I took precalculus as a sophomore, which was was unusual in my unified school district but not very. Halfway through the year — over winter break to be exact — I borrowed a calculus textbook and taught myself the first semester. After break I joined up with a class of seniors and set their first semester final exam curve.
Until that point I had enjoyed math in much the same way I enjoyed hearing those chimes upon completing a level of Super Mario Bros. Precalculus was satisfying but calculus was engrossing. That textbook fed me like only my favorite novels have. I'm realizing today — now — how insidiously and completely calculus has infiltrated my teaching.
If you have never found joy in an indefinite integral, you're pre-emptively forgiven for scratching your head over this post. I hope you'll extend me the same courtesy when I say: you're missing out.
Calculus, on some fundamental level, says that we can understand even the most complex systems if we cut them into thin enough slices and stare long enough at the pieces.1 And so it is with teaching, which is, outside of romantic relationships, the most complex real-life system I have ever encountered.
It is so complex, in fact, that many teachers have given up on its inherent calculus and embraced it holistically, emphasizing care over technique, choosing to believe (sometimes passively) in a mystical force (sometimes referred to as "passion") that endows some people with the ability to teach, when, in fact, it isn't mystical. It's calculus.
My recurring frustration with this flaccid line of inquiry and my persistent campaign to de-mystify this job are both derivations of my enthusiasm for calculus. I just can't get into this idea that some people are "called" to teaching when I am struck in the face every day, every class period, by the obvious slices of our job.
To wit, if you slice a great teacher into a hundred parts you'll find a(n):
- clear writer
- discriminating sartorialist
- confident speaker
- commanding leader
- lucid thinker
- pop-culture scholar
- efficient people manager
- savvy organizationalist
- technical craftsman
- eloquent communicator
- graphic designer
- nurturing caregiver.2
- multi-disciplinary, lifelong learner
- emotionally secure individual
- discerning psychologist
- imperturbable emergency responder3
I'm wagering $20 with myself that the first commenter on this post comes by to point out a gross oversight, a glaring redundancy, or a superfluous inclusion in the list. True, we could debate the effect of matching socks and pressed pants on our students' learning outcome but that would be missing the larger point here:
There is a list.
That was a quick brain-dump back there and, though I gladly welcome additions and exceptions in the comments, the crucial point here is that we can cut teaching into slices, that every one of those items positively affects our classroom in varying degrees, and, most importantly, that we can take practical steps to strengthen every one of them.
In my first year, I spoke too quickly. I was nervous. I realized I was dusting my ELL students by jabbering ceaselessly and so I worked at slowing down, at speaking with my pauses.
In my first year, I realized I often phrased my instructions as questions, tossing out weak mandates like "Would you guys please get down to work now?" because I wanted to be liked. I worked at balancing kindness and firmness ("I need you guys to work quietly now.") so that we could work and learn more.
In my second year, I realized that the clothes I wore affected my students' respect for and perception of their teacher, which directly affected how much time we had for learning.
Here, in my third year, I've realized that graphic design is somewhere near the most neglected slice of our profession, that our students — voracious consumers of magazines, professional web sites, and television promos, each and every one — have subconsciously come to expect better information presentation than we've been delivering. Every one of us realizes they're understimulated. Few know how tightly it hinges on graphic design. Fewer still know what to do about it. But graphic design is nothing special — just another slice. We can work on it.
There is nothing mystical or mysterious about teaching. There is only the calculus. There are only the questions.
What are the slices?
How can I improve them?
We have two options as I see them. Any rational individual will find this list overwhelming, even in such an incomplete form. I sure do, and my options then fork.
I can dismiss the list — as well as any idea of a list — and go about my business holistically as usual, keeping my motives pure and my mind open, relying on an emotional trickle-down effect to further my teaching, trusting on the goodness and purity of my intentions to push my professional development. This isn't a terrible or uncommon option.
Or: I can admit right now that success in every slice is an impossible feat, a fact which can be said of very few professions. I choose to revel in that fact, to let that fact keep me bolted to this job in the moments when I start glancing at grad school brochures. Because in teaching, like few other jobs, I know I will never be bored.
Can we talk about the slices now?
- A cylinder, for example, is just many many really thin circles stacked on top of each other. A slightly more complex example is an Egyptian pyramid which is just many many really thin squares stacked on top of each other, squares which get predictably smaller the higher up the pyramid you go.
- That was kind of hard to write.
- [Update: Dig this one courtesy of Lori]