One of our first assignments for the Math Methods course was to write our own “Math Autobiographies.” The assignment, at first glance, was seemingly simple and straightforward: recall your experiences in math through elementary, middle, and high schools and through the present, keeping in mind teachers’ styles, pedagogy, difficulties encountered, etc. As I traced my experience with math back through time, I found that I had very little – if any – recollection of any math teachers or for that matter, any math classes. I could recall general memories of elementary school and high school days, but nothing much to do with math (save for the difficulties I encountered with algebra and calculus and my enjoyment of geometry). My difficulty with remembering my experiences with math was disconcerting.
Upon deeper reflection on my current, adult experience with math, I realized that I have two “versions” of math: purely theoretical or abstract and strictly practical computation. When I think about my adult experience with math, the greatest portion is in computation: how early do I need to wake up to get to work, balancing finances, taxes, the occasional measurements when I decide to build or repair something, etc. etc. etc. The other portion is theoretical but has little practical use (e.g., again, see Numberphile’s YouTube video, “Infinity is Bigger Than You Think”) or purely conjecture and wondering about questions that address quantities (How many blades of grass in my backyard? How many insects does a single bird eat in a year? How many pieces of kibble in my dog’s food bowl per meal?). These musings have little noticeable practical purposes, and it is extremely rare that I attempt to find answers to these questions. But I wonder if these types of inquiry do have a place in classrooms, and, if so, to what purpose? (And again, that practical-theoretical dualism returns).