jumpingfish

#silentsunday

1.

It was the beginning of seventh period. The tardy bell was about to ring. Reginald came into the room. What was he doing here? He’s in second period.

“Hi Reginald. What’s up?”

“Well… what do you have for me today?”

He had a smirk on his face that stayed glued there. 

2.

Reginald is a bright student. He grasps the algebra almost before I finish speaking, sometimes completing my sentences. A few weeks ago, he proudly showed off some work he had been doing with limits. He’s hungry for more than algebra, so we work together a few times a week.

After it was clear that he had a solid understanding of limits, we started discussing derivatives. He had heard of them, but not in the way I had in mind. I taught him the definition of derivatives in terms of limits. We worked an example together. He ate it up. Then he did one on his own. And another.

I gave him an assignment. “Come back and show me what you find.”

3.

The next day he was back, going on about Taylor series and showing me his cosine and sine expansions.

“I’m not sure what this means,” he said, pointing to factorial terms like 2! and 4! in the denominators of some of the fractions. So we talked about them. And then we talked about taking the derivatives of the terms in the series one at a time. And then we were out of time.

“Take what you understand, and see if you can figure out what the derivative of sin(x) is.” I gave him a couple hints and jotted down some things on a piece of paper which I held out to him.

“Oh I don’t need that,” he said. He had already absorbed it all.

4.

When he returned, he held out a sheet of paper where he had written the series expansion for sin(x) and taken the derivative of each of the terms and done some factoring. At the bottom of the page was his result: the derivative of sin(x) is cos(x).

The next time he came back with the derivative of sin(-x). And with very little prompting he was soon calculating the derivatives of sin(kx) and sin(-kx) and cos(x) and cos(-x) and cos(kx). And I was running out of things for us to talk about. After all, I just teach algebra. 

5.

So there we were. And when he asked, “Well… what do you have for me today?” with a smirk on his face, waiting for me to serve up the next calculus lesson, I was prepared. 

We sketched some things on the board. I gave him the assignment of finding the derivative of sin(x) without using the Taylor series expansion that he had become so adept at manipulating. I suggested that he look it up online, figure out all the steps, and then come back and teach it to me.

“Hmmm…” he said, evidently intrigued at the notion that there might be another way.

It didn’t take long. He came back to report the results of his researches. 

And now I really am running out of things to discuss. I don’t have the time. I think I’ll introduce him to hyperbolic trig functions, sinh(x) and cosh(x). Maybe that will win me a week or so.

Arly is a good artist. She comes into the room with amazing work. She usually works with a blue pen, drawing cross-hatch sketches of eyes and faces and renditions of people that any of us would frame and put on the wall. She keeps them in a notebook.

“Will you draw me one some day?” 

“Yes, Mister,” she said, smiling that wonderful smile.

That was a long time ago. And then last week she came into the room and said that she had one for me. It wasn’t a sketch. It wasn’t torn from her notebook. It was on fancy paper, painted with acrylic.

As she stood there, I taped it to the growing gallery of student masterpieces beside my desk.

And after the year is over, it will be in a frame on the wall at home.

“Mister,” she asked after she finished the test. “Can I use your charger?”

When they ask this, I say to hook their phones to the cable that’s plugged into my laptop. The unspoken implication is that they have to leave their phones on my desk — far from where they sit. After they squirm for a few seconds, I show them my chargers. 

“Take one of these,” I say. “You can plug it into the socket under your desk.”

That is what she did. But then a few minutes later she came back. “Thank you, Mister,” she said, setting my charger on the desk.

“That was fast,” I said. “I thought my charger is slow.”

She smiled slightly and walked back to her desk, where one of her friends reached into their backpack and pulled out a different charger. A faster one.

“I see how it is,” I said, laughing.

Old man. Old charger.

She used to be a student of mine. She struggled with the class. A few times she came in for tutorials, but the amount of material she hoped to make up was just too much.

She had a really hard time. Still, every day she would smile when she came in. But it must have been miserable, the kind of thing that people have nightmares about well into adulthood.

What do students think of their teachers in classes like these? It can’t be good, right? 

But today during lunch, she pokes her head in the room and says hello. She is smiling as usual. I call out her name. She takes long strides across the room. 

“Mr. Hasan,” she says as she walks toward me. “I remember you were in aerospace. I got accepted into fight school. I’m going to be a pilot.”

I guess the smile on her face was genuine.