When 2 + 2 Doesn't Equal 4

I love the act of critical thinking and pushing my students to think further. I almost don't care what they're thinking about, as long as they're doing it, since, in my professional opinion, teenagers are fairly adverse to the act. The instant response to when I assign something that requires legitimate thought rather than performing a mindless task is for them to complain that it's "unfair" or "makes [their] head hurt." When my students fail to see the value in thinking, I am pained. To me, education is about activating those muscles, learning and practicing how to think critically later in life. I will consider my job successful if I've produced students who are capable of thinking and questioning at higher levels outside of academia; ultimately, whether or not they've developed an affinity for Poe is irrelevant to me.

In class, I will often state multiple times that there is more than one correct answer so that my students won't settle for the first correct one I hear. It's disheartening when I see a student erase their equally correct answer for the example I provide, as it shows that these kids see no value in a response of their own. Still, no matter how hard I work to champion an individual's input, ey'll always abandon eir own creations for the one I told eir neighbor was correct.

This fact doesn't dissuade me from trying. On Thursday, after I repeated yet again that multiple answers would be acceptable, a student asked "Is there ever a time when there isn't more than one answer?" I smiled when ey asked me, because I relish any opportunity that a student challenges me to think beyond the realm where I have a ready answer; it probably has something to do with the fact that I enjoy learning more than teaching. "That's a really good question," I said while pausing to think. "I suppose there's often only one answer in math." My reply sat for about five seconds before the student retorted that that wasn't true. Another student that antagonizes the first student said, "When does 2 plus 2 ever equal anything other than 4?" The first student retorted, "Well, you could also say 2 + 2 = 6 - 2." The student was absolutely right, and I was consequently floored. I told the student that I agreed and appreciated em provoking me to think. Though it was entirely sincere, I'm not sure most of the students grasped that, since being made to think is not a worthwhile pursuit for most of them. The second student jumped back in to ask, "Okay, if your math teacher asked you what is 2 + 2, and you wrote down, 6 -2, would that be correct?"

Well, no. But yes. Yes and no, really. The idea that one answer might be inherently more correct than another is an interesting concept; while I can't deny the validity of the first student's answer, there is much truth in the second student's retort. Their brilliant perspectives have given me something to ponder a lot since then, and it excites me again to see that they are capable of thinking.