Except for the final grades, I’ve just wrapped up teaching six weeks of credit recovery for Freshman Algebra. It’s tough enough packing nine months’ of material into six weeks, but consider these are the students who didn’t do well enough the first time to get a passing grade (in this case, a C or higher), thus making the challenge even greater.
So, naturally, it makes sense that I’d have an opinion on this weekend’s piece in the New York Times, asking Is Algebra Necessary? After all, I’ve been dealing first hand with the very students the article is discussing, students who are struggling with algebra and facing the possibility that they won’t graduate from high school if they can’t somehow master it just long enough to get that passing grade.
I’ve been mulling this over for a few days. I didn’t want to knee-jerk out a response, because this is tough to say. Sure, I could talk about the importance of “algebraic thinking”–whatever that is. Or I could talk about the importance of algebra in practical fields; I’m willing to bet that many, many people who claim that they’ve never used algebra since graduation day use Microsoft Excel’s formulas on a regular, if not daily, basis. Of course, there’s the usual business about how students in the United States are lagging behind the rest of the world in mathematics scores, which is why it’s so important for us to increase the quality and quantity of mathematics education, but that would be begging the question.
And I think that last bit is rather a big part of Hacker’s point: We act like the fields of high school mathematics that we have selected as core topics are necessary because we’ve decided they are, but have we, either as a national culture or as a global community, really discussed why we’ve selected those specific fields? Mathematics is important, no doubt. But is it necessary? Or have we overdone it?
There are a lot of things mixed up here. First off, do students struggle with algebra, or do students struggle with the way that algebra is taught? Hacker is begging a question of his own by assuming that algebra as it is taught in public schools is generally taught properly or well. On a certain level, it’s like criticizing socialism because the Soviets made such a hack of it. Socialism wasn’t to blame for the totalitarian mess that was northern Asia and eastern Europe; that was greed, power, and ineptitude. I don’t think the public school system messes up algebra nearly as much as the Soviets messed up socialism, but at the same time, it’s a fair rap to say that many high school students sit through several years of classes called algebra without even understanding what the subject is about, through the fault of instructors who don’t properly articulate it.
Secondly, what is necessary in public education? Literacy is important, sure. There’s not a career out there where people won’t find themselves reading something from time to time. NCLB and other recent education reform policies have upped the ante by requiring not just English teachers but all teachers to promote appropriate reading, and in all cases except perhaps PE this makes sense; people in industrial careers, for instance, will find themselves reading instruction manuals, something that Poe and Shakespeare aren’t going to be immediately applicable towards.
Other than literacy, what is necessary?
My students tell me that when they become the famous rappers, artists, and so forth that they’re destined to become (and I hope some of them do), they’ll have accountants to work out their finances. Even so, basic number sense at least approaches the realm of necessary, if it doesn’t live there.
Science is cool and engages students, but for someone who wonders aloud whether they’ll ever use the Pythagorean Theorem outside of school, I offer: Will you ever use the classification of “noble gas” outside of school? Maybe you’ll have reason to remember, “Do as you oughta, add acid to water,” but most of the science we teach in high school is only immediately relevant to career fields in that area.
There’s something to be said for a nuanced understanding of political and general world history to apply to the current state of affairs and to extrapolate into the future (as George Santayana writes, “Those who cannot remember the past are condemned to repeat it.”), but public school history often suffers even more from the cookbook “memorize this” weakness than mathematics does. Foreign language study, sociology, the arts, and music broaden our horizons. Especially in this world of increasing globalization, that’s important. But Hacker has set a high bar in using the word “necessary”.
On the other hand, a fair question is why Hacker has chosen to select mathematics for his questioning. I love English; I have an English endorsement. But why do we as a culture dwell more on the necessity of the Pythagorean Theorem than on the necessity of reading Jane Austen? The average Joe on the manufacturing line may well never refer to Pythagoras, but I can guarantee that he’ll definitely never refer to Austen (at least, not as part of his official duties).
For me, what this discussion comes down to is not whether algebra is necessary, whether it will provide valuable tools for students regardless of their future careers, and so forth, which are indeed important subjects. What it comes down to is: Why pick on math? And how do we teachers of mathematics improve the PR of our field so that people stop even asking whether it’s necessary. Students generally find science fun, at least the oogie bits. Students find English distracting enough, even if grammar is a bit of an arduous haul. Students are somewhat bored by history, but muddle through. Foreign language, music, arts, band, PE, sports, psychology, and so on… I don’t hear a lot of complaints from students.
And then… mathematics. The necessary evil, and if Hacker would have his way, the not-necessary evil. The rote memorization of elementary school is replaced by impenetrable abstract formulas in algebra and geometric proofs, wherein students are expected to guess which of the obvious steps the book or instructor wants them to write down. Mathematics is beautiful, but somehow through whatever social pressures we’ve allowed ourselves to apply, we’ve made it drudgery. That’s our fault, and our doing. If we want articles like Hacker’s to go away or at least sound silly, we need to find a way to make the beauty of mathematics shine through.
I don’t have answers quite yet. It would be hubris in the extreme for me to pretend that I do. I acknowledge the problem; isn’t that the first step?