25 April 2016

STEAM: Geometry and Topology

I got ambushed at the parent-teacher conference for my son's second grade class. The combination of the teacher saying how nice it was that the other second grade class had Mr. Orlando to do STEM demonstrations and wouldn't it be nice if our class had some too, along with my spouse looking at me, off to my right, I felt like the hunter in Jurassic Park, surrounded by velociraptors ("Clever girl...").

I was trapped. There was no way out. Turned out, that was a Good Thing.

Researching STEAM (I will use the preferred acronym from now on), I quickly discovered my preference for the basic Sciences and Mathematics as opposed to blinky lights and circuitry of Technology and Engineering, so that's where I focused my research.

I would have no more than an hour for each activity, and second graders (seven and eight-year-olds in the United States) do not have the basis to discuss mathematics, or any of the other words in the acronym in depth. So the goal of STEAM in elementary school is not to explain how stuff works, but rather to demonstrate why I became an engineer.

Scientists, mathematicians, and engineers approach life with a sense of wonder. At least the good ones do. They see something novel (or not-so-novel) and think to themselves, "that's cool! I wonder why that is?" then go off and try and figure it out. It is this sense of wonder that STEAM activities are trying to sow.

I've found YouTube to be an invaluable resource in researching STEAM activities. Not only are there a lot of great ideas out there, but the video format lets you see the activity from the participant's standpoint. You get to see what works and what doesn't.

The instant stand outs were two Numberphile videos by Tadashi Tokieda on Geometry and Topology. Now, you may not think Geometry -- and certainly not Topology -- are suitable subjects for second graders. But that's probably because you're thinking of the way Geometry was taught to you back in High School. All definitions and theorems and proofs, sucking the life out of the beauty of mathematics because there was no basis presented for those things, or examples of what you can do with those theorems.

I think Geometry is a perfect subject for young children. It does not require an ability to multiply numbers together, or divide them, or a knowledge of trigonometry, or anything, really. It just requires shapes and objects and a willingness to play, which kids have been doing all their lives.

Tokieda gets this. He has an innate understanding of this. And it comes across in the videos.



Naturally, I ripped him off borrowed heavily from him for my presentation. Only instead of demonstrating, I had the students cut each figure for themselves.

Turns out, cutting paper can be more challenging for some second graders than others. I had not realized this going in, but there is a large distribution of abilities in the classroom. Things ran long, so I dropped the joined loop and Mobius loop from the activity and went directly to the joined Mobius loops. Maybe a third of the class got the chirality correct on their loops, resulting in the joined hearts. Heck, I didn't get the chirality correct when doing the demonstration! But I got the reaction I was looking for -- "that's so cool!" -- from at least a few students, so mission accomplished.