I attended the California Math Council North’s conference in Asilomar last weekend. Because of Covid, it was a dramatically smaller conference than usual. As a consequence, there were fewer sessions to choose from, and probably a smaller turnout for many of them. Here is my nearly annual report.
Ned Diamond presented the Python implementation of turtle geometry. (Python is a programming language.) In that environment, he enthusiastically shared the activities that were pioneered in Logo. Those activities turned him on to math at a young age. I love those, and in fact incorporated them in my geometry classes. I very much agree that they provide a fun introduction to programming, while at the same time getting students to think mathematically in a fascinating microworld. However, I was not convinced that Python was the way to do it when environments such as Scratch (from MIT) and Snap (from UC Berkeley) are so much more inviting to both children and teachers.
On the other hand, I decided that if I ever want to learn Python, this does seem like an excellent way to get started!
Moving in Circles, Dancing with Paper
Karl Schaffer shared an extraordinarily varied bunch of activities involving circular movement, some of them involving the whole body. We rotated our arms in space around x-, y-, and z-axes, manipulated a doll, and yes, we danced with an 8.5 by 11 piece of paper. Karl made connections with math: rotations in three dimensions, finite groups, and the sum of the angles in a polygon, …. He also showed videos of dance: his own and others from various parts of the world. One attendee who happened to be at my table during lunch told me the session “nourished her soul”. I very much enjoyed it, in spite of the fact that some of the activities were beyond what I could manage, as I am extremely uncoordinated. I’m a big fan of kinesthetic activities in the classroom, and encourage you to attend Karl’s workshops if you get a chance.
Building Thinking Classrooms: Beginning the Journey
Abby Bates and one of her colleagues presented the basics of math educator Peter Liljedahl’s approach. I wrote about this back in 2015 (Visibly Random Groups, The Thinking Classroom.) Since then, Liljedahl has put the results of his research in a book, and now has a dedicated following all over the US and Canada. This session started with us standing at white boards around the room, working on a “non-curricular” problem, which I will describe below. The “Thinking Classroom” is not unlike the style of teaching I did when I was in the classroom, though it is enhanced by having the students standing at “vertical, non-permanent surfaces” in groups of three students, reshuffling the groups daily. (I had students at tables, in groups of four, changed every two weeks.)
The problem we worked on was presented as a story about pirates. I actually knew about the problem (but not its solution) from my days as an elementary school teacher. Back then, we called this the “poison” problem. 12 people are sitting around a table. You pass around a cup which contains poison. Someone takes a sip, and dies (or leaves with terrible stomach pains,) after passing the cup not to the next person, but the one after. You repeat this with every other person dying, until only one person is left. The puzzle is: how should you choose the first person to take a sip so as to make sure you’re the last one standing? We explored this for 12 pirates, and then tried other numbers. It turned out to be somewhat curricular: the number of the person you should pick seems to be a linear function of the total number of people in the circle. (But why?) If I remember correctly, in the 1970’s we also explored what happened if you passed the cup to every third person, every fourth person, and so on. I’ll need to think about this some more!
Tiling (Tessellation): A Springboard for Geometry
This was my session. It was based on these blog posts: Tiling, and Tiling and Transformations. I also have a Tiling home page on my site. (This handout includes those three links, and many more.) The session went well, though it would have gone even better if I had had time to learn how to use the document camera. That would have allowed me to show everyone the designs made by the participants.
Well, that’s all for this year. Hoping for a much larger conference next year!