Not a post about measuring things. A post about the book Measurement by Paul Lockhart. I love this page…it’s from page 15 of the edition I own.

This is the kind of thing you have to do as a mathematician: try things. Will they work? Will they yield useful information? Usually not. But you can’t just sit there staring at some shapes or numbers. Try anything and everything. As you do more math, your intuition and your instincts will sharpen, and your ideas will get better. How do you know which ideas to try? You don’t. You just have to guess. Experienced mathematicians have a great deal of sensitivity to structure, and so our guesses are more likely to be right, but we still have to guess. So guess.

I wish for this to be an idea that my (and all) students would have about maths.

“If you want to paint a picture from your heart, there is no ‘answer painting’ on the back of the canvas.”

I had a discussion with my mother the other day, and it went something like this:

Mother: How would you fix math in school?

Me: I don’t know. But I think it’s reversed. Kids learn the boring and mundane stuff like memorizing multiplication algorithms and how to do long division and do worksheets and worksheets during “math time” in elementary school. They learn that all math is, is manually doing the work that a calculator can do; and when they realize this, they feel like they don’t need or don’t like math because it’s not a subject on its own. It’s useful for other things, they are told. But who cares? When the students get curious, they are told there’s more interesting parts of math, but they need a foundation first. Learn the boring stuff now. Gain a hatred for math now. Think that math is all about doing arithmetic now. The interesting stuff will come later, when the kids will all already discount it as something for nerds. Then laugh and ask “when will I use this in real life?” Then laugh again as the teacher struggles. There are a lot of ways to answer this question…I’ve gone with:

You won’t. But you need to pass this class to get through high school.

(incidentally realized this was not the best option. Never used that more than once or twice. That’s it Andrew, feed the hatred…)

Well it depends what you want to do.

Ok — leading to further questions and further digression.

You’re right, maybe you won’t. But when will you need to know the sonnets of Shakespeare or know the states and capitals? You can look them up just as easily as you can use a calculator.

Fantastic. Lets get into a war of school subjects….

Does it HAVE to be useful? Can’t math just be a subject for the sake of being a subject? Interesting to learn?

My personal favorite there. That’s what I generally stick to. Maybe this isn’t the most interesting to the students, but it is the most personally satisfying to me.

Mother: okay, so what can be done about that?

Me: I don’t know. Don’t hand kids multiplication tables to memorize. Hand them pictures. Hand them basic word problems. Read to them and ask them questions. Give them calculators. If they keep pressing 6 times 4 long enough, they’ll realize that it’s 24 and memorize because it’s convenient for them, not because there’s a test on it on Tuesday.

Mother: How do you measure how well they’re doing?

Me: (again) I don’t know. Give a project. Ask questions. Assess on the quality of the work, not the quality of the answer. On the descriptions they give you. On how well they communicate their thoughts to you.

Mother: Would that really be a math teacher’s job?

Me: Maybe we need to rethink what a math teacher is.

**end discussion (which I now realize was more of a soliloquy.)

So that’s it. Sure, I made it a bit more formal for the sake of typing instead of just conversation while driving to get batteries for a loupe. I don’t know if it was useful for me to think about or not, or if I just got frustrated because by the time the students are in high school, they have such a concrete attitude towards math that I have to spend my time convincing them it’s useful when in reality I just want to show them it’s interesting. As the year comes to an end, maybe I’ll focus my energies on getting ready for next year. Stop asking the “how much paint will she need to buy to cover this…” questions, and abstract it to “we have a rectangle. What’s the area? You want to know why anyone would ever want to know this? Here’s a computer. Figure it out. Then write a paragraph telling me why or when area is useful.”

Ugh…frustrating, stressful, time-consuming? Yes.

Thought-provoking? Absolutely. So I wouldn’t trade it for anything.