While teaching similar triangles, I found myself working three specific examples for my students because I know these are the types of questions they will see on the exam. Instead of focusing on concepts like corresponding parts, scale factor, and ratio, I taught procedures for solving each of the "tricky" types of problems. I pointed out why the questions were "tricky", what to keep in mind and how to set up the "correct" mathematical procedure.
Knowing what is going to be on the exam often leads me to poor teaching. I want to make sure I cover all the possibilities and prepare my students for the problems they will see. Of course, deep conceptual understanding coupled with the confidence to think through a new problem would work just as well. Probably better.
I guess I'll see the result of my efforts tomorrow on the test.
Update: Despite (or maybe because of) my explanations yesterday, at least 3/4 of the class still answered the "tricky" questions wrong. They made all the same mistakes I warned them about demonstrating both poor procedural knowledge and a complete lack of conceptual understanding. This just deepens my convictions about 2 things. One, teaching procedures without concepts is next to useless. Two, words are a poor way to communicate concepts.
Great post! I really liked how you summed it up in the last couple sentences. Joe Bower posted on a similar topic on his blog today about the assessment 'tail' waving the learning 'dog'. I also liked how he put it in his concluding sentence: "When assessment drives the learning, we fail our students more than they could ever fail us."
ReplyDelete<A href="www.joebower.org/2011/07/assessment-wagging-dog.html>For the Love of Learning: Assessment Wagging the Dog </A>