Wednesday, June 30, 2010

More Thoughts on Geometry Proofs

What does a math teacher think about on the plane while she's traveling to see her dad in another state? Teaching, of course. I'm still working out how I want to start teaching proofs in geometry this coming year, and I had 2 extra ideas that I haven't quite fleshed out yet.

One idea came from a news article I saw the other day. It was something to the effect of school officials allowing nurses to hand out condoms to elementary school kids. The original article JUST stated that they're going to start making them available for K-5, and if my memory serves me correctly, that was ALL the article stated. Well, of course, it sounds so ridiculous and my 1st thought is, "crazy! why?", etc. Then I had to step back and think, what could be the real story behind this, and I came up with a few possibilities.

I discussed it with my friends, and sure enough, a few days later the WHOLE story came out. The school district was making condoms available to any student of ANY grade that asked for them, and I'm guessing that in their minds they were mostly thinking about high school kids. Then maybe the newspaper people got the story and JUST reported that the condoms were now available to elementary kids.

Anyway. What does this have to do with geometry? Here's my thinking. One reason to teach proof in geometry is to get kids to think logically and to think of all (groups of) events or statements that can lead to other events/statements. In this way, they won't be "victims" of people trying to sell them one version of a situation. So I thought this story would be a perfect example of just such a situation.

Somehow I'll begin the proof unit discussing why we learn them and just show them the 1st news story. Then I'll have them get with a partner or in a group and think of what events may have lead up to this article or that may have justified such a move by the school board. Then show them the 2nd article. Then maybe I'll find a provocative picture (in the sense of it may look like something bad or good is happening at 1st glance), and then have them think of things that may lead to this picture (or result from the picture scenario). Anyway, like I said, it's not fleshed out yet, but I think this will be a good start.

My 2nd idea has to do with Excel programming. I don't know if I can pull it off, but it seems like you can do some cool stuff with Excel if you learn a bit of VBA programming, and I'd like to create some sort of interactive proof-filler-outer that will be a quiz for them. If it's easy, then I can pop out several and have them online for the kids to practice with. I'm guessing that's a big if.

Anyhow, vacation with dad is over, and now I have a glorious week to do mathy stuff ... before my next vacation trip. WooHoo! Maui here I come (me and my fish-white belly). I'm guessing I'll look like a pale white tourist, but guess what? That's because I AM a tourist. Maybe I'll just have to drink a lot to be okay with it :).


  1. Well have fun in Maui. I went in October. It was great. Went to a wedding, visited some teacher friends, and played with my kids on the beach.

    David Cox is a GeoGebra advocate and I was under the impression that this is probably a good tool for that.

    If not, this is probably a very relevant link for you:

  2. Thanks for the tips, Jason. I keep meaning to learn GeoGebra skills because it seems extremely useful. Have you used it? I'll follow up on your links.

    Ms. Cookie

  3. This would be an excellent time to sign up for twitter and ask! Go with @dcox21 or @rileylark for Geogebra questions. They've got crazy geogebra fu.

  4. I would love to see what you come up with for teaching proofs! This year, I had real trouble getting the kids to connect to proofs without overly connecting to proofs (and ignoring logical rules, for instance). For example, if I make the statement that "If it's Friday, then I would hang out with my sister," then half of the class would keep wanting to conclude that whenever I hangout with my sister, it should be Friday. Their conclusion is "reasonable", but not correct. That's an example where their intuition comes in to play TOO MUCH. How do you deal with that issue?

  5. Hi Mimi,

    I know what you mean. If I remember correctly, we started with a more boring statement (for some reason, this one always comes out of my mouth): if it rains, the ground is wet. Then after we talk it up for a while, I ask if there are other ways the ground could get wet, and we brainstorm. Then I may have said, okay, the ground was wet on Tuesday the 9th; did it rain?

    We somehow then link it to p's and q's (p --> q) and possibly I have a sheet of statements and ask what they can conclude.

    Ms. Cookie