Monday, July 8, 2013

The Logic of Geometry

I've noticed a distinct void in the Common Core where geometric logic used to have a home.  This makes me really sad for three reasons:

  •  I think it's a really great way to show students how mathematical thinking can be applied to real life 
  •  I was skipped past geometry in high school and when I got to college, the lack of logic training was a real handicap
  • And I've developed a tiny bit of skepticism about Common Core.  Not a lot, but I read this article about how the Common Core was developed and it creeped me out a little.  The fact that only one teacher helped develop the Common Core seems kind of terrible.  I recently made friends with an economics blogger and he told me that every profession engages in "turf defending" where those in the profession reject outsiders' perspectives.  That immediately made me not want to be a turf defender. I won't be the person who stomps on the school house floor and screams "MINE!"  Of course I want outside input, but can I also add that it's maybe a little out of hand in education?  I want to teach logic damn it! 
  • Oh, also, I've found logic very challenging to teach and to give up on trying to find the perfect way to introduce it now just because Common Core gives me permission feels like a cop out. (so I am pretty selfish after all.) 
I've made a point of always teaching it thoroughly up until now.  This year at least I'm stubbornly sticking to my guns and teaching a bit of logic (although I nixed conjunctions and disjunctions, mostly because I personally never used them in college)

Below are my three logic lessons if you'd like to take a look.  I'm writing lessons for the other math teachers in my school so the notes are kind of overly detailed.  Also my school gives us only 50 hours a year (as opposed to the usual 150-180) to get through a year's worth of material, so it's all super condensed.  I don't know if it's usable outside my school, but feel free to steal and I'd love feedback.  I've uploaded the pdfs below to preserve formatting but the .docx are also available on Scribd.

Note: I borrowed some of the homework problems from Harold R. Jacob's Geometry: Seeing, doing and understanding 2nd ed. and from AMSCO's Geometry.  I also totally stole the formatting from Dan Wekselgreene.


  1. I think logic is definitely important. Last year I tried to give students a "logic set" after we took a quiz for those who finished early. Everyone else could finish it at home for extra credit. They were random problems and puzzles to get them thinking. I still get to teach all of things that you have mentioned above though (and I might borrow/modify one of those worksheets) and I do think it helps my students as they move on to proofs. Thanks for sharing!

  2. The common core is definitely nixing logic. It hurts my soul. Please give me suggestions if they need improvement!