Intellectual Vindication

There is a certain feeling I get all the time as a math teacher, especially when I’m reading blogs. My colleague and I gave it a name, and it has become a staple of my vocabulary. Here is my best attempt at defining it.

Definition: A person experiences intellectual vindication when they are grappling with an unrefined idea, and they discover that someone else has an elegant and thought-provocative representation of the same idea.

For example …

I decided to become a math teacher math during my senior year of college. I had flirted with the idea a few years earlier, but it only felt real during my senior fall when I started applying for grad schools. Around the same time, my parents asked me what I wanted for Christmas, and on a whim, I asked for some math toys and puzzles to populate my future classroom.

When I was younger, I loved math for all sorts of reasons. I loved the competitive way math was presented, the ego satisfaction of besting my peers, the teacher-approval, the grades, and the resultant parent-approval. I was extremely susceptible to extrinsic motivations, but something always puzzled me: I never knew what I wanted to be when I grew up. I did not know for what future career I was learning math.

Often, I was told that my math skills implied that I should be an accountant. In high school, someone taught me what an actuary was and offered that as a solution. Both paths were lucrative and involved mathematics in some way, but I never really understood how these jobs used mathematics. I understood that they involved numbers, but I didn’t really understand how the math-that-I-loved was being used in these professions.

When I got to college, I experimented. I took economics, computer science, and physics, and in each case, there was something about the application of mathematics that lost its essence. Instead, I saw mathematics in philosophy, in history, in Russian, in LJST. Sometimes I saw more of the math I loved in my humanities and social science classes than in my math classes. These courses asked me to analyze texts, contexts, and subtexts; to make connections between the big picture and the tiny detail; to communicate using specialized, precise language; to be creative and to never be satisfied.

I realized that I love creative problem solving. I find joy while immersed in a puzzle.

And teaching – whether math or otherwise – is one crazy puzzle after another.

But there is one puzzle that just never seems to go away. As a math teacher, I am expected to convince my students that math has a purpose; that we are learning math for something. The “real-world” and career-oriented purpose of mathematics is ever-present. I tell my students that math is creative problem solving not number manipulation, and that math is worthy for its inherent pleasure not its worldly applications. I can say as much, but my argument is too abstract to overcome the anxiety of answer-getting and the dozens of voices preaching college and career.

During my first year of teaching, I did not have a solution to this problem. My teaching style and my philosophies took time to develop, but my toys and puzzles quickly found their way into the classroom. I was worried they would be a distraction, but they have been quite the opposite. I kept finding new toys and puzzles and bringing them into school but I couldn’t quite explain why I was doing it.

About halfway through my second year of teaching, I saw that Dan Meyer – inspired by David Foster Wallace – had the following to say:

“If your students worship grades, they won’t complete assignments without knowing how many points it’s worth. If they worship stickers and candy, they won’t work without the promise of those prizes.

If you say a prayer to the “real world” every time you sit down to plan your math lessons, you and your students will never have enough real world, never feel you have enough connection to jobs and solar panels and trains leaving Chicago and things made of stuff.

If you instead say a prayer to the electric sensation of being puzzled and the catharsis that comes from being unpuzzled, you will never get enough of being puzzled and unpuzzled.”

And just like that, I had it!
In my classroom, I communicate why I love math with an altar to perplexity:

That quote is everything I love about the Math-Twitter-Blogosphere (MTBOS). I started collecting toys and bringing them into class on a whim, but some stranger was able to capture my lifelong experience with mathematics education. I love the MTBOS because I am constantly vindicated in my belief that mathematics is so much more than extrinsic rewards and real-world consequences; math is about creativity and confidence and curiosity, and somehow I found a career that gets to do it everyday.

And with that, I have finished my first post, and officially started my new puzzle: blogging.