Thursday, December 1, 2011

Mathy Conversations with Students

I use many non-verbal cues in my classroom. Often, I'll use hand signals or facial expressions to convey my requests/commands to students quietly. The signals and expressions help me avoid interrupting the class just to address a single student when other students are already working.

Today, I gave a student a judgmental look to hint that he wasn't doing what he was supposed to be doing. Usually students just go back to work, but today he decided to point it out.

Jimmy: You always give me that look!
Me feigning innocence: What look?
Jimmy: The one where your eyebrows are like this (student signs the letter v with his hands).
Me acting clueless while giving a subtler version of the expression I gave him: Huh?
Jimmy: Yeah. Your eyebrows look like a V. It's like they're perpendicular.
Me giving my best perpendicular brows: That's impossible! I'll even take a picture and show you that they aren't perpendicular! Eyebrows can't be perpendicular.
Jill: Some girls will draw 90 degree eyebrows using a Sharpie!
Me signing a V on my forehead: Like a 90 degree unibrow?
Jill: No, they draw sharp corners for eyebrows like this (she signals a circumflex).
Me: Are you saying I have a continuous function for an eyebrow?
Jimmy: No, you don't have a unibrow, it's discontinuous.
Jill laughs: Yea. You have a removable discontinuity!
Me laughing at their insight: Because the limit exists! My eyebrows meet from the left and right and it's undefined in the middle.
Me sensing more students getting off-task: Alrighty, back to work!

A spontaneous opportunity like this doesn't come up often which is why I'm mad I missed an opportunity for review here. I should have asked "what would my eyebrows have to look like for there to be a non-removable discontinuity?" instead of hurrying the kids back to work. Maybe someone would have responded with "you just raise one eyebrow so they don't meet in the middle." I need to be more open to opportunities like this one. I love it when students can apply a concept learned in class in unexpected ways. I love the fact that I get to have these conversations at all. I love my job!

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