A nearly-verbatim dialogue, in honor of one of the hardest-working students I’ve ever taught.
Student: Can you explain this problem to me?
Me: Sure, the idea is… Wait. You got it right.
Student: But I don’t feel like I did. I feel like I guessed.
Me: Well, explain how you got your answer.
(He proceeds to give a perfect explanation of the problem, justifying every detail.)
Me: See? You understand it.
Student: No, I just guessed.
Me: You “guessed” a flawless, conceptually motivated solution to the problem?
Student: Yes. You have to explain it to me.
Me: I mean… okay…
(I proceed to parrot back his explanation to him, virtually word for word.)
Student: Ah, thanks. That helps.