Sunday, July 29, 2012

Draw a Picture, You Idiot!

I'd like to make my lesson on writing algebraic expressions more concrete for students. My hope is that students' understanding of simple expressions will lead to better interpretation of equation word problems. I was inspired by Steve Leinwand's book, Accessible Mathematics, where he argues that diagrams should be drawn as much as possible to help students conceptualize material. Here is an excerpt:

"Without question, one of the most common responses I have when sitting in the back of a mathematics class is screaming under my breath, 'Draw a picture!' or 'Use a number line!' or 'Ask them what it looks like!'" (page something or other...I don't know, it's on my Kindle app, how am I supposed to cite these things?)

I think he really meant to say, "Draw a picture, you idiot!" (hence, my post title). So I figured, why not apply it to this lesson:
What does everyone think about teaching this way? Will this help students gain a better understanding of variables and operations? Should I preface this with diagramming of numerical expressions first? What about expressions that don't lend themselves well to a diagram (such as 5 divided by n)? Any suggestions?

Nathan Kraft