Why Teaching?

"Reductio ad absurdum is one of a mathematician's finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but the mathematician offers the game."--G.H. Hardy

When I came up with the idea of becoming a teacher, the reason was a simple, narrow question: why math?

Already I see the answers surfacing unbidden from your own beliefs, whatever they may be. You might point to mathematics as a "gatekeeper" for high school and higher education. You might ask pointedly, why math indeed? You might assert that this nation will require an increasingly skilled and educated workforce. You might believe that the tradition of teaching and learning math is important to maintain.

My original goal was to help others find their own answers, whatever they might be, to that question; to expose them to the fantastic worlds of fractions or fractals, parabolas or prepositional logic, and realms beyond; to demonstrate the power of mathematics as a way of thinking and problem-solving rather than a straitjacket of unmemorable lectures or logarithms stripped of all meaning.

Why math?

"Philosophy is a game with objectives and no rules.
Mathematics is a game with rules and no objectives."--unattributed tagline

I went through my schooling convinced that I would someday major in English or history. Math was the tyrant that demanded that I show all my steps, struggle through endless textbook assignments, and wrestle with unfriendly numbers. If polynomials or permutations had any bearing on my existence, I couldn't have told you about it at the time.

Yet two years into college, I had switched my prospective major from history to computer science or mathematics. I peer-tutored writing for three years at Cornell, reading anything from master's theses in mechanical engineering to analyses of Gulliver's Travels, yet it was my one year peer-tutoring calculus as a senior math major that I chose to explore further.

"Math illiteracy affects eight of every five people."--unattributed tagline

During that time I found that many intelligent people are scared of math, or bored by it, or confused. I also found that there was almost always some way to make the material approachable in a way that, it seemed, failed to happen in their math classes. I grant you that Cornell's student population is already selected in ways that are beyond the means of the average school, but it was my own experience as a former math-hater and as a tutor on both sides of the humanities-sciences divide that convinced me that many more people could be better at math than they realized, and attain, if not love for the subject, a working relationship with it. I started as a math-hater who nevertheless was fascinated by anamorphisms, logical paradoxes, and hyperspheres, and came to love the subject passionately; what, then, would it take to offer this same transformation to others?

"Math problems? Call 1-800-[(10x)(13i)]-[sin(xy)/2.362x]."--unattributed tagline

Why does math intimidate or confuse people? Maybe it's because in many classes, the beginnings of math--the basics--involve hours of drill. Maybe it's because nobody makes the purpose of this drill clear: "Can't I just use a calculator?"--and never mind that some circumstances render the calculator's magic answer useless without analysis on your part. Maybe it's the emphasis on the One True Answer to rule them all--and never mind that the consensus of a mathematical community, not a single teacher's fiat, is the arbiter of mathematical "truth," that mathematics itself has been divided by contradictions and unexpected results such as Russell's paradox or non-Euclidean geometry.

I have gotten self-professed math-haters to show a flicker of interest when I describe Sierpinski gaskets and my own understanding of Godel's incompleteness theorems. I got an "artsy" roommate to look at color plates of fractally-generated "flowers" with wonder. If these people can appreciate the unexpected beauty that blossoms in math, shouldn't mathematical pedagogy, too, reflect this so everyone can appreciate it?

"A mathematician is a machine for turning coffee into theorems."--Paul Erdös

There is also the history of math, the sense of mathematics as a discipline started by various cultures in various times and continued today. Most people I know don't think of mathematicians, dead or alive, as people with goals and interests of their own within a social context. Mathematicians must drink equations for breakfast and chew on theorems for dinner. The idea that mathematics comes into being because it is useful or interesting is often lost in classes where students ask, rightly, Why the quadratic formula? Why plane geometry? Why math?

"The most incomprehensible thing about the universe is that it is comprehensible."--Albert Einstein

"The future belongs to those who prepare for it."--Ralph Waldo Emerson

My answer and my truth is that math, like all knowledge, is power. It is a way of reasoning about the world and illuminating the hidden structures that govern the universe. It is a way to describe anything from the nautilus' Fibonacci carapace to the recursive structure of Bach's cantatas, from quasicrystal formation to fairness in cake-cutting algorithms (a nontrivial task, I assure you). As a corollary, it is a way to predict the world's workings, and hence to direct your own future.

This brings me to the broader goal that has emerged in my year of student-teaching and learning to accommodate the freshman in the Algebra II class, the student who was failing every class but Guitar, the student who never began classwork but showed interest in tangrams. For in answering the simple question--why math?--it seems I have begun to answer the more powerful question, which I didn't know to ask before: why education?

Whatever the discipline, whether it be writing, math, history, or other topics I am still learning about, that is why I teach.

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