Monday, July 30, 2012

Fishing for Geniuses

There was an opinion piece in the NYTimes yesterday entitled “Is Algebra Necessary?” It is the opinion of Andrew Hacker, the writer of the piece, that math above the level of arithmetic should not be indiscriminately taught to all high school and college students. He posits that mandatory algebra classes “[prevent] us from discovering and developing young talent.” He also cites anecdotal evidence that the current math requirements are responsible for the alarming high school and college dropout rates.

It’s an impassioned article, but Mr. Hacker’s argument is a particularly blatant petitio principii. He says that algebra-level math has no practical application for 95% of entry-level workers or for creative artists, and therefore should not be taught to everyone. This line of reasoning reveals a belief that the purpose of math classes is to make everyone proficient in math. This is an erroneous assumption.

The point of math classes isn’t to teach everyone math. The point is to find geniuses.

I have a bit of insight into this. In college, I briefly toyed with the idea of majoring in something that required a solid foundation in higher-level math. After barely keeping my head above water in Calc I during the first semester, I got absolutely demolished by Calc II in the second. I remember getting back the first test in Calc II, a test I failed, as did 80% of the class. These test results were met by the professors and TAs with little more than a nonchalant shrug; they just applied a curve to the grading and moved on. They didn’t care that so many had failed, but you can bet the ones who passed certainly caught their attention. Having been disabused of the notion that I had the chops to become a biochemist, I quickly switched majors and moved on with my life.

So why not just let the students decide for themselves what they are good at and let them drop math as early as possible? The answer is simple: The education system is designed to root out the best of the best. And the bigger the pool of people, the better the odds of finding that person with exceptional skills.

Think of it like you’re running a high school basketball team. Let’s say that the team needs a capable 3-point shooter. So you start your search for someone who can fulfill this very specific role. How do you find this person? Ideally, you’d have all the students in the school come to the gym and take a hundred 3-pointers, regardless of how tall or athletic they were. You’d want everyone to take a hundred shots, even those who didn’t want to play basketball. Why? Because you never know. In the end you’d have a good idea who your 3-point shooter should be, and it might be someone who never considered picking up a basketball, someone with a natural skill that can’t be taught. If you did manage to find an especially gifted 3-point shooter, you wouldn’t care that you just put 99% of the student body through a pointless and stressful shooting drill. The end justified the means. That’s how math departments operate. They are perfectly willing to leave behind smoking ash heaps of defeated, demoralized students if it allows them to find that one promising mind. In fact, the more who fail, the easier their search is.

Must we put our students through such a draconian process? Is it that important to find people who are good at math? The simple and obvious answer is: Of course. Even Mr. Hacker concedes that “mathematics, both pure and applied, is integral to our civilization.” The people who understand and practice the highest levels of math change all our lives for the better. That is why math classes will continue to be compulsory.

But make no mistake about it, the other academic departments are run the same way. Mr. Hacker quotes a math professor as saying, “Our civilization would collapse without mathematics.” Every other professor would say the same about his or her respective field. Teachers of English, History, Philosophy—they all think their subjects are of paramount importance. And they are all looking for geniuses to contribute to their field. That’s why everyone in high school is forced to learn about WWII, write essays about the categorical imperative, read The Catcher in the Rye. For the mathematically inclined students, doing these things is probably just as excruciating as taking an algebra class is to everyone else. But, again, it’s all for the cause of discovering brilliance. In this way, each professor is like a recruitment ambassador for his or her field. It is with this perspective that a lot of the unintentional humor of Mr. Hacker’s editorial can be appreciated. His byline reveals that he’s an emeritus professor of political science at Queens College. A poli-sci guy railing against algebra is like a Duke basketball recruiter disparaging the program at UNC. There’s hardly pure objectivity going on here.

The NYTimes has run a couple of articles about math’s difficulty lately. Is there something that’s making this a talking point in the culture right now? How’s this for a theory: Until fairly recently, if you wanted to learn about higher-level math, you had to go to a textbook. Now that same information—once locked securely away in $99 textbooks—is a Google or Wikipedia search away, readily accessible to everyone. That is not to say that you can pick up all there is to know about calculus by reading its Wikipedia page. But reading it will probably give you at least a rudimentary idea of a few of its concepts. You’ll probably end up knowing enough to know that there’s a lot you don’t know. This can be a discomfiting state to be in. A few years ago it was hard to even be exposed to this stuff outside a classroom setting, and so a total ignorance of it was not only possible but likely. And as we know, ignorance is bliss. But a little knowledge can be burdensome and stress-inducing. The realization that we are unable to grasp something we’ve been conditioned, through years of academic inculcation, to think of as part of the “standard” curriculum may be causing an anxiety and acute feeling of inadequacy that is manifesting itself in the lashing-out at the thing causing that feeling, viz. difficult math.

But I don’t know. We might have to turn to the psychology geniuses for an answer to that one.


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