Thursday, October 7, 2010

Math in Unusual Places

Boing Boing has a great article based on Sherry Turkle's book Falling for Science.

Turkle's book contains "a collection of interviews with MIT students, and established scientists, about the objects that first drew their minds to math, computers, science and technology. Some were what you'd expect: Broken radios, Legos, a computer. But one story, about a My Little Pony, really caught my attention."

The Boing Boing post goes on to relate, in full, professor Christine Alvarado's story of playful mathematical discovery.
I had several small plastic Ponies that I used to play make-believe with my friends. But I had one larger, plush My Little Pony, a bright-green stuffed horse with a vivid pink mane and tail that I played with all by myself. I would sit for hours on my own, braiding and rebraiding its tail. I developed a system for braiding the tail of my Pony that taught me about mathematical concepts-- from division to recursion...

When I started, I took the hair on the Pony's tail and divided it into three pieces for braiding. Soon I became bored with a single braid. I then divided the tail into nine pieces and made three groups. I braided each group of three until I had three braids, then took these three braids and braided them together.

Soon I was up to starting with twenty-seven pieces (nested down to nine braids, then to three and then one) and then on to eighty-one. All the while I was learning about math: I saw that division is the process of taking a large number of things and grouping them into a smaller number of groups. In order to end up with one even braid at the end, I had to be able to divide the initial number evenly by three, then by three,and then by three again, until I ended up with just one braid.

I learned that I had to start with specific numbers of pieces in order for the braid to come out evenly. These specific numbers, of course, turned out to be powers of three. Overall, though, what I liked most about braiding was recursion. The large braid was made up of smaller braids that in turn were also made up of smaller braids, and I pushed this structure as far as I could take it. I once attempted to begin the braiding process with 243 pieces, but because each of these sections consisted of only about five strands of hair, I was forced to give it up.

With braiding on my mind, I began to see recursion everywhere. One night at the dinner table, I was eating cauliflower and I noticed that it had the same recursive structure of my braids. Moreover, the cauliflower seemed to continue to recurse forever. I began to divide the piece of cauliflower on my plate, determined to find the base level, but it split further and further until the pieces were too tiny to hold. My parents gave me a strange glance, and I continued to eat, still fascinated by the underlying structure of my vegetables.
(excerpted from Sherry Turkle's book Falling for Science: Objects in Mind)

This story so reminds me of my rich (and memorable) learning experiences as a kid, that it seems important to share about it here, especially when so many of us are looking for non-coercive ways to support our children's learning.

Another book about how scientists came to be where they are is Curious Minds: How a Child Becomes a Scientist. From Books in Canada:
Curious Minds left me with the conviction that scientists are the most interesting people in the world, which is just the conviction its editor must have begun with. The 27 contributors whose backgrounds John Brockman asks about are not just scientists-they are also philosophers, activists, humourists, wunderkinds and prima donnas, and even if you are a humanities sort of person you will find their minds uncommonly curious in both senses of the word. The contributors were asked “what inspired them to choose their paths” in science. Some write about family, while others talk about their university years; some describe their favourite books, but most are at their best when writing about science itself. Science makes poets of them all and they in turn make science captivating.