Starting Math Circle

It was to be the first Math Circle, and Vera didn’t want to miss the wonderful opportunity to mock me. She was at our house half an hour before we were supposed to start. And she brought her grandchildren too.

"You are nervous, young boy!" she said.

"I am not young!" I said.

"And you are trembling," she added.

"Vera, you are terrible."

"Tell me, what are you going to teach them?"

"You’ll see."

"You know," said Vera. "I had a wonderful teacher in fourth grade. He taught us how to multiply using a rectangle."

"That’s the right way," I said, excited. "Rows and columns. Or towers. Anything that kids can visualize. I would love to see your notebooks, Vera!"

"Not possible. Only God knows where they ended."

Then the other kids arrived – in a stampede-like fashion. Their fathers, my friends (and yes, fachidiots), left them in front of the house and sped away. They didn’t want to have anything to do with a house full of kids. Well, the kids knew our home, and they were soon jumping up and down all over the place.

"These kids are going to listen to you?" asked Vera. But it was not really a question.

And the same thought crossed my mind. How do you persuade kids to stop running about and do mathematics instead? What a fool I am.

Somehow I managed to maneuver them into what was supposed to be a classroom. And banged the door shut. Vesna, my second-born, escaped almost immediately. Three others followed her. And the remaining two followed right after.

I spent the next ten minutes trying to get them in the classroom again. Once we were all there, I didn’t want to lose any more time. I gave each kid a shape cut out of paper – triangles for three-year-olds, pentagons for five, hexagons for six, and a heptagon for the seven-year-old. I asked them why these particular shapes, and they knew the correct answer – it was about their age.

I asked them to draw something they liked on their shapes.

We counted the edges and marked them as follows: | for 1, || for 2, ||| for 3, ||| | for 4, ||| || for 5, ||| ||| for 6, and ||| ||| | for 7.

A digital recreation of the oldest boy’s shape would be something like this:

Then I gave them cotton swabs.

"Yeah," I said. "We’re going to clean our ears."

I was joking. But they were looking at me and waiting for instructions on how to clean their ears.

"No, no!" I exclaimed. "It was a joke. Let’s just construct some shapes. Shapes that present your age."

This was more difficult than expected. I helped them construct a triangle. And a rectangle. Things became easier with a pentagon and hexagon. And finally, a heptagon.

But how would they present a one-year-old kid? Or a two-year-old? I wanted them to figure out that we couldn’t construct the shapes with only one or two swabs. But, of course, their reasoning went in totally different directions. Various suggestions came out – like breaking up or bending the swabs.

For the grand finale, we constructed a shape with 35 edges. When ten or twelve swabs were laid out, the kids realized they would need a much bigger thing to use all 35 swabs. It started to look like a circle. They widened the constellation. And then they needed to do it again. And again.

"That’s my age, kids," I said.

You might expect they said something like: "Don’t worry. That’s really not that old!"

But no. They were astounded by how ancient I was.

"So, why does my shape look like a circle?" I asked.

A vicious debate started. But soon enough, Vera interrupted.

"It’s time, young boy," she said. "Half an hour has passed."