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.

This is such an important topic – thank you for blogging about it, and much more eloquently than I ever could. I love the distinction of “doing” vs. “making” math. I often talk to my students about “owning their” math when they want me to “just tell us how to do it,” but I think that I’m going to use your terminology from now on – it really gets to the heart of the matter.

Ownership is key. It’s like “making sense” – it’s the only way to have sense. You can’t get around it, there’s no other way than to make your own.

This is spot on. Your messages to parents are so succinct and say so much that is important. Looking forward to reading more!

Thanks for reading. Succinctness with parents has been a product of trial and error. I get a little evangelical about math and things get rambling – so I try to stick to my cue cards when possible. :)

Interesting that you and I would agree on so much (I think) when the title of my blog is “Doing Mathematics.” I believe that part of the issue here is in the predominant definition of mathematics in our society. As you mention, it is viewed as something existing outside of the individual and that, through schooling, students will know “the” mathematics.

But, much like you mention, the construction of new ideas and mental models is a personal (and perhaps subjective) endeavor. Doing mathematics is to create these mental models; to conjecture, test, justify, revise, etc. I happen to think that as long as having students know “the” mathematics (the one outlined by standards) takes priority over merely engaging students in being mathematical together, “doing” will mostly be about calculation as you have described it here.

Great post…thanks!

Great post! I am going to bookmark it, read it again later, and reflect on it further. I love this topic, and I hope that I can add some small piece of wisdom to it at some point.

I loved your angle-measure-discovery post as well. I never would have guessed that I (a high school teacher) would be interested in the blog of a 5th grade teacher, but you’re on my Google Reader list now. :-)

Thanks, and keep up the great work!