Last time I wrote I laid out the foundation of why I teach, or at least what I thought those reasons were. With the benefit of hindsight I realize I was so very misguided. My moment of grand realization, this epiphany, occurred during the 2010-2011 school year. I had been teaching Geometry, Algebra I, and Calculus. I had noticed that my geometry had centered around memorizing a whole bunch of theorems. Not in the sense to just regurgitate them, but so that students could apply them to algebraic equations. I told myself that this made me a good teacher. Students criticized me for this style of teaching, but the criticism came in the form of complaints, so I usually brushed it off and kept moving forward.
One day, in my Calculus class, a student simply asked, “Why?” There was no complaining, no questioning of the premise of school, just, “why?” He could have just copied and memorized the procedure, like most students do, but in that moment he decided he wanted to know why the procedure worked. And guess how I answered, “I don’t know.”
That really frustrated me at the time. I had struggled teaching Calculus and I had simply blamed the problem on the fact that I had not spent time with the course for five years. But this time it was different. I started reflecting on the idea that math was just about all the procedures I had accumulated in class. I realized that I was able to DO most of the math problems that came my way, but I didn’t understand WHY the procedures I was using were working. As I spent more and more time reflecting, I came to the conclusion that for me, math was nothing more than a contrived system of rules for students to memorize and apply in the context of math class.
At the same time though, I knew that math was not invented in some vacuum away from reality. I knew that math was and is used by builders, engineers, scientists and many others, so why should it be viewed in school within the context of hoop jumping. Too many students, teachers, and people in general only view math as something that has to be done without any real value too it. I have heard far too many people describe my content as a way to weed out the lazy, stupid, and unmotivated. I didn’t want to be a part of that.
I also had a personal crisis. I had struggled to teach Calculus I. I had a BA in Mathematics. That thought caused some serious cognitive dissonance. What was the purpose of my math major if I couldn’t apply, let alone remember what I had done several years ago? At the same time I was thinking this I had just begun work on a History Masters, which has really transformed the way I view authority, power, and knowledge. I slowly began to rework my math understanding, moving into a realm where math had to make sense. It was no longer enough to get my answers to match the book because the book did not have authority of knowledge. The book only had authority of title. As math began to make sense I started to organically see the applications of the math subjects I would be teaching. I began to view complex math schema rather than a jumbled collection of memorized examples.
As math started to make sense to me, for the first time in my life really, I became very frustrated with my former self. I thought about all the opportunity that I had wasted striving for grades rather than understanding. To this very day I look back at my high school and college experience with regret because I was a label chaser, I wanted the GPA, I wanted the degrees. I achieved them, but knew nothing.
I never want my students to go through that.