What's in the list you keep (internally or physically) of things we still traditionally teach in our math courses that just feel "wrong" in 2014?
Memorizing formulas is probably one of my least favorite things, and I know I have that in common with my students, so wherever and whenever possible! I like to teach them the concept on a pattern level or with strategies that have more than one application. In other words, if the only reason for me to teach it is to maybe get lucky and steal a question or two on a test, then I usually won't stress it.
I was having a good week with my Applied Math class. The kids have been more or less focused recently, and we were all getting along. Kids love Pythagorean Theorem, for some reason. Right up there with "y=mx+b!" It's hard to find a kid who at least doesn't think they know how to use it. Taking advantage of those good vibes, I would have rather rolled on into circles, but the ugly special right triangles lesson stood in my way.
I went through the trouble of having them use Pythag the night before to actually solve the SRTs, and my first example showed them again how they can just use Pythag on any right triangle to find a third side. Good feelings were still flowing, and then our first question from the book had a 60 degree angle and ONE side. "Try and do THIS ONE with Pythagorean Theorem," it seemed to taunt me. I took the bait and walked the class through the relationships. And one by onem my confident students fell to the wayside, and my focused, eager students started to check out.
So, why? Why invest time in a chunk of knowledge that isn't necessary if you know Pythagorean Theorem or basic trig ratios?
Here's a note sheet I plan to share with my students tomorrow to articulate the alternatives again.