They always say figuring out how to teach a topic is the best way to make yourself proficient at a topic. This is why I try to dedicate as much time as I can to the students getting to talk to each other instead of having to listen to me. The strugglers will listen intently to the ones that understand, and the ones that understand will understand it BETTER because they have to translate what's in their head to something another person can grasp. It's the main reason I passed a number of my college exams, we sat there and shot the breeze in the library trying to figure out this or that thermodynamic process.

I've tried to incorporate this into my assessments because I want to see the students try to think. Often we get so focused on whether or not they can do a math problem that we have no idea if the errors are being caused by something going on in their head. So the second time I assessed substitution and elimination in Algebra II, I had no interest in whether or not they could do the problem, I wanted them to tell me how both were done and how I would know which one to use:


"No Fair! You just picked some smart kid's example!" you say? Well, duh. But you'd be surprised to learn that lengthy explanations like this were way more common than you'd think. Even in my Algebra II section that struggles, most of them were able to make a decent description. Several even worked the problems as you can see in this one.

Second, I want to teach thinking to Pre-Cal as well, so I presented them with a problem they couldn't really solve because too much was missing:


This was not as successful. A lot of them ignored the part where I asked for a specific reference to trig, but most of them knew what was missing and how they could get it. I did have to facepalm a bit at the number of them that referred to the space shuttle as an airplane though.

AuthorJonathan Claydon