Back to School

I'm pretty smart.

I would also say I am intelligent.

I am not, however, brilliant.

By "brilliant," I mean the type of person that learns stuff without anyone ever really teaching them. The Einsteins of the world. The prodigies.

For the last 5 years, I taught a freshman honors geometry course. As much as geometry is my weakest mathematical subject (I'd say trig is my favorite), there were few times I remember a student ever challenged me.

At the beginning, I was... I might not have known the answer to a question right away, or have more than one way to explain a certain concept, but that was due more to my lack of experience teaching the subject matter, and not the subject matter itself.

There was one girl, 5 years ago. She was pretty smart. I start off my logic unit with excerpts from "Discourse on the Method of Reason," by Descartes. It sets the foundation for proof. To me, he is where modern reason begins. I think the piece is beautiful. I didn't tell the kids what they were reading, or by whom, and this one girl raises her hand and says:

"Was that Descartes? Or was that Hume?"

How the hell did she know that? Of course, a pre-High School course on philosophy she took in some program.

That girl was smarter than me. She corrected me a couple of times throughout the year. Nicely. I would remind her it's not polite to make her teacher feel stupid.

Every year, I would tell these kids something along the lines of, "Some of you in here are smarter than me. I really hope you are. Someone has to go out there and cure cancer, do life-saving work. Save the world. It's my greatest hope."

And yet, for most teachers, it is their greatest fear- being stuck in a room with a kid who is smarter then they are.

Two years later, I had a kid who was really smart. Smarter than me. He went out of his way to challenge me, but due to his unfocused nature at that time, he never won. Not just because I didn't allow him to win, but because his ideas were not fully formed. To him, I would say:

"You may be smarter than me, and one day, you may know more than me. But that day is not today."

I am now teaching honors precalculus, and although I am completely confident that some day I will be as knowledgeable about the subject as I became with geometry, it's like starting all over again. I'm writing a lesson that takes me three hours to complete, because I need to refamiliarize myself with the material, think about the best way to teach it, and then plan the lesson. I need to think about what might not be so obvious (like the fact that a "subset" does not necessarily mean a "smaller" set!) but I have to plan extra, because I have no idea about pacing. Which make it look like I never get through a lesson. Which is embarassing.

I started the year with some intimidating-looking notation: set theory, universal and existential quantifiers, and asked them to translate some sentences. Pretty cool, definitely different from what they were used to, but do-able.

One of the statements, which I found on the internet, was a somewhat interesting way of stating the yet unproven mathematical conjecture that there are infinitely many twin primes (two primes that have a difference of 2.) I didn't tell them that this is what it was called, or what the conjecture was. I told them, that for extra credit, they might want to go home, try to figure out what famous theorem (heck, I didn't even call it a conjecture so as not to lead them!) it was, and to explain it to me on a piece of paper.

One young man raises his hand.

"Yes?" I say.
"I think I know it," he says.
"Well, don't tell us, because then no one will get extra credit."
"Can I whisper it to you?"
"You can write it on a piece of paper and give it to me at the end of the period."

At the end of the period, the young man hands me a folded piece of paper.

It says simply, "Twin Prime Conjecture."

Turns out he read a book over the summer that explored a lot of these topics. He named other conjectures. He understood most of them, but not all of them.

The next day, he explained the conjecture and its notation as beautifully as a poet reading a Shakespearean sonnet.

Now they're smarter than me AND they know more than me. I'm in for quite an exciting and humbling year.