Ricky update

Wednesday, I had a tutoring session with Ricky, the 8th grader. The topic was limits.

I've learned to look at all of his worksheets first, to see what they're really covering, since their idea of covering a topic is very different from mine. He had three worksheets, all of them with odd little exercises on them that went something like this: "Get a bowl of Hershey's Kisses and take half the Kisses out of the bowl. Keep taking half of the Kisses out of the bowl. When you get down to only one Kiss, cut it in half and take out half. Will you ever empty the bowl? Why or why not?"

Uhm, okay. I see where this is supposed to go, but couldn't they at least give a definition? Even if they wanted to use induction, how about a definition at the end of the third worksheet?

Keep in mind that they haven't done Cartesian geometry yet. No y = mx + b. It's kind of hard to talk about limits in terms of math -- particularly to an 8th grader -- without being able to use a graph as an exemplar. Try it.

This is the first time he has questioned the curriculum. Not directly, but he's been remarkably willing to led the course lead him down the garden path, without questioning where the class is headed, until Wednesday. He appropriately asked me what limits were for.

"Trigonometry. Calculus. Engineering."

"What are we doing to do with them?"

"You'll have to ask your teacher."

And indeed, the boy had a point: What is an 8th grade class going to do with limits?

"You don't know?"

"I have no idea."

"Then why are we doing this?"

Well, one may well wonder. And I understand his mystification. Limits, as they were covering them, don't generate numbers, or seem to an 8th grader to have much to do with mathematics.

It was the following week that Ricky told me what had happened in class -- and I had to laugh a little (silently, of course). To demonstrate limits, the teacher had had all of the students stand on one side of the room. She had then had half of them move to the other side of the room, over and over again.

There is a problem with using discrete objects to demonstrate limits (the same problem was in the Hershey Kiss exercise): You eventually get down to one. So when they got down to one student, Ricky said the teacher told them, "Never mind, let's do this example instead."

When you're teaching, you really need to think things out before you run them in the classroom. Been there, done that.

Next up that week was quadratic equations. To review, let's look at the preceding list of topics: Division, graphs (pie, bar, column, and area, not Cartesian), fractions, limits, quadratic equations. By the time I started this gig, they had already "done" linear equations -- except that they hadn't really, and we covered it.

For the first time, Ricky had an amnesia attack. I'm used to this. Teaching in a two-semester course sequence, you see lots of students the second semester you had the first who seem to have forgotten nearly everything you did the previous semester. But Ricky had a complete blackout. He couldn't solve 50 = 25 + x.

So I gently nudged him by doing it for him, step by step, then writing down another for him to do. Again, blackout.

I have a son, and I also have three younger brothers (well, had: my youngest brother died a couple of years ago). I know what a frustrated adolescent looks like, and he was getting frustrated. I backed off, and suggested I come back the next evening, and in the meantime, told him I'd email him some stuff he could do before I came back to refresh his memory of linear equations.

That worked pretty well, but he's still frustrated, and I can't blame him. Again, I got, "Why can't my teacher explain it like this?" and I have no (ethical) answer to that question, which doesn't help his frustration. He wants me to validate it, and it really wouldn't be appropriate for me to do so, though he's right. The problem is that he's turning his frustration not on the class or his teacher, but on math in general, and that's not good because he's very sharp, and he picks it up very quickly.

So who knows. Maybe I'll be turning into a therapist next. Sigh.