Mathematics does not simply mean arithmetic.


Everyone noticed the drawing of the birthday cake on the board as they entered today.  As kids were arriving, we played “Mathematician Concentration” to focus our attention, but attention was split between the game and the birthday.

“Whose birthday is it?” said the kids, looking around the room.

“One of these mathematicians,” I replied, pointing to the mathematician cards laid out on the floor.  “When someone turns up the card with his picture, we’ll end the game and I’ll tell you about him.”   The cards pictured all the mathematicians we mentioned all year in the various Math Circles at Talking Stick.  A was excited to see Galileo, and mentioned something she knew about him.  J and P were excited to see Howard Gardner.  Both J and P had been in our map coloring math circle last fall and remembered his contribution to that field.  P begged to switch gears and get back to that topic, but we didn’t since half the kids in the room today didn’t know what we were talking about.  Finally, someone turned over the card with a colorful picture of a man who “looks like a farmer.”

“That’s Omar Kayyim, the birthday boy!”  I announced. (Kayyim was a Persian mathematician, poet, and astronomer.)

We moved to the table and I read them a few of Kayyim’s poems.  The students stuggled to understand what they meant.  Then we examined the structure of the poem “Here with a Loaf of Bread beneath the Bough.”  The kids were able to deduce the meter from my reciting it with hand clapping.  I remember struggling with iambic pentameter in high school, but these guys picked it up right away.  (Of course, I supplied the name of this rhythm; the kids did the work of describing it.)  They also figured out the “AABA” rhyming pattern used in this poetic form – the rubiyat.  The usual question from this group came up (“What does this have to do with math?”), but the question was dismissed quickly as, well, it was kinda obvious.  But, D, M, and a few others went on to brainstorm other things that might not have to do with math.  I told them that next week, if they’d like, they can each challenge me with one thing that might not be related to math, and I’ll see if I can figure out a relationship.  E reminded us that she might be too busy to think of something, so I reminded the group that there is never required homework in Math Circle.

“But I thought you said everything had to do with math,” mentioned one child, concerned that she had misremembered.

“I put that out there as a conjecture, not a fact,” I replied.   They were satisfied that the question is open, and I was satisfied that they knew without question the difference between a conjecture and a fact.

We moved on to last week’s conjectures about the lapis-lazuli brick path challenge from our sorcerer story.  The kids collaborated to continue the pattern.  The discovered that when you use 4 bricks, there are 5 ways to arrange them, therefore demonstrating that the Sorcerer of the Four-Pointed Hat was wrong in her conjecture.  Many kids changed their own conjecture to the Fibonacci conjecture.  V and M reminded everyone of the arithmetic function behind those numbers.  Many kids lost interest at this point.  It was enough for them to know that the sorcerer was wrong, and it was time for a new challenge and challenger.   We talked about what would have to be done to prove the answer (more work), but no one was willing to do it.  Some kids got physically restless, so we moved back to the other side of the room, set the chairs in a semicircle, and moved on to a new challenge.

The new challenge involved a drawing of a tree that I had put on that board last week, and was still there.  Last week, A had commented that it looked like a baobob tree, and her comment took on a life of its own.  Everyone wanted to know what a baobob tree was.  She explained this week.  At this point, our entire narrative story has taken on a life of its own, with kids providing parts of the story.  It feels like a Choose Your Own Adventure book.  By the way, there was an excellent post on the Let’s Play Math blog about the importance of using storytelling in math with young children.

The new challenge involved squirrels digging holes and climbing trees, and the new sorcerer (and, of course, the kids) needed to figure out at what location the squirrel ended up.  The locations below ground level turned out to be negative numbers.  When I looked at my notes during this activity, H noticed in my notebook a picture of the Hydra from Greek mythology.  He asked a couple of times to learn about this.  I told him that we don’t have time in this Math Circle, but that I’d give him some info about it and about how it applies to math.  Here’s that info:  watch the Vi Hart video “Binary Trees” .  Most of the math in here will be way over the level of this group, but it’s an excellent way to start hitting them over the head with the idea that mathematics does not simply mean arithmetic.  And we do need to keep hitting them (and ourselves, maybe) over the head with this idea.

— Rodi

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