(March 31, 2016)  Some older kids helped to lead the circle.  At the beginning, R (age 16) sat down on the floor with them to play nim, which the kids know how to play.  She asked some open-ended questions:

  • “How do you want to play?”
  • “How do you want to set it up?”
  • “Do you guys want to go first or should I?”

Some of the stones are different colors so the kids put each type in a different pile, calling some eyeballs, others blueberries.  “We gotta make the Illuminati!” said someone, so one pile got named the Illumati.  R went with that right away, recognizing and respecting the kids’ ownership in the math via naming, making comments as play progressed:

  • “Talk about extracting eyeballs!”
  • “I took this Illuminati over here. It’s too good to pass up.”
  • “It’s a change with the blueberries.”

The kids spoke strategy with each other, making comments such as

  • “Put it back! Put it back!”
  • “That would work.”
  • “That wouldn’t work!”

By the end of several rounds, the kids had a definite working strategy, although they couldn’t yet verbalize it.  Maybe next week…

If you google it, you’ll find that there are many versions of nim.  I’ve chosen to play this version (start with any number of piles with any number of stones, versus a specific number of stones in a specific number of piles) in the hopes that the kids eventually start asking questions like “what if we start with more piles, few stones, etc.”  So far, this hasn’t happened.



We tried some new parity activities today:  the Parity Bit Trick and also later on the Penny and Dime Magic Trick described by Julia Brodsky and her colleagues for their “Playing with Parity” math circle.  (Click here for detailed instructions on the games and a video.*)    The students thoroughly enjoyed the Parity Bit Trick, which is a game with columns and rows of sticky notes.  The kids set up every row and every column with an odd number of yellow sticky notes.  The remaining notes in each column or row are blue.  One child turns her back, the others quickly switch the color of one sticky note, and the child with her back turned has to figure out which was switched.  In our group, the collaborative process of deducing the “guessing” strategy over multiple rounds was magical to watch.  (See photo of three kids plotting the switch while another is hiding.)

Then the kids begged for a 1-minute break in the middle to play tag.  “Sure,” I said.  In retrospect, this was probably a bad call.



While the students were playing tag, my other two helpers, J and M (both age 11), came into the classroom to get ready to lead their activity, a game we played last week.  When the students and I came back into the room, J and M were at the board with the name of the game, “Fingers Multiplication,” on the board.  (This is the game I also called “Math Rock Paper Scissors” last week.)  The kids were really revved up from the tag game, and started rolling around the floor with their arms inside their shirts turtle-style.  Poor J and M.  They tried to explain the game to the kids.  “We already know how to play this game!” shouted one of the rolling turtles.  J and M made valiant attempts at engagement.  At first, I sat back uninvolved so as not to usurp their facilitation.  Finally they looked at me with pleading eyes.

“Okay, L, you’re with me!” I commanded L.  “Ready, set, shoot!” I ordered.  I stuck out three fingers and he stuck out two, and the game was afoot.

“You’re with me, B,” commanded M to B, while J said to S and M, “You two are playing together, ready set shoot!”  Both helpers, J and L, immediately reacted to my intervention and had things totally under control within 10 seconds.  They were awesome!  I had given them little, if any, pedagogical coaching.  Immediately after today’s session, I was thinking that J and M could have used this, that I was remiss in my lack of coaching.  Looking back on it with some reflection time, though, I think that maybe it was better for them to learn by immersion.  (I’m using the term “immersion” as a euphemism for a process more like throwing a baby into a pool to teach him to swim.)

I like to have kids help to lead the math circle.  In general, the students are often more motivated with someone closer to their own age (in other words, cool) doing cool math.  This can clearly backfire, of course, such as when the helpers are too close in age, are siblings of the students, or when the helpers aren’t well-versed or experienced in math circle pedagogy.  J has helped a few times over the past year.  Today was M’s first time.  Contrast that with my description of the part of the circle that R led.  R has been helping for 3 or 4 years, attending as a participant, is well-versed in the pedagogy, and even writes about math circles.  She’s essentially my formal assistant or even co-leader at this point.  So what was I doing giving her instead of the younger helpers the easier half of the circle (the first half, when the kids are more excited and less tired)?  Beats me.  And to the kids’ credit, these kids are eight, have been doing other important things all day, and are just starting an hour-long math class at 3:30pm!  Kudos to them for being here and for their enthusiasm.

The demands of the day were too much for one student, who I finally asked to sit outside of the classroom for a few minutes until he was ready to focus.  That enabled him to settle down and rejoin near the end of our time, when I introduced the Penny and Dime Magic Trick.  The students were close to figuring out the reasoning behind it when I saw that we had gone into overtime, so we’ll have to revisit that one another day.


PS  Please contact me if you are a student who would like to help lead math circle sometime.

*Here’s the URL for the Playing with Parity math circle, in case that hyperlink doesn’t work:  http://www.mathcircles.org/content/playing-parity.  We’re never going to have enough time in our 5 weeks to thoroughly explore each activity, parents, so this will give you everything you need to keep on doing these things at home.  I’d suggest asking your kids to teach you the games.

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