Since 2005 I have lived in two countries, four states, and fifteen different dwellings (I use the term dwelling so I can include the trailer in a church parking lot and the tent that I stayed in for two months). I bring this up, because for the past week I have been preparing to move again. This move is unique to me, as it is the first time I am going somewhere without explicit plans to leave again. Although I have changed locations so many times, this move is by far the hardest relocation I have ever put myself through – it seems that when it rains, it pours.
But that is not what this post, nor this blog, is about. As a mathematician (who can only think in analogies), I tend to equate everything to mathematics. Such has been the motif for the past week and the focus of this post.
When I got here last Monday, nothing seemed to make sense. I missed California… California was something I knew. There, I could get around with relative ease; I rarely had to look at maps; I had friends and family and a life there. Every day since I arrived here I have oscillated between thinking of this move as an adventure and wondering if I’ve made the biggest mistake of my life. This past week I have felt more lost, confused, and alone than I have in as long as I can remember.
I can’t help but wonder if this is how my unconfident mathematics students feel when they walk into my classroom. I feel safe with mathematics because it makes sense to me and I know how to navigate and control it. But I don’t think that safety is the feeling commonly associated with my field of study. I think that the general gut reaction to mathematics (at least when it comes to those whose response to me being a math teacher is “I suck at math”) is that of fear, confusion, and a general lack of control. It’s not just a question of being bad at math, but being afraid of the mathematical wolverine - the new place outside of one’s comfort zone; an unexplored, dangerous landscape.
Allow me to provide an anecdote to my experience (and attempt to put a slightly more positive twist on this post).
One evening I had to get from where I was staying to a colleague’s house for dinner. I had a plan to bring along a friend with a car, but in the spirit of this crazy week, my plans fell through. With a vague idea of the general direction of where I wanted to go, and a basic understanding of the types of public transportation in the city, I set off towards my destination. I rode buses in the wrong direction, took trains to trains to buses to dead ends, and walked miles when I probably could have gone feet. But in the end, I made it to my goal. I was confused most of the way, not sure if I what I was doing was right or wrong. I didn’t even know what systems I was working in, what was allowed or not, what went where or how to master my own direction, but somehow, against all odds, I made it.
When I got to where I was going I still felt lost and confused, but I also felt a sense of power. I had mastered a route from one place to another. It wasn’t the fastest way, nor the cheapest, but it was a way – my way. My domain was expanded as I could now freely move between two places. This was the first time since arriving here that I felt some semblance of control of my life. I still knew almost nothing about the city, but I knew I could learn and that I was getting better.
If I didn’t know public transportation existed I never could have made it the twenty miles to my destination, and attempting to walk there would have been like trying to solve trig functions on my fingers. I understood the existence of public transportation, so, with enough effort, I could solve my problems.
I wonder how often students walk into a math classroom without an understanding of the rules of mathematics; How many students don’t even know that something exists to help them solve their problem – I bet even less understand the painful and frustrating process of mastering those tools.
I wonder how often we give students a goal when they don’t even know the system they are working in. How often do we miss the forest for the trees? Miss the process for the destination? Miss the tools for the end product?
Navigating Chicago is like mathematics, not because it is built like a Cartesian coordinate system (with Northeast, Northwest, Southwest and Southeast equivalent to quadrants one through four respectively), but because getting around doesn’t make sense until you have spent enough time fooling around, being lost, and screwing up. Only through the arduous and painful process of making mistakes can one really understand how to navigate a new land, be it physical or mental.
you’ll be fine. it’ll be amazing. i already know.
Public transportation in the Chicago suburbs is not what it should be, but it is possible to get around. Into and out of Chicago is fairly straightforward, but point to point in the suburbs is often very awkward. Missing sidewalks is also a major problem for many of the important connections.
To extend your analogy in a direction you may not want to go—a little reading the book before class can go a long way. Spending some time with the on-line route schedules and Google maps can save you a lot of hassle. I don’t know how good the Google public transit routing is around Chicago, but around here it works reasonably well. (When I’ve come back to my family home in the Chicago suburbs, I’ve either walked or relied on my siblings for transportation, with the only public transportation being the train to and from Chicago.)
When the weather is not too awful, you may find bicycling to be faster than public transit, though, even at 20 miles.
Disequilibrium is a sign of new learning. (Gene Meyer, Linda Foreman, and others at the Math Learning Center in Portland, Oregon.