Compass-edge constructions, curiosity

I’m introducing the basic compass-straightedge constructions in Geometry this week. For the most part lessons seem OK; it’s helpful that everyone has something to do. Busy hands are less the devil’s playground than bored hands. My biggest disappointment is that only one or two kids in each section seem to wonder – like, at all wonder – why something like the angle bisector construction works.

This is a big contrast from last year, when I taught at an alternative high school. There, the students were historically low achievers in math (and most other subjects) and in many cases had done some construction or other labor. Hands-on geometry was the best thing I did with those kids. For them, finding the balance point of a cardboard triangle was, like, very cool math. And what I loved was they always wanted to know why something like that worked. It was a very natural, in-the-world kind of curiosity, that felt to me like a true mathematical instinct.

My geometry classes this year are mostly composed of what we would classify as better students. They will undoubtedly be more successful on average on the state end-of-course math test than the cohort I had last year. But I’m waiting – impatiently – for their curiosity to emerge. And I’m wondering what things I can do to inspire and nurture that quality in them.


2 Responses to “Compass-edge constructions, curiosity”

  1. 1 Anna (@Borschtwithanna) October 19, 2012 at 4:46 pm

    That’s an interesting observation. I wonder if it would be helpful to include a writing component to the constructions where students have to explain what they did and why it worked or have them come up with their own construction steps to achieve a specific result. Another possibility would be to have them do some of the constructions using Sketchpad. I’ve found that lends itself better to playing around and thinking through some constructions.

    • 2 Paul Gitchos October 20, 2012 at 5:02 pm

      Thanks for your comment! Getting more writing into math class is one of my long-term goals. So far, this has been limited (in Geometry class) to a few “Explain how you know” test questions. I like your idea of having students write to explain and justify constructions.
      I have introduced these classes to Geogebra (rather than Sketchpad) and plan to have them explore constructions in the software environment next week. Perhaps I will tie in a writing component with that.

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We are all born into this world, and at some point we will die and that will be that. In the meantime, let’s enjoy our minds and the wonderful and ridiculous things we can do with them. I don’t know about you, but I’m here to have FUN.
-Paul Lockhart

In theory, theory and practice are the same. In practice, they are not.

-Yogi Berra


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