Wrong But Not Stupid

Math with Bad Drawings

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…

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