A recent article in Inside Higher Ed brought to mind a couple of tense interactions I’ve had with the chairs of math departments around the CSU. This is unusual because, in the words of one member, “the math chairs are the most liberal minded broad based group of mathematicians you will be likely to deal with.” This is true. Consistently they’ve gone out of the way to deal collegially with everyone, even those they feel badgered by. And they’ve followed through with genuine innovation.
But lately they’ve had two compelling reasons to talk to me, a pair of documents that question which topics from intermediate algebra we expect every college graduate to know. We’ve traditionally set the bar high, to include topics like logarithmic equations, factoring quadratics, and what kind of formulas turn into hyperbolas when you graph them.
The problem is that setting the bar at this height has kept many students from finishing college who otherwise would. So people all over the country, including those in the CSU, want to revisit the standing standards.
I like math, even though I’m not a mathematician. But liking it is one thing, and using it is another. In a recent and very funny essay in Harper’s Magazine called “Wrong Answer,” Nicholson Baker ridicules the math hawks like Education Secretary Arne Duncan, who insist that everyone needs all of those skills or shouldn’t get out of high school, let alone college. My favorite part of the essay, as it reviews a recently released textbook:
Then you learn something more about points of discontinuity: they can be either removable or non-removable. For instance: “The graph of y=[(x + 3)(x + 2)]/(x+2) has a removable discontinuity at x = −2.” Simple as pie on a parsonage table.
To reinforce your learning—to make it really bake itself in your mind, so that you’ll be able to call upon it in times of quantitative uncertainty in the years to come—there are some exercises to do.
The lacerating sarcasm between those dashes is to me an amazing piece of writing. There’s no doubt in Baker’s mind, nor presumably in his readers’, that those moments of quantitative uncertainty won’t come. We will never draw on this skill.
When I first read this essay I thought he was right. As it happens, I do understand why there would be a discontinuity at -2: it’s because you can’t divide anything by zero. But I wouldn’t dream of drawing on such skills “in times of quantitative uncertainty.”
So then why is it the litmus test for holding a college degree?
Or conversely, how ripped off would I feel if I couldn’t follow this excerpt? Would I consider my alma mater a diploma mill? Would you?
But the more I thought about his essay, the less distracted I was by the good writing. The fact is, if I couldn’t read that equation, I would feel short-changed.
There’s a problem here, and it bleeds into disciplines other than math. We may have used the manipulation of abstract symbols so mocked by Baker as a proxy for what we really mean by quantitative reasoning. It’s a little like making people memorize state capitals to stand for a sense of history. Or conduct “cookbook” chemistry experiments with foregone conclusions, to promote scientific curiosity. We know these aren’t the same things; they’re just easier to deliver and test.
But they also trivialize what we’re really after, and so leave us vulnerable to skeptics.
The policy documents I wrote for the CSU authorize alternate approaches to math curriculum, ones that would be likelier to please Nicholson Baker than Arne Duncan. They lower the bar, for a subset of students on a pilot basis, and then monitor their performance in subsequent coursework.
Educators quake at this. There are a handful of professions where your assertion of quality is essentially all that you sell. Jewelers for one, vintners for another, because – as with higher education – lay buyers lack the expertise to assess the worth of their wares. So outsiders pay you for informed, honest judgment. Fudge the facts and you degrade the profession, and eventually blow the gig.
So when the chairs of the CSU math departments see compromises like this, they are put in an impossible situation. I think consciously or not, they feel forced to misrepresent the value of the degree. Their response is deep and visceral. And it should be.
But visceral doesn’t mean right. (Consider our grandparents’ take on gay marriage.) Their long-held assumption about what a degree means isn’t enough to make it so, even though it once was.
Instead, we need to get closer to defining, developing, and assessing the real learning that we care about. If we want our graduates to be confident modeling a world that includes unknown quantities, then we should make it clearer that intermediate algebra does that. And if we can’t make it clearer, then intermediate algebra will face continued assault.
The rationale of “learn it because I’m an expert who tells you to” just isn’t working anymore, and shouldn’t. The public is right to expect better answers. Coming up with those is the urgent work of us all, and not just the math chairs.
Because in this coal mine, they’re the canaries.