She asked, "Did you just take a picture of the whiteboard?"

Yeah (little defensively).

"Is that your writing topic today, a word problem?"

Yeah. Well, no. Not really a word problem. A math problem.

"Well, you shouldn't have any trouble writing about that. You love math."

(Did she just roll her eyes?)

When the facilitator of a family math group adopts an exploratory and holistic approach to math, what changes occur in parents’ attitudes to math and to helping their children with math learning?
Kate Nonsuch
Family Math Groups: An Exploration of Content and Style (pdf)

I was caught right away by Kate's question about how a facilitator's approach might change learners' attitudes toward mathematics. It resonated with my own musings about how learner views of math are influenced by the spoken and unspoken views of facilitators. I didn't much care for math in public school. But now... well, see for yourself.

My day started with Kate's paper (a quick, superficial reading) and then, in the mid-morning lull, I went back to The Problem.

The Problem popped up two years ago when I tried making sense of the Chinese Remainder Theorem.

Imagine you have a box of stones. If you remove them two at a time, there is one left over at the end. If you remove them three at a time, everything works out evenly. If you remove them four at a time, you end up with three left over. The question is, "How many stones are in the box?" The theory is that you can do a bit of math magic and find the result.

Now, frankly, I've lost faith in this whole Asian Left-Overs thingy. I don't believe it works. But I'm still curious about what might work.

So, anyway, for two years, a couple a times a month, I've been writing algebra-like things on the whiteboard and interrupting learners with my vaguely frustrated mumblings.

Today I discovered an error I've been making (for two years!) and got a bit excited about it. I also had a new thought and uncovered a new fact....

Are you ready? Here it is: the possible solutions are separated by 12.

See? Yeah! I know! That's what I said. Freaky, eh? And how could you guess? What does "12" have to do with

Ooo... I just thought of something else while typing this. I do know what "2" and "3" and "4" have in common with each other and "12". Twelve is the common denominator-thingy for those three numbers.

K. I'm going to have to cut this post short.

um.. Bye.

Edit: Well... I didn't get much further on The Problem. But I did do (again) something I wanted to do - model authentic curiousity about and enjoyment with math. I really believe I can't help learners unless I'm a learner as well. And I also think it's important to stand up to those oft-heard complaints that mathematics is stupid or too hard or pointless or scary. Math is swell. It's orderly and lovely and fun. Don't believe it? Come do some math with me. :)


Kate Nonesuch said...

Well, I read the problem and was intrigued. I looked at the photo of your whiteboard, but immediately looked away--I couldn't understand what you had written there, and I felt a little nauseous at the thought that there was some complex math thinking going on and I didn't get it.
So I took two or three stabs at solving the problem, separated by periods of working on something quite different, and finally talked myself through to some sort of solution, although I couldn't get to stating it algebraically.
Then I went back to your whiteboard, and suddenly, it made sense. I could see your equations separately, and understood where they came from. I could do a little subtracting to see what you meant by the recurring difference of twelve. There seemed to be more white space on the white board. No more nausea.
Thanks for the insight into how my feelings/mind work together.

Wendell said...


There's a lot of richness there in your comment.

Maybe we can't walk into somebody else's figurings. Maybe can't be taught math.

Maybe we can only learn it on our own, "separated by periods of working on something else."

Maybe too much being-taught math impairs our vision and makes us physically ill....

... or sends us into long day-dreams where we're Tom Swift fighting space aliens (which is how I sent math classes grades 6 through 12).