People working together to solve a problem.
This photo tells half the story of today’s Math Circle: people working together to solve a problem. The question was whether the famous “Gas Water Electricity" problem is solvable or impossible. Some students first tried to find loopholes in the problem to make it easily solvable (go through the house, get the households to cooperate, spank the uncooperative ones if necessary). Most of the group, however, agreed with X that we should use a pure (vs. applied) mathematical approach, with all its limitations, to preserve the challenge and the fun. Everyone had something to say.
“Can it be curved?” (D)
“Make a graph, make a graph, make a graph!” (N)
“I’m just drawing random things and confusing myself.”
“Wait, K’s right, you can’t draw a line under.”
“Yes, that would work, but I need M and K’s drawing.” (G)
“Tell us if there’s a way!”
“It’s easier when you can erase it.” (A)
“Let’s do it with straight lines and sharp curves. This may just be the solution. Well, maybe not. That wouldn’t work.” (D)
Now we get to the other half of the story of today’s Math Circle: frustration. Kids were working with little interaction with me today. Some automatically took a time out from the problem to regroup. X and K came over to the polydron table. D and N curled up like rocks under their sweatshirts on the floor. (I had a feeling that these “rocks” were really meditating mathematicians.) G, J, M, and A continued to collaborate at the board. J came over to me at the table with a proposed solution. The rocks jumped up to look at her group’s attempt, which turned out to be flawed. After loud sighs of disappointment, we discussed how real mathematics does often produce frustration. I asked for strategies for dealing with it.
“Go bananas!” (This suggestion was accompanied by a demonstration of the “Go Bananas Dance.”)
“Eat ice cream!”
“I would eat ice cream and then try again.”
At that, G came over to the table from the board, as frustrated as can be. “I know there’s a way to do it. I feel like there’s a way. I am really, really frustrated!” We told her about the above suggestions, and then I called everyone over to take a break from that problem for the day. They were relieved to hear that it is actually possible to increase your frustration tolerance. (Increasing this is one goal of Math Circles.) I then started to tell them about the Scottish Neolithic carved stone balls. Fortunately, G knew something about these, and was able to recover from her distress by focusing on a different topic. We ended with a promise that next week, we will revisit (and solve!) today’s problem, the Konigsberg Bridge problem (N thinks he has the solution), and have some fun with function machines.