And now for something completely different…
Well, not really, but kind of different.
I realize that my niche here has become discussing science-based medicine, evidence-based medicine, and the atrocities committed against both by proponents of so-called “complementary and alternative” medicine, but every so often I need a change of pace. Unfortunately, that change of pace was something I came across in the New York Times on Sunday in the form of a commentary so bad that I seriously wondered if it was a parody or a practical joke. Alas, it wasn’t. I’m referring to an article by Andrew Hacker, and emeritus professor of political science at Queens College, City University of New York, entitled Is Algebra Necessary?
The short answer is yes (actually, hell, yes!). The longer answer follows. First, though, let’s start out with the premise, which hits you in the face in the very first paragraph of this incredibly misguided and, quite frankly, mind-numbingly silly proposal:
A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.
Hmmm. I wonder what Hacker would say if I were to rewrite his paragraph thusly:
A typical American school day finds some six million high school students and two million college freshmen struggling with English and English composition. In both high school and colleged, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.
Or substitute history or science for algebra in the same paragraph. Actually, come to think of it, if we deemphasize algebra, we might as well add science to the mix, because without algebra it is damned near impossible to become proficient at any science. It’s the very minimal that is necessary to understand basic physics, for example, and perhaps not even enough for that given how much of physics is based on calculus. However, algebra is probably enough to undergird a basic understanding of classical physics that is adequate for an average educated citizen to need to know. Of course, without algebra, chemistry would be completely indecipherable, at least anything quantitative. Forget about reaction stoichiometries, kinetics, and the like. That will be out of reach, except for mushy generalities. Then forget about biology and biochemistry as well. No enzyme kinetics, membrane potentials, half-lives, or anything quantitative. And for you budding doctors out there, forget about medicine! A solid understanding of all these sciences, and more (pharmacology and human physiology in particular) is beyond your understanding if you don’t understand the basics of algebra.
It’s not just science, though. Without the basics of algebra, it’s really difficult to understand the basics of statistics. We live in an increasingly data-driven world, and our citizenry is already pretty statistically illiterate anyway. But, heck, it’s too hard; so let’s drop it.
Hacker’s “logic” (such as it is) for recommending that not everyone should be required to have a basic competence in algebra is strange, too. Get a load of this:
This debate matters. 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.
For someone claiming to rely heavily on the use of numbers, one can’t help but note that Hacker’s arguments are not particularly powerful and play a little bit fast and loose with numbers himself. He cites a lot of statistics, but his interpretation of many of them leaves something to be desired. (Hey, that’s something that a good grounding in algebra and other mathematics would help those of us reading Hacker’s little proposal guard against, isn’t it?) For instance, Hacker says that “most of the educators” that he’s talked with cit algebra as the major reason why our high school dropout rate is so high, but he doesn’t cite any actual…oh, you know…figures that support such a blanket statement. For example, he cites various failure rates at algebra proficiency tests but doesn’t show evidence that these are the primary reason why these high school students dropped out of high school or, more importantly, compared these figures with the numbers of students who fail other core topics that all high school students are expected to demonstrate minimal proficiency at. That is the very minimum information necessary to put the figures describing students’ difficulty with mathematics and algebra into proper context. It wouldn’t surprise me at all if students who drop out don’t just fail algebra. They probably fail a lot of other major core curriculum topics as well.
True, hacker does cite some numbers that suggest that seem to indicate that freshman mathematics is a barrier to retention in college, but a better question to ask is: Why are freshmen so woefully unprepared in something as basic as algebra, such that they have difficulty learning it as a college freshman. If a student arrives in college without a basic understanding of algebra, as far as I’m concerned that student is not ready for college, any more than a student who can’t read and write at a sufficiently high level. I can understand, although not necessarily support, an argument that perhaps calculus is not necessary for all college students. Perhaps, it could be argued, students who are not majoring in a science don’t need to take calculus or that perhaps a year of statistics could be substituted for a year of calculus. One could even make the argument that in the “real world” statistics is a much more useful topic to have been exposed to for most people. Those would not be unreasonable arguments.
Instead, Hacker claims that mathematics is “used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status,” giving examples that veterinary technicians are required to be proficient at algebra for their certification but never use it in diagnosing or treating animals. (Oh, really? How do they scale up drug dosages?) He also cites Harvard and and Johns Hopkins medical schools as requiring calculus for entrance, “even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice.” Well, there are a lot of things required to get into medical school and taught in the first two years of medical school that do not figure in subsequent clinical practice or the curriculum. Much blood has been spilt on the floor, metaphorically speaking, arguing what sciences should be required in order to be a good physician. Hacker might have a point that physicians don’t need to be proficient in calculus (although it helps if they wish to go into, for instance, radiation oncology), but that is a separate issue than whether students need to know algebra. Physicians, for instance, do need algebra for many things, including calculating blood gases, drug dosages, half-lives, cardiac outputs, and a number of other parameters. True, there are now many minicomputers and medical instruments that automatically calculate these numbers, but to understand the significance of the results, and, more importantly, changes in the results requires an understanding of the underlying equations, which in turn requires an understanding of algebra. Perhaps that’s why Hacker mentioned calculus instead of algebra. In fact, one wonders if what we have here is a big case of math envy, given that he harps on the use of mathematics as a means of adding prestige to a field.
Be that as it may, what does Hacker propose instead? Well, this for one:
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 of climate 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.
So, let’s see. Quantitative literacy is critical to being an educated citizen who can weigh public policies, but algebra isn’t necessary? Silly Hacker, what he is arguing here is not that a basic understanding of algebra isn’t of critical importance to all citizens, but rather that it’s taught badly. And I agree! Mathematics and algebra are all too often taught badly, with no good hook into the real world usefulness of the disciplines. No wonder students lose interest! They’re never taught just how deeply mathematics of all types underlies, well, pretty much everything quantitative in society. Later, Hacker proposes:
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.
Except that it would be rather difficult to understand in the first place what a weighted average like the CPI is if the students don’t understand the basics of algebra to begin with.
The bottom line is that we as a society have to decide what it means to have a well-rounded education. In general, we all tend to agree that reading at a certain level is essential. We can argue what, exactly, that level should be, but in today’s society it’s no longer possible to function well if you can’t read and write, particularly in this increasingly Internet-driven world. Similarly, an understanding of mathematics is essential, and, from my perspective, algebra is actually a pretty low bar. True, many, if not most, people will never use much algebra, but the habits learned and the methods of using mathematics to solve problems will be useful almost no matter what a person does in life. Then, of course, there are the sciences and humanities, in particular history. If one-third of students are doing poorly at a subject that is so basic, such as algebra, then the answer is not to drop the requirement or to absolve those students who are having trouble passing it, but rather to find ways to teach it better. No one expects that everyone can excel at every topic, but there are certain topics that one should have a minimal proficiency at in order to be considered educated.