The Talking Stick Blog

News, Updates, Program Recaps, and Homeschooling Information

Francs, Fractals, and Kovalevsky

The idea that math is an art and not a science is not a new idea.

 

Today we examined the life of mathematician/writer Sonya Kovalevsky. We first talked about some of the childhood experiences that shape her life, then took a break to watch Vi Hart’s film “Triangle Party.” This overwhelming film may be my favorite Hart film: 6 minutes of rapid-fire bombardment of concepts and doodles. At the end, a few kids said, “I didn’t get any of that.”

When they returned to the table, however, it was apparent that they did get something out of it. They constructed various triangle doodles as I returned to telling Kovalevsky’s story. We got to the famous part where she entered an anonymous mathematics contest, and the judges were so impressed with “his” exceptional work that they increased the prize from 3,000 francs to 5,000 francs. “You mean they paid her in hot dogs!?” exclaimed an incredulous M. We detoured from the story for a few kids to explain older European currencies. When we returned to the story, a chime unexpectedly sounded from my laptop.

“Nice ringtone,” said someone. But it was not a phone.

“What’s the gong for?” asked someone else. I explained that it’s an attention reminder - a mindfulness chime that goes off randomly. I had forgotten it was on there, and told the kids that it’s a reminder to me to notice three things: where I am at this exact moment, who I am with, and what I am doing. The kids then looked around the room at each other, noticing who they were with and what they were doing. I asked them why an attention reminder might be important for math (or anything), and they discussed it. I wish I had the following quote about attention at hand at the time; maybe I’ll read it to the kids next week:

Attention without tension sets you not so much in or above or around the problem as at it; it lets you understand by fitting your mind to the shape of what it contemplates: ‘unassuming, like a piece of wood not yet carved’; as a Zen master put it, ‘vacant, like a valley.’”*

I read the students a passage from Kovalevsky’s writings about the link between mathematics and poetry. The passage ends with “It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.”** The idea that math is an art and not a science is not a new idea. Neither is the idea that attention, poetry, and math are connected. Nor is the idea (expressed by Kovalevsky and many others) that mathematics is not just arithmetic. Many kids (and adults) are stuck in the belief that math is only arithmetic, and that only those with “number sense” can enjoy it. In Math Circles, we hope to dispel that belief.

I will be celebrating the art of mathematics this weekend at the Math Circles on the Road Festival in Washington, DC. I will bring back a new lot of ideas to explore in future math circles. Speaking of future math circles, a few kids in this group have expressed an interest in statistics, which I may incorporate into our fall math circles. Last week, I attended some Delaware Valley Science Fair teacher workshops on the topic of using statistics to interpret scientific data. The presenters were statisticians, who afterwards gave me ideas on how to incorporate statistics into a math circle. I also recently attended the Mindfulness in Education conference, which I try to attend every year. I have been learning, over the past 4 years or so, how to integrate contemplative (attention-strengthening) practices into teaching, and am currently investigating this with particular regard to math and science.

Anyway, back to this week’s Circle, which ended with two fractals. First, N came to the board to demonstrate how to construct the Snowflake Curve, a fractal Vi Hart demonstrated in about 5 seconds in the film. Then, we discussed whether one can really calculate the perimeter of the coast of England. Or, is a coastline really an infinite fractal?

See you all next week. If you have time, “Triangle Party” is a film worth looking at again and again on your own at home.

-- Rodi

*Bob and Ellen Kaplan, Out of the Labyrinth, p46

**Lynn Osen, Women in Mathematics, p136