To teach the right answers for the wrong reasons/my own experience is not for all seasons

(With apologies to T.S. Eliot…)

My students sometimes ask if I actually like math, or what brought me to be a math teacher. I have struggled to answer, and for a long time I thought it was because I actually didn’t like math. But that’s not quite it. I didn’t want to share because I understood on some level that what I gathered from my years of success in math classes was not at all what I wanted them to gather.

What drew me to math is precisely that quality that most people ascribe to it: it’s very neat packaging of the complexities of the world into some lines of scratchwork, terminating in a simple and correct answer.

I was very good at this. It was also bullshit.

I got some hint of this in college, when procedure or example pronblems could no longer guarantee success. I learned dramatically the need for a more open-ended, heuristic approach, which usually went hand in hand with group work. Sure, there were still right answers, but the path to them was not linear, and was not supported by faithfully copying every word uttered in a lecture, either.

Right answers even become dubious in the lauded “real world” problems so commonly proposed in math education. True, in as much as math models the world, you can model more or less successfully, and this is central to all kinds of endeavors. But the path there is not a path you can follow by rote, so much as one you must create by walking it. It is a creative act, both in that you are making something new, and that you are pursuing your own authentic approach in doing so. 

In this way, mathematics is as intuitive and subjective as any creative form. Because it can model the world, it has some value as a clarifying tool, and its basic tools (number, shape, pattern) are such ubiquitous tools to human thought that we can speak of their objectivity. But this is true of the humanities as well — equally subjective and objective, equally intuitive and intellectual, equally individual and communal; and completely, fundamentally creative.

This practice requires a classroom characterized by fruitful disorder, skillfully channeled; conjectures that are open to constant revision; and my student talk, thoughts, and attitudes being the engines that drive the class.

But this is not why I became a math teacher! I became a math teacher because I remembered loving its false order and its neatly packaged right answers! But what I found when I was a math teacher long enough to catch my breath and look around was:

  1. The surprising diversity with which students can understand any topic no matter how simple I assume it is: from trigonometry to linear modeling to fractions to multiplication, if you have 25 students, you have 25 ways of understanding and expressing those concepts. I’m still be surprised by the insights and ingenuity that even my most struggling students can share.
  2. The baffling resistance that students will put up to even the most simplified expressions of some idea. This can be interpreted as some kind of childish willfulness, or it can indicate that there’s something lacking in the approach. While the habit in our field is the former ( the so-called deficincy model of teaching, conveniently pathologizing the child), I think the latter is more generous and closer to the truth.

Both of these contradicted my model of Math-as-Truth-with-a-capital-T. There was more diversity and complexity than I expected, and when I tried to push those differences aside, it only created fruitless anxiety — for both my students and me.

So my idea of what I’m doing and why it’s important has changed — but habit lives in the body, and is not so easily moved. It is not unlike an emotional/psychological defense, which had its place in its time, and must have helped me at some point, but has outgrown its use.

Luckily, habitual patterns can be addressed with practice as well. Intentional, mindful, even humble practice. As often happens, my students are my best teachers, revealing the emotional patterns that I long ago learned to suppress or manage. They will learn to manage them as well, but this can be done a way that affirms their authentic approaches to thought and creativity. Listening to them, giving due dignity to their thought process and their feelings, they can be cultivated for self-possession, a confidence given naturally and not reliant on any correct answer, and found again and again within the support of a community.

That’s a math class, right there. As a math teacher, my role is to embody that practice while handling the tools of mathematics. Even in the most supportive professional environment it can be hard to remember and to return to that practice, because it is at odds with what I value as a math student.

The hardest thing about teaching math isn’t the students, or the math. It’s getting out of my own way.

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