One morning during my twelve years in blue-light purgatory, I was sitting over coffee with my co-worker Dolores and Steve, her district manager in the ladies’ apparel department. I can scarcely imagine how the topic of higher mathematics arose in the Kmart cafeteria, but I clearly remember the sneer that accompanied the challenge Steve hurled at me: “Just tell me this: How often to you use all that calculus now?” And with that, he gestured broadly at our grubby retail surroundings. Unwittingly using, long ahead of its time, the punctuation of the social media generation, I snapped back, “Every. Single. Day.”
Steve was prepared neither for my response nor for a retort of his own–except for the supercilious eye-rolling that masqueraded as wit even then. Thus, I was unable to explain my reasoning to him, which is probably just as well. Lacking sufficient training in higher mathematics, he probably hadn’t developed the mental agility needed to follow a logical argument.
Obviously, it didn’t take integral calculus to sell–or even identify–three-aught bass hooks or double-aught buckshot. Frankly, even then I could no longer recall what I learned in my last calculus class, Linear Algebra and Differential Equations. I didn’t even know what those arcane disciplines were!
However, what I did know was how to think. What I still know is how to think. And I am convinced that the mathematics I imbibed prior to the age of 20–not only from math classes, but also from chemistry and physics, as well as music theory and performance, made my brain strong and supple and and ready to take on the questions of history and philosophy and literature that have occupied it for the subsequent four decades.
Thus, it was with dismay that I read Andrew Hacker’s 2012 New York Times article entitled “Is Algebra Necessary?” Although I chuckled when Keith Devlin, NPR’s math guy, wrote, “Yes, I thought you’d remember it! It’s almost up there with John Lennon’s murder in terms of knowing where you were when you first heard it,” I do remember exactly. I was in the cramped office I shared with five other college instructors at the Army’s Special Warfare Center and School. I first wondered, “How can the author of the brilliant Two Nations: Black and White, Separate, Hostile, Unequal have written such anti-intellectual claptrap?” I next fired off an email to the two math instructors, my colleagues at SWCS, who I knew would share my pain. And then I wrote an impassioned rebuttal to Hacker’s article that probably ended up, in those pre-blog days, in a manila–or circular–file somewhere. Early this year, Hacker turned his wildly popular article into a book entitled the Math Myth: And Other STEM Delusions.
Sadly, I was forced to recall my own reaction to Hacker’s argument on June 12, when I read in the Detroit Free Press that as of fall 2018, Wayne State University has decided to drop mathematics from its university-wide general education requirements, which include writing, oral communication, critical thinking, natural science, humanities, and “society and institutions” (?). I was even more dismayed when I read in the The New American (I know, I know) that the school’s General Education Reform Committee is considering replacing mathematics with a three-hour class in “diversity.” I am afraid this disturbing sign of malaise will become an epidemic.
I confess that I have not read Hacker’s book; his article was enough of a strain on my 63-year-old cardiovascular system. However, Anya Kamenetz of NPR makes it clear that his thesis remains the same–“that advanced mathematics requirements, like algebra, trigonometry and calculus, are ‘a harsh and senseless hurdle’ keeping far too many Americans from completing their education and leading productive lives.” In his interview with Kamenetz, Hacker provided some statistics–and some explanations: “One in five people don’t graduate [from] high school. . . . And the chief academic reason is that they fail algebra. . . . In our community colleges, 80 percent don’t get a college degree. The chief reason is that 70 percent fail remedial math. And even in our four-year colleges, 40 percent don’t get B.A.s [after 6 years]. And the biggest reason is they fail freshman math.” Clearly, Hacker believes in high graduation rates. He believes, along with an alarming number of co-religionists, in college degrees. They all believe that everyone should have one–which is, in my view, a highly dubious article of faith.
On the one hand, we obviously need auto mechanics, welders, plumbers, HVAC technicians, carpenters, and brick masons. These tradesmen vital to our civilized comforts do not require a college degree. Certainly an apprenticeship or a certificate from a vocational school would give a stamp of legitimacy to their qualifications, but they need to know MLA documentation style and the causes of the Peloponnesian Wars as much as they need the algebraic skills Hacker decries. Sadly, the schools that once prided themselves on their vocational training–the technical schools–have now spurned that rôle and become merely feeder institutions in the college-transfer system. Some of these community colleges have even dropped the word “technical” from the names of their schools. The goal of our society, in my view, should be to restore to the trades the respect they deserve, not to turn their practitioners into college graduates who can’t solve algebraic equations–or get a job.
On the other hand, I strongly believe what I told that man at Kmart 30 years ago. I believe that mathematical thinking is necessary for an educated populace and that one learns that kind of thinking by doing math, the higher the better. Keith Devlin, cited above, explains the concept far better than I could in “What IS Mathematical Thinking?” I don’t have any statistics, and I don’t have any case studies. But I do have the strong belief that going to calculus class at 7:40 every weekday morning of my freshman year at the University of Arizona enabled me to think mathematically and helped make me into the critical thinker I am today. That way of thinking informs my reading, my judgments about the world, and most tellingly, my ability to construct a persuasive argument.
One the other . . . Oops. Two hands, three hands–who cares? I have high self-esteem! And I do have an important third point. I fear that one of the reasons Andrew Hacker and the educational policy-makers have it in for the math department is that it is the last bastion of the correct answer. In the humanities, of course, the proliferation of answers is the whole point. There wouldn’t be much use in studying philosophy if the meaning of life were at the end of an equation. History isn’t what we study at the university level; we study historiography. Even in chemistry and physics, the answers are always changing, at least in the long term.
In the English classroom, there are no more correct answers because we have abdicated our duty to teach grammar and usage in favor of free expression and the idea (popularized by Mona Chalabi) that prescriptive grammar is a racist tool of “white privilege.” Admittedly, I say “we have abdicated” in the broadest sense; I still go through the motions of correcting dangling participles and run-on sentences and even tell my students that the subject of a gerund must be in the possessive. However, department policy prohibits giving instructional time to grammar, even in remedial classes.
Inevitably, when there are no right answers, there are no wrong answers either. All assessment is subjective. Finally, all students can be, like all the children in Lake Wobegon, above average. They will all be on the dean’s list, and they will all get a degree. And my only anxiety about math is that soon, no one will even get the joke.