Tuesday, August 14, 2012

Algebra dead?

"In defense of algebra"

Make Us Do the Math


Jennifer Ouellette

August 14th, 2012

Scientific American

Forgive Jen-Luc Piquant for being a bit rant-y, but today we are defending algebra. Again. We also defended algebra last night on the newly launched Huffington Post LIVE streaming network, along with a few other like-minded sorts. My high school algebra teacher is having a good laugh, because believe me, as a teenager, if I had read Andrew Hacker’s recent New York Times op-ed, advocating that schools ditch algebra, my kneejerk reaction would have been “Hell yeah!” And, like Hacker, I would have been so very wrong.

You probably heard about the controversy surrounding Hacker’s article; it was the op-ed that launched a thousand outraged blog posts. Cognitive scientist Daniel Willingham argued in the Washington Post that “The inability to cope with math is not the main reason that students drop out of high school.” Rob Knop asked why we’re not getting to the bottom of “why it becomes normal not to ‘get’ math,” and bemoans the willingness of students to “just do what’s necessary to get by without actually learning anything.” PZ Myers went for satire, questioning why we’re bothering to teach students antiquated skills like grammar and punctuation, when they’re all just texting nowadays anyway. Educating students is so much easier if you “strip out the difficult learning part.”

Mark Chu-Carroll trounced Hacker’s assertion that most students don’t need algebra in real life (so did Blake Stacey). And Melanie Tannenbaum of PsySociety weighed in with a thoughtful look at how algebra is taught, compared to what psychologists now know about how we learn: namely, “people are better able to remember events, facts and knowledge when it is integrated into people’s self-concepts,” and when “it’s situated within a social context.”

You get the idea. What else would you expect from all those scientists? Well, I’m a former math phobe. I hated algebra, and avoided all advanced math and science until well into my 20s. But I’m standing in solidarity with the fusty old scientific establishment on this one.

There is, indeed, an important conversation to be had about education reform, and I heartily applaud any effort to address different learning styles and methodologies. If nothing else, Hacker’s misguided op-ed has fostered a discussion. And I agree that learning practical math like statistics and probabilities is dead useful for a good social citizen. I just think it should augment, not replace, the traditional curriculum.

Hacker tosses out a lot of statistics on students unable to pass algebra to support his “case,” but I don’t think anyone disagrees that this is a problem. I just can’t see how ditching algebra comprises a sensible solution. Hacker’s thinking seems to be that, because algebra is such a stumbling block for many students, we should throw up our hands and despair of ever teaching it to them. But do we really want to throw in the algebraic towel just because it’s, like, rilly hard?

This kind of experiment has already been done. We need only look to our Eastern neighbor, Japan, for a glimpse of the kind of future this could bring. Caltech string theorist Hirosi Ooguri minced no words when he reacted to Hacker’s article on Facebook:

    “This is extremely dangerous, and we should not just laugh at it. A similar argument led the Japanese Government to reduce elementary, junior high, and high school math education significantly during the 1990?s. In the past few years, the Government realized the mistake and is trying to reverse it. Unfortunately, a generation of children missed opportunities to get decent education in mathematics, and I am afraid that its negative effects will be felt for many years to come.” (Ooguri graciously granted permission to quote him).

He is referring to the yutori kyoiku (“room to grow”) educational policy that dramatically altered the elementary, junior high and high school curricula in Japan. It sounds great on paper: convinced that traditional rote memorization is insufficient in a 21st century world, Japanese students now were encouraged to develop individuality and initiative, and foster critical thinking and problem solving. The number of classroom hours was reduced, and so was the amount of required math. “Japanese had good basic study skills, so the idea was to add the more individualistic things that westerners have on top of that,” psychologist and author Hideki Wada told the Financial Times.

The results, as Ooguri says, were disastrous. According to the Mathematical Society of Japan, a recent study revealed that 1 in 4 Japanese college students can’t even explain what taking an average means. Of the five questions on the survey, only 1.2 percent answered them all correctly. Per an article in Asian Correspondent: “Students can still calculate the problems, but are not correctly answering proof questions. Educators say less time spent studying fundamental maths problems means students don’t understand why a problem is solved a certain way.”

Nor has it pleased employers. The Financial Times piece points out that Sumitomo Metal now offers remedial science classes for its factory near Osaka, and other companies have followed suit, because students “don’t know anything” when they graduate from college.

Granted, this a complicated issue, and certain Japanese educators maintain that the problem lies not in the ideology, but the execution, exacerbated by unique cultural factors. (This article by Ogi Naoki is an enlightening read.) But as we mull over how to address our own educational shortcomings, we might draw some lessons and guidance from our Eastern neighbors.

Maybe we can start by reaffirming the importance of learning for the sake of knowledge, in stark contrast to the commodifiction that has overtaken our educational system. No employer has ever asked me to analyze a Petrarchan sonnet, or expound on the intricacies of a Bach fugue, but I’m not sorry I have that knowledge, even if the latter meant suffering through the daily grind of musical scales on the piano as a child. The drudgery meant I might one day, in my teens, attempt Chopin. Granted, I didn’t become a professional musician; I didn’t ultimately have the chops. But my life is so much richer with Chopin in it.

I spent ten years training in jujitsu, yet I have yet to use my skills to defend myself from a real-world attack. So I guess those ten years were a waste, right? Wrong! The most important lessons I gleaned from martial arts had to do with learning to fail: getting my ass kicked and getting back up, again and again and again, until I mastered a given skill. Why wasn’t I willing to do the same for math?

All we’d end up teaching kids with Hacker’s strategy is avoidance. I was a master of avoidance. But learning to buckle down and do unpleasant things that don’t come easily to us prepares us for life. Consider this excellent response by Judy Bolton-Fasman, my fellow math-phobe, who learned geometry through the Khan Academy so she wouldn’t pass on her own math anxiety to her daughter:

    To make it to the desk is the first of many small victories. Then it’s time to confront the equation that has to be solved, the Latin paragraph that has to be translated, the essay to say what you intend to communicate. These intellectual conundrums don’t simply loom large, they haunt one. You have to do this work because it matters. Hacker, on the other hand, reinforces the ultimate phobic behavior in education: avoidance.

There’s a lot to be said for confronting fear and anxiety head-on, and fighting through a wall rather than throwing up one’s hands in defeat.

Finally, there is a deeper, uglier under-current to Hacker’s article. What he’s really saying is that we should know our place in society, accept that we’re just not smart enough and don’t need to worry our pretty little heads anymore about anything that might interfere with our enjoyment of American Idol. It’s not like we were ever going to amount to much anyway, amirite? As journalist/science fan Jesse Emspak observed on Twitter: “The argument isn’t about math. It’s really about whether anyone but the privileged should be educated.”

USC string theorist Nick Warner addressed this point in his own response to Hacker, eloquently articulating what is at stake:

    Algebra is not just the language of mathematical elites, it is one of the cornerstones by which we have emerged from a peasant society, ruled by the small elites sometimes capable of abstract thought, to become a complex, vibrant democracy. Algebra has helped us to rise beyond the simple understanding of immediate, tangible experiences and frame questions and look for the essential data that will give us deeper understanding.

    Only authoritarian and reactionary politicians benefit from a population for whom abstractions have no meaning. Such a population will be satisfied by sound bites and flag waving and will be placated by bread and circuses while their economy is subverted and their democracy implodes. Like mechanics problems in physics, the study of algebra, and the skills it develops, are not just critical to our long-term health individually but to our survival as a society.

This is a deeply personal issue for me. My father was the first member of his blue collar family to receive a college education, under the G.I. bill. Sure, he struggled at times to fill in the gaps in his background knowledge, but he persevered. He became a civil engineer, enabling him to give his children (including me) the kind of stable, middle-class upbringing he had lacked. And he made sure we got a college education, too, believing it to be the key to a better life.

Make no mistake: eliminating algebra for most students would end up disenfranchising them from any number of potential careers: physics, engineering, biology, chemistry, epidemiology, and psychology, as PZ points out. This matters because most of us have no idea what we want to do as a profession as teenagers. We have no idea what knowledge we’ll need. I didn’t even know science writing was an option. By the time we figure that out, more pften than not, it’s too late to remedy our lack of background knowledge.

Educating Rita is a charming comedy from 1983, about a British hairdresser named Rita (Julie Walters) who decides she wants something more from life. Her husband thinks she just needs a baby; instead, Rita signs up for private tutoring lessons with an alcoholic English professor, Frank (Michael Caine), who is steeped in cynicism and self-loathing.

It doesn’t start off well; she simply doesn’t have the cultural background and supportive framework to even begin to grasp what is expected of her. Her idea of literature is Harold Robbins and Jackie Collins, and she struggles mightily with E.M. Forster. Her first essay assignment: “Suggest ways to deal with the staging difficulties in a production of Ibsen’s Peer Gynt.” Her cheeky response: “Do it on the radio.”

But Rita presses on. She experiences some nasty growing pains. And in the end, she passes the university exam with distinction. The first question she sees when she turns over the exam? “Suggest ways to deal with the staging difficulties in a production of Ibsen’s Peer Gynt.” She could have written “Do it on the radio.” Frank would have dearly relished such an act. And there was once a time when sarcasm was her only option. But because of Frank, “I had a choice. I did the exam.” What he gave her, apart from an education, was a choice.

When we take away fundamental subjects like algebra because most students “will never need it,” we are, in essence, taking away their choice, before they know enough to make an informed decision. We are limiting them before they’ve even begun. Life doesn’t end in high school or college. Some of us, like me and Judy Bolton-Fasman, take longer to appreciate the cultural richness and significance of math. But we get there eventually. And when our interest rekindles later in life, we’re very grateful for the math we did take. Yes, including algebra.

Dear educators: I get that you’re frustrated, that you are under tremendous pressure to accomplish more with fewer and fewer resources. I get that you are underpaid and unappreciated. No doubt it is demoralizing to stare out at all those apathetic, unmotivated faces week after week, and hear the kneejerk whinging about how awful it is, this subject you love so much.

But please don’t give up on us. Not yet. We need algebra, whether we realize it or not, regardless of whether we use it on the job or not. Help us appreciate that there is more to education than mere job training, and that “culture” doesn’t just encompass art, literature, music, history and philosophy; it also includes math and science. Don’t let us get away with doing just enough to get by, of being less than our best. Make us realize that just because something is hard, and doesn’t come easily, that’s no reason just to give up and stop trying. Some things are supposed to be hard, and those hard things are worth doing.

Make us do the math. Some day, we’ll thank you.

[Jennifer Ouellette is a recovering English major turned science writer who loves to indulge her inner geek by finding quirky connections between physics, popular culture, and the world at large.]

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