This is my first attempt at a “Made 4 Math Monday” post. What follows is certainly making, and definitely math. I hope you enjoy!
The other day I tagged along with Paul when he went to NYC Resistor to laser cut a piece of mathematical art. For a while now, Paul’s been creating all kinds of amazing art that involves stars. That’s STARt, for short. He should really put up a gallery of his artwork on his blog. nudge, nudge.
Anyway, for this piece he was cutting all of the twelve-pointed stars out of plexiglass, planning to stack and glue them into a sculpture. There were of course some leftover scraps from the cutting, including 12 nice isosceles triangles that he passed on to me. They’re just the shape of triangle that you get when you pizza-slice a dodecagon.
After our outing, I was in an artsy mood and found myself playing with the triangles. I was amazed by how many ways of arranging them presented themselves to me, just by futzing around with them. It was a pleasant and exciting activity. Here are a couple of pictures I took of my creations:
Playing with the triangles got me thinking about some further patterns that I wanted to try out. Like: what would happen if I stuck the triangles together along their long sides in a chain, pointing up and down at random? What would the long-term behavior look like?
So I did some programming, first in Scratch and then in Processing. Here’s a short clip of what I’ve gotten to see so far. It’s given me food for thought about connections between this pattern and David Chappell’s meander patterns.
And if you tweak a few parameters–including weighting the probabilities as a function of the number of triangles that have been laid down–you can get something like this instead. Nice!
What I took away from this was how having unfamiliar and tangible mathematical objects around led to play and product and inquiry. This felt real and striking to me.
What does this mean for my classroom? I want my students to have experiences like these—open, creative, productive experiences with mathematical objects that they feel connected to. Having lots of accessible and flexible mathematical objects in the room is a good direction to head in.
Writing Math Munch is one way I try to expose my students to new objects, patterns, and structures, but now I’m vicariously craving really tangible math experiences for my students. This gave me the thought (a recurring one) of how I want there to be a superabundance of supplies in my room. I was in an art classroom at school earlier this week working on another project, and I was just so struck by how much stuff there is in that room. I want there to be stuff in my room, too—both clearly mathematical stuff and stuff that has the potential to be.
What do you make sure to keep around in your classroom for kids to have access to? Or would like to? There are some things I keep around, like pipe cleaners and twisty balloons and poster board; markers and protractors and geometry building tools (Zome, Geofix, pattern blocks). But I want more. Because I want my students to futz. Thoughts?
Hooray for making and math! #made4math
P.S. One final product of futzing: a further riff on STARt, inspired by Paul’s. Made of thread and a water bottle.