or, How to Call Out Mistakes without Trampling the Mistaken
It was the end of our first day on limits—a deep and slippery concept, the engine of calculus—when Melanie exclaimed, “Wait. Shouldn’t that limit be 4, not 6?”
Nope—it was 6. Melanie’s error suggested that she’d missed the lesson’s most basic truth, an idea that the class had spent the day paraphrasing, analyzing, and shouting in chorus. Talking one-on-one, I could have coached her through the misconception. But hers was a public declaration, in front of the whole room.
Even before the words had left Melanie’s mouth, I could hear the groan welling up among the students, murmured ridicule and the slapping of foreheads soon to follow. They all knew it. She didn’t. From Melanie’s blushing, you could read her self-esteem falling like a mercury thermometer.
And so I found myself confronting one of the teacher’s daily puzzles: what do you say when a student is wrong?
In the classroom—and beyond it—dealing with mistakes is delicate and crucial territory. At one extreme, we can deride errors, ridicule them, chase them out of town with a pitchfork—to the dismay of the poor kids who were trying their best.
At the other extreme, we risk coddling wrong statements, embracing them as “perspectives,” waiting in vain for the mistaken to see the light, and in the meantime allowing confusion to reign.
It’s no easy balance to strike, exposing falsehoods without steamrolling egos. To solve the predicament means tackling a deeper issue: what kind of dialogue, exactly, are we having? Which is primary: ideas, or the people voicing them?
Most of our daily conversations are centered on people. Consider the meandering path of dinner table chatter. It drifts from topic to topic, following tangents, pursuing loose connections. Questions are posed and never answered. Thoughts dissipate, half-articulated. A conversation, after all, is about sharing each other’s company. It’s a meal, not an interrogation.
Academic discussions differ. We’re hashing out ideas, each person pitching in to advance the conversation, not necessarily tabulating whose insight is whose. I say A; you say B; and we both think of C simultaneously. It’d be counterproductive to insist that your ideas deserve special status simply because they’re yours. The truth is indifferent to its speakers. Reason doesn’t notice who gives it voice.
In an academic dialogue, ideas ought to matter more than egos.
The challenge for teachers is that we’re having both conversations at once. Our students matter as people—we care about their thoughts, their feelings, their ambitions and fears. But ideas matter, too—we want to spread truth, to help our students master bodies of fact that past generations have painstakingly uncovered (and that textbook authors have clumsily compiled).
So how do we address wrong ideas, without trampling the people who espouse them? Here are four time-tested techniques that I’ve stolen from teachers far nimbler than I.
“That’s exactly the mistake I made when I first learned this material.” Or: “That’s a tricky point. In last year’s class, more than half of them made that error on the quiz.” Or the simplest: “That’s a really natural mistake to make.”
“It sounds like you’re generalizing from the pattern we saw earlier. But I’m not so sure those same results will apply here.” Even the most egregious mistakes have their roots in some identifiable thought process, and tracing that process helps students recognize that their ideas are not them. A train of thought can derail, and it doesn’t make the thinker any less worthy or intelligent.
“Hmm… go ahead and check that calculation again, then get back to me.” Private mistakes sting far less than public failures.
“Remember, mistakes are the essence of learning. When someone commits an error, we respectfully help them understand it, so that everybody can learn from it.” At its best, conversation is a beautiful thing—collaborative thinking, a shared brain. But students need to be taught the rules of the game.
With proper preparation, a class will rarely respond with the hostility they showed Melanie that day. But sometimes even a friendly pack can turn on one of its own.
“I’m glad you brought that up, Melanie,” I shouted over the groans. “It goes to show how tricky this transition is. You’ve all spent the last three years approaching graphs one way. This new perspective is the conceptual core of calculus, and the mental shift will take some time.”
The groans faded. Melanie nodded.