Unsound Opinons in the NYT

Is algebra necessary? This is the question posed by Dr. Andrew Hacker in an opinion piece, which appeared in the New York times earlier this week. Dr. Hacker, an emeritus professor of political science at CUNY Queens College, argues that requiring a traditional mathematics sequence up to and including algebra -- yes, algebra's the one you take in 8th grade -- is stifling the intellect of young people, by causing them undue stress and dampening their creativity. I understand that math is difficult; trust me, I'm attempting to make a career out of struggling with math. But shouldn't we be teaching our students that struggling is a necessary, acceptable, even valuable part of the process? In fact, what ever happened to that time-honored axiom of hardship ``building character," which parents have been using to torture their children since the beginning of time?

I do believe that our early education approach to mathematics needs some retooling, but I don't think that making it easier -- or extinct -- is the answer. I may be biased towards the inherent benefits of calculus, but let me point out that the main objective of primary education is learning how to learn. The most effective exercise in knowledge acquisition is to take a pile of things that you don't understand, and turn it into a pile of things that you do understand. To that end, I believe that mathematics provides the ideal venue for this sort of exercise. It is all sitting there in a book, all you have to do is open it up and read. There's nothing sneaky or mysterious about it. Math is truth and beauty. Math is satisfying. The answers exist and are completely objective. Math is abundantly fair. To say that math is discriminating and unfair is absurd. In fact, one would be hard pressed to find a more egalitarian line of study than pure mathematics.

Dr. Hacker argues that learning mathematics in the classroom is pointless, since most jobs requiring any STEM knowledge will provide it in on-the-job training. But then why do countries with more rigorous mathematics curricula produce more desirable job candidates? Dr. Hacker concedes, ``It's true that students in Finland, South Korea and Canada score better on mathematics tests." But he continues on to say ``it's their perseverance, not their classroom algebra, that fits them for demanding jobs." Perseverance? How do we teach students about perseverance? Might I suggest factoring a few polynomials?

The author points out that California's university system only considers applications from students who have taken three years of mathematics. This ``prohibitive wall," he says, excludes many otherwise talented students from entering the university system. If a standard high school education were to require only two years of mathematics, how would the students be filling their days? Certainly not with physics or chemistry, since these students would lack the quantitative skills to manage such courses. We would be creating students, who at a very young age, have put themselves at a grievous disadvantage for the rest of their academic lives.

Unsurprisingly, he proceeds to trot out that age-old argument: When am I ever going to use this? Dr. Hacker claims that certain elite medical schools require all applicants to have taken calculus -- a course which is not necessary in the practice of medicine -- as ``a hoop, a badge, a totem to impress outsiders and elevate a profession's status." I don't know if requiring medical doctors to jump through some additional academic hoops is such a bad thing. The outstanding medical school applicant is a strong student, who is unafraid to face challenges and able to maintain prudence in the face of uncertainty. With the level of academic rigor demanded of these students, I can't imagine that calculus is too much of an outlier as far as difficulty. It is certainly no less relevant to the practice of medicine than the myriad extracurricular activities which are demanded of applicants. More importantly, I like to imagine that my medical doctors are self-assured and confident in their problem solving skills. If a person lacks the fortitude to integrate a function, I would imagine that they also lack the fortitude to cut me open with a scalpel.

But even the above argument I could accept on a case-by-case basis. It's true that not all people need calculus. But Algebra? Seriously? That's the mathematical equivalent of learning how to read a chapter book. Were Dr. Hacker willing to accept an equivalently low bar for literacy, then most of our nation's high schoolers wouldn't even be able to read his article.

I may have chosen to make mathematics my career, but I'm certainly glad to have learned enough english to recognize satire, because given the absurd and borderline dangerous implications of his arguments, Dr. Hacker could not possibly be serious about this.

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