Should math class be hard?

A few weeks ago, I’d have deemed this question pointless. Less a real question than a kind of vague hand gesture.

But I just read a great book that shifted my thinking. [EDIT: I forgot to say which book! It’s The New Math: A Political History, by Christopher Phillips.] Now, rather than a vague hand gesture, I see the hard/easy question as a quite precise and pointed gesture. (No, not that gesture.) Specifically, the question points toward another, bigger question:

What is math class really about?

One possibility: Is math education for cultivating a general excellence of thought? For building the capacity to reason logically? For sharpening the mind into an all-purpose tool?

In that case, it should probably be as hard as possible. The mind, like a pencil, needs friction to grow sharper. Not too much friction, or you’ll break the pencil (and the metaphor), but all else being equal, a good challenge is a good thing.

Or, another possibility: is math education for imparting a specific set of useful skills? Is it about data literacy, arithmetical know-how, and algebraic fluency?

In that case, it should be as easy as possible. Break it down into itty-bitty tasks, and practice each one until you have it cold. Math ed ought to be like drivers’ ed: so blindingly simple that any citizen can acquire these basic, necessary skills.

A simplified contrast, to be sure. But for me, it’s a surprising inversion of my usual thinking.

I most relish the challenges of mathematics when I’m in “traditionalist” mode, when I feel real faith in the skills and methods that constitute the historical discipline. (This isn’t my usual operating mode, but hey, I enjoy the chain rule as much as anyone.)

But wait. If manipulating polynomials is truly a human good, shouldn’t I want to make it easy? Shouldn’t Iwant algebraic literacy to become like English literacy, with 99% of kids achieving it?

In the moments when I’m most indulgent of “hard,” I perhaps ought to be pursuing “easy.”

Meanwhile, I’m wariest of math feeling too hard when I’m in “progressive” mode, envisioning a human-centered math education. On these days, I tend to think that math is not about a specific skill set, but expanding our intellectual toolkit and enhancing our ability to reason.

But if this is my priority, why should I be bothered if math is painful or unpleasant? Sure, too much challenge will drive my students away. But if my task is improving minds, then aren’t hard days a good thing?

Of course, “hard” is not one thing—its definition varies student to student, task to task, moment to moment. There’s no “difficulty” dial I can turn. Still, these thoughts leave me with a strange conclusion that I’m struggling to absorb.

When math education is about the math, I should be striving to make it easy. And when math education is about the education, I shouldn’t shy away from making it hard.