when you pry them out of my cold, dead hands.

I apologize in advance that I'm going to get a little critical of people I don't know who are trying to do a good thing, and are probably very nice. This landed in my inbox today from someone who offhandedly described it as "cute" with no further commentary.

"How do we know something is true?" is a big, maybe The Big Question in Geometry. At least, in my course. I hope in yours, too. It's a big, bad, fun, important idea.

Don't get me wrong, the makers of this video did a very slick job with it. It is very, very well done. But I don't get the point of cutesy-ing up exposition on the topic. When is a learner supposed to watch it? Before or after they have looked at a bunch of examples of something and made a conjecture and paused to wonder if that thing always has to be true, and just how they can go about knowing that? Before or after they encounter a surprising consequence of a ho-hum construction? I really, really hope this isn't any learner's introduction to what proof is for. They need to get their brains in the weeds of puzzles they can't leave alone. They need to get their hands dirty. Please, teachers of Geometry. I am begging you, here.

I suppose maybe I'd show it after. Like, way after. Months from now. It is pretty cute. Maybe it will help snap into place some ideas they will have knocking around in their heads. But my prediction is it will not hold their attention.

I did what you said at the end there. After working on proofs for a while, as a quick distraction, I showed the cute video. I also found it rather weird, though, as did my students. Some even yelled at the screen, "But how do you KNOW those sides are congruent?! Nothing was given and they aren't marked on the picture!"

ReplyDeleteSo, in the same way that teachers might pick apart a Khan vid, I thought it was interesting to show the kids and they picked apart the errors and oddities.

I thought it was OK (it implies Euclid invented the idea of geometric proof, but I'll let that slide) until it whipped out the two columns and congruence notation; then it enters the "who would this be for?" territory.

ReplyDeleteIf your intent is showing "what is a proof?" I think you'd be better off doing something simple from number theory.

You're much nicer than me. I think I would show this at the end of triangle congruency solely for the purpose of making fun of it. Seriously, I don't think I could show that to ninth or tenth graders without feeling like I was patronizing them. And I hope that everyone's students would feel the same way. It's written as if the intended audience is in 6th grade and I would expect the "You'll never impress me" teenagers in geometry to pick up on that immediately.

ReplyDeleteThough, as Dave says, it could be a nice way to pick apart a bad proof, too.

I expected this would be far more engaging and interesting. I also thought I was alone in not finding it terribly worthwhile. . .

ReplyDelete