Friday, June 10, 2016

Geometric Constructions

Some of my fondest memories of being at my grandparents' house are of pencils, t-squares, the scent of WD-40. I loved being out in the garage with my grandpa, a former drafting and technical drawing teacher, as he was fascinating to me- it seemed like art.  And above all, I knew it was something that he loved. When he was working, you could see his whole demeanor relax. He was focused on something entirely outside himself, almost a form of therapy for him. Since I first learned geometric constructions as a teenager,I always associated the act of geometric construction with my time spent in my grandpa's garage. 

My first experience teaching geometric constructions was anything but therapeutic. I was teaching a group of students who were repeating geometry and had no interest in an overenthusiastic 21 year old trying to teach them a skill they felt they'd never use. I will never forget them moment a girl stood up and said, "Look at this b*tch up here preaching" as I over-enthusiastically tried to get them invested in bisecting a line. My next experience was with a group of highly accelerated 8th graders who would gobble up anything I asked them to attempt. It was cool because it was math and because I asked them to do it. 

Next year I will be in a less extreme geometric situation, so I'm trying to start from the beginning and figure out a way to make this as relevant as possible for my kiddos. Here's where I'm starting:

Instinct #1: Math Nerd Prospective
I had a professor in college who always said "the history of math is the history of the world." Major events in mathematics and science innovation are so closely tied with major events in history and geometry has a fascinating one. How can you not love a good story about Euclid and Poincare and all the other amazing geometers who have battled over things like the parallel postulate??? Unless you're 16. And focussed on your football game Friday night. Or the boy sitting in front of you in class. Got it....might need a different approach.

Instinct #2: Applications to Drafting and Architecture
With my Grandpa in mind, I contacted our drafting teacher to get her perspective. She said to think about building and construction.  
"You could look at building roof trusses with balsa wood or bass wood.  With the demise of pencil drawing and going almost all AutoCAD I don't teach my kids how to do this anymore.  The computer does it for them. "
So while it's a foundational skill for a lot of careers, it's not something that's obviously useful with all the new technology. Our drafting teacher followed up with a comment that I loved...
"I, of course, still like to draw with tools though seldom do.  The focus required is kind of meditative.  I did actually demo a complete drawing using tools and the kids were amazed I did it faster than they draw on the computer.  Some times it is fun and instructive to show off." 
This is something I want to make sure I hit in class. There are some kids who will identify with the hands on, fascinating process of creating something that is exact. There will also be kids who are more into the technological aspects to help them see the why. 

Preliminary Thoughts: 
A lot of the idea behind the history of math is creating restrictions (axiomatic system) and seeing the results that follow from it. It's why I love this Geometric Constructions Game that I found through Crazy Math Teacher Lady Kids are put under restrictions and need to try to create the objects in the fewest moves possible. I love how open ended this game is and for an honors class I can see this becoming a huge competition. However, for my standard kids I'm trying to develop some entry points to help them connect what they're doing with the mathematics. I spent most of this week researching and talking to peers. I'll be designing some entry level activities  and hopefully some PBL scenarios for next week!

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