I started thinking about this while planning a math workshop for 5th grade parents last year. I’ve been hosting these twice a year for long time now and they’re always slightly different. The main messages are the same:
- Math is accessible and fun.
- Computation is just a tiny part of a rich world of numbers and is not an end in itself.
- Struggle is the heart of problem solving; resist the urge to interrupt your child to show her the “easy” way.
- Don’t ever boast about how bad at math you are, or your family is, or how little you understand your child’s homework.
Each year, depending on what I’m thinking about, and what parents seem to want or need, these mornings are a little different. Last fall I started wondering about the verb we use with math. Why do we do math (and science)? Other do’s: we do laundry, do exercises, we do card tricks. We don’t do English or history – those have their own verbs: read, write, discuss, analyze. We make art and music. Why? And what is the thing we do when we do math?
Doing is for things that already exist. The only contribution you can make is to be obedient to the routine – ie, doing chores. Making is for new things. Even though the artistic process is full of borrowing (techniques, themes, and materials), we think of its product as unique, so we say making art, not doing art. Doing math implies that math exists already and the best we can do is to not screw it up. Many adults seem to feel this way – that is, weirdly cowed by the whole discipline of mathematics – like it’s looking down on them, waiting for them to show weakness.
In my experience, when people say, “do the math” what they actually mean is, “compute.” Or, more precisely, they mean: do the steps you were taught. Also, do them quickly and get the same answer that a calculator would get. It’s no wonder most people remember math class as being totally joyless (and by extension, think anyone teaching the subject must be a little off – maybe brilliant, maybe just defective). Most computing is more paint-by-numbers than math. Is this dog, who can bark out the correct answers to basic arithmetic, doing math?
Problem-solving is creative, not imitative, and it deserves an appropriately active verb. When a kid, through her own (often non-linear) efforts, realizes how something is true (ie, any whole number times an even number will always be even), she’s created a new idea, a new model. It doesn’t matter that someone else has seen it, proved it, published about it, because it feels like she made it. And didn’t she?
Students make sense of things, and make connections. I told the assembled 5th grade parents last year that we should set our sights higher than just doing the steps – what Jo Boaler calls “intellectual obedience,” in which the teacher offers a (great) explanation and lightbulbs go off around the room. Explaining feels so good – so productive. But I don’t really want my students to do as I do. I want them to have their own mathematical experience – wondering, predicting, testing, comparing, sketching, discussing, modeling, proving, and – ultimately – making a new idea, then another and another.