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# A spoonful of transgression

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

I saw the answer coming halfway through, but had no choice but to complete the process on the board. It was every middle schooler’s giggly favorite, 69. And again, I hated it, and I loved it. Hated, because that was the last place I want to have anything even remotely sexual suggested to me. Loved, because these girls owned that problem, and they showed it by showing they could hit any target number they wanted. They picked the funniest one they knew.

When we’re trying to interest students, we have to respect what interest them. Reliable standbys are matters of power, death & danger, women & men. Transgressions lie perfectly at the intersection of these topics: they are instances of breaking rules with all the hilarity and danger that involves. I want a math classroom that is safe for all the students. But I don’t want one that’s sterile. A spoonful of transgression helps the math stay memorable.

Let me end with a plug for an underused but incredible educational resource that mines the ridiculous: check out Randall Munroe’s What If? Just look how he seamlessly interweaves the ridiculous and real issues of power into a readable math calculation as he investigates how many punch cards it would take to store all of Google’s data. Anyone else see the class project dying to happen here?

1. April

Haha. This is great! Thank you for an interesting yet fun idea. I couldn’t agree more, and I think your post definitely has a lot of truth to it.

2. EngineerMom

I had to comment, because of my most memorable math moments was centered right around that “spoonful of transgression.”

I was in 7th grade pre-algebra in a middle school held in a Cold War era building (complete with notices that it was a nuclear bomb shelter!). Our teacher sort of matched the school – almost white hair, slightly hunched man, elderly to our eyes.

He was teaching us about understanding what your answer means, not just the numbers, but how it relates to the “real world.” So he told us this story:

A mathematician and an engineer were kidnapped and brought to locked room. At their end of the room was a solid line. At the other end was a beautiful woman. They were told they could walk towards the woman, and that the room had a special property so that each step would take them half the distance they had remaining. So their first step would cover half the length of the room, the second step would then cover a quarter, and so on.

The mathematician gives up in despair and sits down. The engineer takes his first step. The mathematician says “why bother, you’ll never actually get all the way across the room!”

The engineer responds, “yes, but in just a few more steps, I’ll be close enough!”

The rest he left to our middle school imaginations.

That story has stuck with me since that class. It makes me giggle, but it also taught an important lesson about not getting lost in the numbers when you’re talking about things in the real world!

I ended up as a mechanical engineer, in part because that teacher made math interesting! Well, and he handed me 1984 to read when I ran out of math problems one day, and he started teaching us programming in Basic when we ran out of curriculum at the end of the year!

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