Archives for the month of: April, 2011

I took a page out of Jesse’s book today. My seniors shuffled zombie-like into AP Calc from AP Chem, clearly brain-dead. So I asked them to close their eyes, told them it was okay to fall asleep and that we’d wake them if they did. Then I asked them to imagine themselves in the most relaxing place they’ve ever been. Notice how it felt to be there, how their muscles felt, how the space between their eyebrows felt. What colors are there? What does it smell like? I reminded them that somehow they know the name of that place for them-maybe it’s real name, maybe not-and that anytime they want (in the middle of an AP test, for example), they can close their eyes and have the feeling they’re having right now. “Stay there for a little while, just enjoying what it feels like to be there, and when you’re ready, open your eyes.”

I don’t know how it affected them, but I felt better.

“Dude did you see that guy get shot? You live on that street, right?”
“Yeah, I saw him lying down.”
“You saw him get shot?”
“I didn’t see them, I saw the car. They shot him in the head.”
“Did you see the blood and everything?”
“The guy that got shot, he was my mom’s friend’s son. Mister do you want us to go get breakfast?”

I just nod. I’ve just been listening, not knowing how to get involved. By the time they’re back, they’re on to another topic. By lunch, I’m more worried about lesson planning than I am about that conversation.

It’s not like it’s everyday. This is day 143, and this is the first conversation like this I’ve heard this year. It can’t be the first they’ve had.

I don’t know that I’ll do anything any different because of it. But it seems somehow important that I heard it.

I’m tinkering with a longer post that considers the different directions or models I know about for what math is and what teaching it means, but in the mean time, Michael Lomuscio’s comment on Dan Meyer’s blog has done a lot of the spade work. He covers some ground that reminded me of Riley’s discussions of fluency, but to me the best snippet is this one:

A problem’s worth should be based on the level of creativity it demands from the student. Does the problem give them room to engage in the creative process of mathematics? If mathematics IS a creative process, then no math can be accomplished in the absence of creativity or creative potential. Are we handing students a blank canvas that they can express themselves on? Can they be proud of their work of art? Or, are we handing them a paint by numbers picture instantly killing any chance for creativity and robbing them of ownership and pride that they could, and should, feel in their work?

When they produce work without really absorbing it deeply, just getting the steps done without reflecting on them, I wish they had stopped me and said “We really don’t get this!” But when they don’t produce anything and tell me “We really don’t get this!”, I wish they would not give up, keep looking, keep going. It seems I may be trapping them in some conflicting expectations.

What’s in between being stopped cold, and getting someone (me, another student) to show you a procedure you can carry out mindlessly? Prior to having any understanding, what’s in between is to “try something”. What does that mean? When I solve math problems, it means executing one or another procedure on paper and then looking at the result to see if it seems to move me toward a solution.

Miguel Cura, one of my coaches (I am lucky to have a number of great coaches this year), pointed out that many of my students don’t know how to represent their guesses, conjectures, and trials-and-errors on paper. They know how to do guess-and-check by substituting values and simplifying, but rewriting expressions, substituting variables, factoring expressions and other techniques are all things they’ve learned to do when told, but not things that occur to them to try, just to see if the result looks like something they can move forward from.

Ben’s right: the problems are too hard at this stage. But not grasping the nature of the puzzle being posed is only half the reason. The other half is, I want them to keep looking, but “looking” at this stage usually means rewriting things many different ways without knowing in advance how it’s going to work out, and they are unfamiliar with that whole mode of exploration.

All the modeling that I’ve done, that other students have done, none of it is showing up on the tests (even from the students who did the modeling!) because they are still trying to memorize routes from A to B rather than wandering around, getting oriented to landmarks, so when they have to get from C to B or from B back to A they can do it because they know the neighborhood.

It’s not the curriculum: CPM is good about this, even explicit about it. It’s just taken me this long to figure out that this is what I need to use these materials to teach them how to do.


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