Today was one of those days. I was teaching my students about rewriting equations to express x in terms of y. Then the students were asked to find out what x equaled when y was -2. My students abhor this task. They believe that changing an equation into x= is dumb. They’re right. What was the purpose of what I was asking the students to do? Was it a far off concept for graphing in y=mx+b? If that’s the case why are we doing this now. There was no need for it, no context for the rewriting of the equations.
My students understand that you can rearrange and manipulate equations and that they are the same as before. That’s what I care about at this point. My students understand how to plug in for y or x and solve the equation. They visualize Xs as unknown parts and can manipulate mentally many equations. My students loved arguments about where in the manipulation of the equation would they rather plug in for y. They liked that everyone had a different preference and that was okay. I loved that part of the problem. But here’s the problem. I wasn’t asking that of them I was asking them to rewrite equations into one format for no reason and no context.. and they were frustrated. No… they were beyond mad.
...and they should have been. I became a bit narrow sighted on the text and what the chapter wanted them to know rather than the purpose of why we are rearranging equations. Reflecting on this and my students’ anxiety around it, why was I?
So I hit the pause button. I reframed my lesson in that moment to “how many ways can we see the equation?” It was very much thrown together. It was perhaps too late. It did change the tone in the room. The whys stopped, the anxiety came down a bit, and I was able to have the students drive the discussion again. It wasn’t perfect and I had already caused more anxiety than I had in total ALL YEAR. I’m sure my students are over it now that a block has passed, but I am not. Today will live with me for a while.
It is important to remember why we teach concepts and the purpose of our lesson. In hindsight I would probably bring this lesson into a graphing lesson once they grasped the concept of y=mx+b and gave them a problem that was not in a familiar format (y=mx+b) and posed the question, “hmm… interesting, how do we approach this?” Put a context to why we are reformatting into y= rather than my implied “you’ll see…”
Perhaps I would reformat the whole lesson around “how can we make this equation EASIER” or more approachable? My students get that. They LIVE for that! They’re in middle school. They are constantly talking about how to “hack” the games they play and that is important for them to do. I may even start tomorrow as a refresh. My students appreciate when I retake how I approach something. It shows I am not always exhibiting, nor do I expect, perfection. From anyone.
Teach with purpose and teach with meaning. Students are constantly looking for a meaning in what we give them. Don’t force context because students see right through that and it becomes yet another waste of their time.
MS Math Department Head located in Massachusetts. I mainly work with LBDB students teaching them meaningful mathematical procedures through context. I also look to open students' eyes to the mathematical world around them