The Duality of the Math Teacher and Student pt 2: superposition

When I was a junior at the Academy, I was taking a Trig test.  It was going ok.  Not great. not terrible.  At the end of the test was an extra credit question.  It was a complicated bit about a helicopter hanging in the air.  It was all distances and angles.  Your classic trig problem.    I was never a gifted math student, but ok. I was getting it for the most part. And then I got to the extra credit question. At first it looked relatively straight forward but try as I might I couldn’t get the answer. The period ended. I handed in the test. Throughout the day I kept thinking about the question. And then throughout the evening. Eventually after working on it for a while I figured it out. It hurt my brain, but I figured it out. By this time is was late evening. I called my teacher’s house to see if I could still turn in the problem.  He was at some board meeting and wouldn’t be back until late. I woke up early to get  to his office before his first class. Asked if I could hand in the question feeling very proud of myself, but a little chagrined for trying to get extra credit the day after the test and left. Fast forward 15 years later what I understand now that I didn’t then is students do this all the time. I probably wasn’t the only student to try that on that very test. They all try to pull this stunt and it’s usually almost always useless. So I can easily imagine what my teacher thought. I kind of want to track him down and let him know that this time it was different. This time it was important. This was one of the few moments in my life where I felt a true sense of accomplishment.

I also know why he didn’t reject my extra credit answer.  It had nothing to do with my pathetic supplication or about my personal relationship with the teacher.  Students always believe that the teachers like the best students the best.  It makes a kind of intuitive sense, but that’s actually not true.  Teachers best like those students who try their hardest.  Generally speaking effort and success go hand in hand so this misperception on the part of the students is understandable.  This was my misperception.  At the time I thought I had just gotten lucky.  My relationship with my math teacher suffered from my laboring on the misperception that I was bad at math.  As a result I never really put in the amount of effort it would have taken to truly excel.   It’s true that I have no special talent in Mathematics just as I hold no special gifts in sprinting, painting, crochet, and a host of other things, but math is a skill like any other.  To quote Ruskin, “I know of no genius other than the genius of hard work”.  The vast majority of people can become competent in math given enough effort and motivation.  In that moment I was putting forth considerable effort to stretch my mind and that is what every teacher is looking for in his students.  So he rewarded that effort.

Today imagine my state as the superposition of the math teacher and the math student.  When I was a math student I never considered the possibility that I would teach anything — let alone math — and be good at it.  Part of me is still 16 and still trying to impress people with the least amount of effort humanly possible.  That I was trying to do this with math does not speak well of my overall intelligence.  The larger part of me is 31 and trying to help students expand their minds just that little bit further because they’ll need to in order to meet the challenges they’ll be facing.