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Thursday, October 6, 2016

A Day With No Foldables, Instead Notice and Wonder

Lately I've been getting a little burned out with how jazzy my Geometry INB is getting. It's a lot of paper. A lot of cutting. A lot of pasting. I'm sure that these are good things to do, but there are other effective ways to teach too.

So for my lesson on exterior angles of a triangles, I tried a take on the Number Strings that I heard about at TMC NYC '16. I used 8 straightforward problems where students could use their prior knowledge on linear pairs and the sum of the interior angles of a triangle to find a particular missing angle (either the exterior angle or one of the remote interior angles). Then I asked them to take a step back and tell me what they noticed and wondered.

Here's what I noticed:

  • Of my 3 geometry classes, only one did an awesome job noticing/wondering and was able to tell me the relationship between the exterior angle and the remote interior angles. 
  • My sophomore group was cooperative in writing down what they noticed and wondered, but they wrote trivial things, probably just to finish the task quickly in hopes of satisfying me. 
  • My other upperclassmen didn't notice or wonder anything. They mostly didn't want to write anything down. Maybe they were just anticipating the final bell. Maybe they didn't feel like thinking. I don't know. 
  • The questions generated by the sophomores made me realize that they didn't notice that there was a purpose to which angle I was asking them to find in each question. They didn't notice that I never once asked them to find the adjacent interior angle (though they knew they had to find it as an intermediate step to finding the answer). 
Overall, the lesson went very well and I'm pleased with it. But I'm still bothered by some students' general lack of perseverance and unwillingness to write their thoughts down on paper. 

Here's what I wonder:
  • How do you get students to persevere, especially when faced with a low-floor task?
  • How do you get students to write in math? 
  • How do you convince students that no idea or question is silly? That all ideas are valued and worth using? 

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