Sometimes, we teachers have moments of inspiration where we hit on just the right explanation at just the right moment to help a student make sense of something that frustrates them. I had one of those moments last week.
In all fairness, it probably wasn’t as much an inspiration as it was a moment to realize how to put something I’d already realized into use. In working through material for Dead Bunny, I’d already thought about how coordinate geometry teaches us to locate things in space (among other things). I had already noted that (x,y) is an address, a location for a point in space. I just hadn’t spent much time thinking about what that really meant because I didn’t get that far with Dead Bunny’s various activities.
Last week, I got a fraction of a second to think about it. A student was working on converting standard linear equations into slope-intercept form, except she kept dropping the y out of the equation as she worked. I kept reminding her to keep track of the y, but it didn’t help. Suddenly, it hit me. I showed her the following:
and asked her if a postman could deliver a letter addressed this way. She acknowledged that he couldn’t, and I told her that’s what she was effectively doing. When she lost track of the y, she was creating an address of (x , and no point was going to be able to be found. The proverbial light bulb went off, and she didn’t lose track of the y again.
There is a lot of discussion around the web and among teachers in general about whether or not teaching just the process is better than creating associations. I’ve tried both and find that it really depends on the material I’m trying to teach. More often than not, though, I find that if I can hit on the right metaphor, retell the right story, then my students are more likely to understand the skill or concept. Even better, they’re more likely to remember it. I can’t tell you how many students have caught their own mistakes, recounting my own story to me as they fix the problem.
Teaching by metaphor (or by association, really) can be helpful in that it can show the student how something should go if done correctly, and it can give them an emotional connection that will better help them remember what to do in the future because they can draw on that story.