This week, I’m supposed to teach my students how to solve a system of equations by elimination. It’s the hardest of the four ways for solving systems (graphing, substitution, guess-and-checking), and I’m not entirely sure everyone in the class gets the first three. The main point of the unit is to determine exactly where two or more linear relationships meet, if they ever do. The situation could be realistic (two cars running a race, two trains on a schedule, cell phone pricing plans) or already abstracted (simultaneous equations), but I’m hoping they can find this meeting point because it’s really interesting. Is it relevant to their daily lives? Perhaps. Do I care? Not necessarily.

Really, I don’t always want the things that people learn to be within the realm of possibility, because I’m trying to prepare them for the improbable as well.

One missing piece of the Common Core State Standards debate is that, while I’m glad to teach students higher order math that puts them on the pathway to do well in high school algebra (and trickles into geometry, trig, and hopefully calculus / statistics), I can’t, and sometimes don’t want to, *always* do what the standards are asking me to do.

After nine years, I’m still trying to find ways to push my teaching – and their learning – further, and I believe I’ve earned the right to say what works and what doesn’t with any group of students. I often find it’s a waste to try and create a week’s worth of lesson plans when things are bound to change from day to day. I know *what* they have to learn and I have a given window of time I’d like to finish the learning by, but I’m also trying to maximize student learning if possible, meaning that I’ll have to come up with six ways of explaining something and hoping the students catch at least two of those.

That’s the thing with math generally. People are taught that we ought to teach math only one way, and, if not taught this way, they’ll never get it. I’m happy just knowing that, out of the hundreds of ways of doing a problem, they at least caught on to one. Because I *really* don’t have all the answers. I have mine. The next person might have a better way. I have no ego or qualms mentioning this all the time.

At some point, however, I’d like to get them confident enough to not have to depend on whether I know it or not, but that I gave them some tools for them to do it themselves. Because maybe the math we’re doing isn’t necessarily relevant, but it could be useful for the things we haven’t yet used, or necessary for the things we haven’t yet needed.