### Out of the mouths of babes

The student I’m tutoring, explaining why he didn’t do the last five questions of the homework, each of which defined a new term, and then required students to investigate how it applied to a few given functions:

These questions seem like they should have been in the lesson, not the homework. It seems like they’re trying to

teachme somethingnew.

The result of this unfortunate run-in with new material *in the homework*, of all places: we took a half hour break from going over new mathematical content, to spend on developing the skill of reading mathematics. Teaching this is easier than it sounds, when you’re starting from zero and dealing with straightforward material: today’s lesson consisted of me asking him to read the definition, and then following up with such prompts as “ok, so now what is the question asking?”, “What should we do?”, and “How can we do that?”, *all of which he answered correctly*. Not bad for someone who reaches for his calculator every time he is required to add one single-digit number to another.

“You did all of that by yourself,” I pointed out when we were finished. “Why couldn’t you do it last night?”

“You were here this time,” he replied.

“Yes, and I prompted you,” I agreed, “but the questions I asked you weren’t the slightest bit leading. I just told you to read the question, and then I asked you what the question was asking, and how to go about answering it. Basically - I asked you the stuff that the *question itself* is asking you to do. And you did that all - correctly.”

He thought for a minute. “I guess,” he said. He then paused, and looked up as my statement registered: “So I’m supposed to be doing that whenever I see a question I don’t know how to do?”