Circle Circe
rotating mentor — narrates the problem then deliberately disappears
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The kids at Tama's house did not, at first, understand that Circle Circe was supposed to disappear.
They had set up the iPad in the middle of the kitchen table. Tama, who was eleven, was in charge of the iPad because it was her birthday party and because she had been to a math circle once at the library and knew, vaguely, how it worked. Her cousin Joon, who was twelve, sat across from her. Their friends Mira and Bex, both ten, took the other two sides of the table. The kitchen smelled like the cake that was still cooling on the counter.
"Okay," Tama said, opening the app. "We're going to do a Circle. Circle Circe is going to give us a problem."
Joon, who was new to all of this, frowned. "Who's Circle Circe?"
"She's the lady. She tells us the problem and then... I don't actually know what happens next. She did something weird the last time."
On the screen, Circle Circe appeared. She was tall and thin with long dark hair tied back loosely, and she was wearing a deep blue scarf that swept down past her shoulders. She had the kind of smile that did not perform itself.
"Welcome to your Circle," she said, looking at the four of them through the screen. "I have a problem for you today. It is a problem about counting. Specifically: how many ways can you arrange four kids around a table?"
The four of them looked at each other.
"That's the problem?" Bex said. "That seems easy."
"It might be. It might not be," Circle Circe said. "I'm going to be here for the next minute. After that, I'll be quiet for a while. While I'm quiet, you'll talk to each other. When you've worked out an answer that all four of you agree on, tap the bell, and I'll come back."
Mira said, "Wait — you're not staying?"
"I'm staying. I'm just going to be quiet. Quiet is also a kind of staying."
She smiled — small, deliberate — and then a little timer appeared in the corner of the screen and her face faded to a dim outline. She was still there. She just wasn't speaking.
The four of them looked at the screen. Then at each other.
There was a strange silence. The kind that happens when a grown-up leaves a room and the kids realize, slowly, that they are now the people in charge.
"Okay," Tama said. "Um. Joon, you want to go first?"
Tama had been to one circle before, at the library, when she was nine. She remembered most of it as a blur. She remembered there had been a woman who introduced a problem and then went very quiet, and she remembered being annoyed that the woman would not just tell them the answer. She had been nine. She had wanted the answer.
But what she remembered most, looking back, was that the four kids at her circle had eventually started talking to each other, and that the talking had gone better than she had expected. One kid had been quiet at first. Another had been bossy. A third had drawn a picture that everyone else had argued with. Eventually — and Tama could not remember exactly when — they had figured out the answer together. And then Circle Circe had come back on the screen and said, "Tell me what you figured out."
The thing Tama remembered, after all this time, was that the moment Circle Circe came back, the kid who had been quiet at first had been the one who explained the answer. The bossy kid had let it happen. The picture-drawer had added one extra detail at the end.
Tama had not understood any of that, at age nine. She had just gone home and told her mother that the woman in the app had been weird.
Now, at age eleven, in her own kitchen, with the cake cooling on the counter and her cousin Joon staring at her expectantly, Tama suddenly understood what Circle Circe had been doing.
She was supposed to leave so the kids could become the kids who solved it.
"Joon," Tama said. "Go first."
The four of them worked for almost half an hour.
Joon started by listing arrangements. Mira started by drawing them. Bex started by counting in a way that did not work and then changing strategies twice. Tama, who had been to a circle before, did not try to take over. She tried instead to do what she had seen Circle Circe do.
When Joon's voice got loud, Tama got quiet.
When Mira got stuck, Tama asked Mira what she had drawn so far.
When Bex changed strategies, Tama said, "Wait — what made you change?" and Bex explained, and the explanation turned out to be useful.
There were two moments where everyone agreed and then one moment where everyone disagreed and one long moment where Bex sat with her hands over her face thinking very hard. There was also one moment where the cake got accidentally bumped and they all stopped to make sure it was still cooling correctly.
Eventually they arrived at an answer they all believed.
The answer was twenty-four.
Tama tapped the bell.
Circle Circe reappeared.
"Tell me what you figured out," she said.
There was a small pause. Three of the kids looked at Bex.
Bex, who had spent most of the half-hour quiet, said, "It's twenty-four. There are four kids. For the first chair you can pick any of four kids. For the second, three. For the third, two. For the last, one. Four times three times two times one. Twenty-four."
Circle Circe nodded.
"What did each of you do?"
Joon said, "I listed."
Mira said, "I drew."
Bex said, "I counted, and I was wrong, and then I switched."
Tama said, "I... I think I tried to make sure everyone had a turn."
Circle Circe smiled — small, deliberate, real.
"That is also math," she said. "That is the math of how four people figure something out together. Now I am going to give you a harder problem, if you want. Or you can stop. Your circle. Your call."
The four of them looked at each other.
"Harder," Joon said.
"Harder," Mira said.
"Harder," Bex said.
"Harder," Tama said.
Circle Circe smiled again and then she faded back to a dim outline.
The kids leaned in over the table.
The MathCircle ensemble
Circle Circe is part of MathCircle's distributed-narrative cast. Each character embodies a different curricular primitive; together they teach the full subject.