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:

123
Anytown

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.

I don’t hear it often, but occasionally a student will ask me why I’m forcing him to learn a math skill he’s struggling with. I usually start asking about hobbies, interests, and future plans and tie what he’s doing to that. The student still grumbles, but he gets back to work, soon mastering the skill and grumbling about the next one.

While I love to learn new things, I can sympathize with my students. It’s hard to make yourself work through challenging skills when you can’t see where you’re going.

A couple of summers ago, I decided I’d had it with not being able to draw anything more than a stick figure and started working through the beginning lessons at Drawspace. The first lessons were simple enough, but I quickly got to the real-life human lessons. I hated them. I dreaded them. In fact, I kind of put them off because I didn’t want to do them. I completely ignored the last lesson because I felt like I couldn’t handle yet another failure (and a friend had loaned me an anatomy book that was proving far more useful).

While I was avoiding the lessons I didn’t want to do, I was enjoying the cartoon lessons. It didn’t take long to realize that if I wanted those to come out well, then I had to learn about human proportions and the basics of drawing a well-constructed, believable person. I didn’t go back to the lessons I’d skipped. Instead, I started experimenting with drawing people. Then, I discovered a manga how-to that showed me a way to take my stick figures and build them up to people.

I can almost draw human-shaped people now, as long as you don’t look at their hands, but I wouldn’t have reached that point if I hadn’t put myself through the challenge of actually learning about human shapes and proportions, my people would still have this grammar-school blob quality to them.

Sometimes, when a student is really struggling to see where he is in the big picture and I can see that he needs that big picture clarified for him, I share that with him. He usually asks to draw instead of doing math, but I just laugh and make him get back to work. When the next skill is easier, he more often than not tackles it because he can see that he knows part of the skill already. The big picture is that much clearer because he pushed himself through the challenge.

Most of my students head back to school tomorrow, and they’re excited.

Okay, maybe they aren’t, but they’re already asking that one question every teacher dreads: Why do I have to learn this?

We’re taught in teacher prep programs that this is a learner’s driving question once they become a teenager. Sometimes, it’s obvious why they have to learn something. They can see how it will help them in their desired career or allow them to pursue a hobby. Some of my high schoolers are willing to learn anything that they think will make them look better than their friends; others just want to know what they need to survive the next test, and they don’t look at applicability past that.

Adult learners are also driven by this question. They’re looking for things to help them perform their job more efficiently. Some are looking to be more creative in their job. Some are just looking to strengthen or diversify their skill set. But just like teenagers, adults aren’t always so willing to sit through lessons that they can see that they need without giving into the whiny teenager voice asking, “Why do I have to learn this?”

Is there a cure? Yes, help learners see how what they’re working on connects to what they will be doing in the future. It’s not foolproof (teenagers seem particularly talented at thinking they’ll never have to do anything they don’t want to once they’re adults), but it can make teaching a tiny bit easier.