One of the most worthwhile tasks I was asked to do in my graduate course work was write a detailed investigation of the history of mathematics, along with a personal statement detailing my own philosophy of math. My "What is Math" paper is still my baby- that paper you've moved from laptop to flash drive to laptop (to iPad). Maybe it's the sentimental memories of my roommate's dog peeing on my library books in the wee hours as I wrote. Or the fact that my entire thesis was based around the fact that I've seen the movie Inception too many times (more on that later). Somewhere along the line, though, this became what defines me as a teacher.
So what is math? My investigations led me to some great books and some interesting theories. To anyone interested, Joseph Mazur's Euclid in the Rainforest seemed the most reader-friendly for those who didn't decide a theoretical math degree was the best path into teaching (I mentioned I LOVE math, right?). Hours of Diet Coke, dance parties in the School of Education computer lab, and mindless babbling to my poor boyfriend later....I was struggling with putting my own theories of mathematics into words. They say the best cure for writer's block is to get your mind off it....so I put Inception into the DVD player and cuddled up with the aforementioned roommate's dog (this might explain the incident that ruined my reputation at the library). And there it was....
"Well, imagine you're designing a building. You consciously create each aspect. But sometimes it feels like it's almost "creating itself", if you know what I mean...Genuine inspiration, right? Now, in a dream, our mind continuously does this. We create and perceive our world simultaneously, and our mind does this so well that we don't even know it's happening. That allows us to get right in the middle of that process."
I grabbed a pen and started writing....
"I believe that at its core the subject of mathematics represents the study of relationships. It is simultaneous perception and creation, which function in an endless cycle. The more we perceive relationships, the more mathematics we are able to create.The more mathematics we create, the more we are able to perceive new relationships."
This has become the way I view my own learning and the way I teach my classes. By studying relationships and patterns, we are able to make conjectures. From these, we are able to perceive new relationships and new patterns. And it's one of the reasons I love my job....getting to see the genuine problem solving and sense of curiosity present in my students each day.
So think about it.....what is math to YOU? It might just change how you teach!