Should I use elimination or substitution?

Be forewarn, this is probably not the post you are looking for.

A teacher I was coaching sent our this tweet after a recent observation. The class was looking at solving systems of linear equations using elimination and substitution and we had talked about how he could use data from recent Big Ten basketball games to set up scenarios that might encourage them to use the different techniques. Early in the lesson, several of the students (the class is all boys) made it clear that they were huge basketball fans.

Here are a couple of examples I came up with:

Against Wisconsin, Trey Burke scored 19 points. He made 1 free throw and 2 three pointers. What would his box score look like for scoring?

Trey Burke scored 18 points against Michigan State. He made 1 free throw and 7 shots from the field. What would his box score look like for scoring? 

Christopher Danielson has thought more and deeper about this topic than I, so I defer to his expertise (here). Sorry for the bait-and-switch, but I want to think about how this experience helped me to re-evaluate my homework policy.

About two years ago, I wrote about how overwhelmed our novice teachers are during their first teaching experience. We do this somewhat intentionally so that they can experience firsthand all that is expected of teachers, and so that they can become better at managing their time. Part of that time-management is learning to prioritize what is important and learning how to say, "No!" -- in other words, elimination. (I know that we aren't talking about mathematical elimination anymore, but this is where my mind goes. Pity my wife and my co-workers.) In that post, I went as far as to say, "It is okay to skip this assignment."

Looking back, I think that suggesting this technique, elimination, was a mistake in this situation. Simply skipping work does not match the reality of teaching. In order to prepare them for that reality, what I want them to be good at is substitution. If something else on their plate is more important than one of our assignments, then they ought to make a substitution. However, as they do their other work, I want them to recognize they are doing it on our time and look for ways to synthesize the concepts and skills we have been exploring into their "more important" work. Hopefully, this mindful effort to synthesize across classes will provide practice in attempting to meld ideas in their teaching practice.

Again, my apologies for bringing you here under potentially false pretenses. And for making you wade through the ramblings of my mind. As I tweeted Christopher recently, I need an editor. If you have your own thoughts, please add them to the comments.