# A spoonful of transgression

September 17, 2013

I was just observing a third grade class learning/reviewing basic fraction to decimal conversion, and I overheard a great remark. A girl, reading a word problem, said to her table mate, “Jessica ate 6/10 of a cake?! She’s fat.”

There’s a part of me that hates comments like that, and a part that loves them.

I hate the comment because, you know: here’s more evidence of our appearance-obsessed culture getting into the heads of young girls, etc., etc. But I love it because this girl just showed that her relationship with this fraction goes beyond shading in the appropriate portion of the drawing. Six tenths means something to her. Maybe I’m not fully happy with what it means, but at least it’s not meaningless.

My first thought is, why don’t we have more ridiculous math story problems? People eating horrific quantities of food is funny. And what’s funny and horrible has a way of sticking in the mind. Why does Tom always eat 3/8 of a pizza?Why not 49/8? Or 149/8? Save us from the blandness of the unoffensive story problem.

(Of course, we don’t want an unsafe environment for kids. But flatlining all the content is clearly a mistake. Better to talk about issues when they come up.)

Or maybe they’re tiny pizzas, and eating 149/8 is absolutely natural, because each one has a diameter of 1 inch.  I now I don’t even now anymore: is that a lot, or a little? (A new game: I say the number of pizzas Tom ate as a fraction, and you tell me the biggest they could be without Tom suffering permanent damage.)

The point is, being able to tell when something is ridiculous or not is part of understanding math. And straying into the ridiculous is fun, and interesting.

An even more transgressive example happened to me when I was demo-ing an algebra lesson last spring in an all-girls eighth grade classroom. (Herbert Kohl, in On Teaching, remarks that those who work with middle schoolers need to have a high tolerance for the profane. I’ll find the exact quote later. Update: the quote is, “A lack of sexual prudery is almost a prerequisite for junior high school teachers.”) The lesson began with the old magic trick (try it if you haven’t seen it before):

think of a number
multiply by 2
subtract 2
divide by 2

And then I tell you what number you’re left with, which in this case is 1. (Ta-da!) The trick to it, which we got into, is to let x represent your original number, and keep track of the algebra. In one class, though, someone asked what would happen if you could replace the twos by threes, or fours. I set the class to play around with it, and see if they could predict how changing all the twos to another number would affect the final answer. Is there a pattern?

After they’d worked on it and I was bringing them together again, one group showed me how thoroughly they understood by suggesting we try:

think of a number
multiply by 70
subtract 70
divide by 70