a curve and I was above it. I failed Calculus II and barely got through Physics and wound up washing out. It was just as well, as there were still several more math and engineering courses ahead of me on the curriculum, including Differential Equations, a course which ended the careers of many a cadet.
Now, I suspect that I’d have been able to pass Calculus II and do better at Physics at the University of Alabama than at West Point, simply because I wouldn’t have also been drowning in extracurriculars and the stresses of a pressure cooker that aimed at driving out a third of each class. Then again, I likely wouldn’t have been in those classes to begin with as a poli-sci major. I would go on to take several graduate courses in statistics as part of my doctoral study. While they were not as intuitive as my poli-sci classes, I nonetheless understood the concepts and got A’s in the classes.
Despite these frustrations and the fact that the lack of proficiency in abstract math was never an issue outside the classroom, I’ve nonetheless defended the notion that forcing kids to grapple with the subject was useful. Six years ago, in addressing a Richard Cohen column, I wrote a post titled “Is Algebra Worthless?” and argued in the negative.
If a degree is merely a credential for employment, there’s not much argument for requiring algebra for those not aspiring to scientific and technical fields. Ditto literature and the arts for those who are not headed in that direction. Or foreign languages for those not intending to travel. If it is about broadening the mind-in a sense, an end into itself rather than merely a means-then all those things must be part of the curriculum.
English (or whatever written and spoken language predominates in a given society) and mathematics are the two essential languages of education. One is simply not educated without a solid foundation in both.
But Hacker isn’t arguing that we should take math out of the curriculum:
Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required. Toyota, for example, recently chose to locate a plant in a remote Mississippi county, even though its schools are far from stellar. It works with a nearby community college, which has tailored classes in “machine tool mathematics.”
That sort of collaboration has long undergirded German apprenticeship programs. I fully concur that high-tech knowledge is needed to sustain an advanced industrial economy. But we’re deluding ourselves if we believe the solution is largely academic.
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Algebraic algorithms underpin animated movies, investment strategies and airline ticket prices. And we need people to understand how those things work and to advance our frontiers.
Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact ofclimate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² – y²)² + (2xy)² leads to more credible political opinions or social analysis.
Many of those who struggled through a traditional math regimen feel that doing so annealed their character. This may or may not speak to the fact that institutions and occupations often install prerequisites just to look rigorous — hardly a rational justification for maintaining so many mathematics mandates. Certification programs for veterinary technicians require algebra, although none of the graduates I’ve met have ever used it in diagnosing or treating their patients. Medical schools like Harvard and Johns Hopkins demand calculus of all their applicants, even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice. Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.
It’s not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics. But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar. Demanding algebra across the board actually skews a student body, not necessarily for the better.
I WANT to end on a positive note. Mathematics, both pure and applied, is integral to our civilization, whether the realm is aesthetic or electronic. But for most adults, it is more feared or revered than understood. It’s clear that requiring algebra for everyone has not increased our appreciation of a calling someone once called “the poetry of the universe.” (How many college graduates remember what Fermat’s dilemma was all about?)
Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.
It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.
This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry. More and more colleges are requiring courses in “quantitative reasoning.” In fact, we should be starting that in kindergarten.
This strikes me as a sensible approach. My experiences teaching college and engaging in blog comment thread discussions over the years have highlighted how bad most people are at this sort of “walking around math.” And people who are attending college and commenting on blogs are an elite slice of our society; I shudder to think how innumerate the bottom half must be.
At the same time, while most of us will never need to solve a quadratic equation, much less do whatever it is that Calculus is used for, at least one in twenty will. How will our future mathematicians, physicists, chemists, and engineers discover their interest and aptitude for those endeavors if they’re not exposed to abstract math in high school? Maybe there’s some middle ground solution that allows people to graduate high school and college taking courses in practical math and science but offering non-punitive opportunities for students to see whether they have the aptitude for the more abstract varieties? Part of the problem is that our entire system is geared around semester-long sequences that result in the earning of credit hours. So, there’s no way to take algebra or calculus—or, for that matter, introductory philosophy or Latin—for a few weeks, struggle to stretch one’s mental facilities–and then move on to something else without penalty. That means that either we make mandatory courses that everyone doesn’t strictly “need” or else we make optional courses that everyone should at least be exposed to. Instead, we should allow for broad exposure and familiarization with the opportunity to move on without penalty into subjects where one’s natural talents and aptitudes lie.
