jumpingfish

It was a long day. Full-periods working on function transformations with the kids. A pep rally after classes before the kids began filing out of the school. Some after-school tutoring to a student who has been working hard to keep up and to understand. Grabbing something to eat before heading to the football stadium for the Friday night game agains out cross-town rivals.

The fair and industrious Trudy drove there after work. The bleachers were full, and I didn’t notice her text. She found the principal, and I saw the two of them scanning the crowd. Trudy had asked her, “Have you seen my husband?” after they hugged. I stood up and waved my arms. 

The associate principal saw me waving, and thinking I was trying to get help, he shouted to see what was wrong. (The admin staff works the stadium during football games, and not much goes unnoticed by them.) I gave him a smile and a thumbs-up to let him know that all was well, by which time Trudy had joined me. I handed her a blue cowbell to cheer the team.

At the half, the Eagles were ahead. After halftime, Trudy and I looked at each other. “Now?” we silently asked. And we got up to leave, because there was still a 30 minute drive home. And because we were both tired.

An hour later, horizontal on the bed, my feet hurt, as they often do these days. I drifted off to sleep wondering if they would still be sore when I woke up. They were, although two cups of coffee helped. But then, two cups of coffee on any Saturday usually can make most things better.

Here’s to Monday!

1. The Question

The room was dark. There were equations and graphs projected on the screen at the front. The students were just beginning to get settled back down from the fire drill.

“Mister,” one of the students asked, “why are you here?”

I forget why she asked that. 

“Why am I here?”

“Mister,” the boy behind her added, “high school students are jerks. Why do you want to teach us.”

I was beginning to get their drift.

“And mister,” a third student said. “Why did you give up a seven digit salary.”

“Ok,” I said. “Let’s be clear. It wasn’t seven digits.”

I did not elaborate. They did not ask further. I stood there and looked out in the dark room with them looking back at me, waiting for me to say something else.

I looked at the equations and graphs and then back at them, and then I shrugged, smiled and threw my hands in the air.

“Oh well,” I said. “It’s Friday!”

And in this way I began to explain why I am there.

2. The Answer

I told them about visiting a friend in college years ago. How I recklessly and pseudo-boastfully told him and his wife and some of their friends that I wasn’t sure what I was going to do after I got out of school — how I was thinking of the Peace Corps. 

They didn’t know what the Peace Corps is. I explained. And then I stopped and looked at my students.

“But I didn’t join the Peace Corps after all,” I said. “I got a job at NASA and later in tech. And at some point I began wondering what it was going to be like when to be 95 on my death bed wondering why I never joined the Peace Corps.”

That made them laugh — not the prospect of joining but rather the notion of being 95 and the notion of being on your death bed. But they laughed quietly, because they understood what I was saying, and because they wanted to know what came next.

I talked about meaning. How I wanted to have a job with real meaning. My explanation continued for a while, circling through tiny Walkerville, Michigan (which one of the students knows!) and my grandparents and how it’s so wonderful to work around young people. But eventually I stopped and said, “So here I am.”

A few of the students clapped.

“No… no…,” I said. “No clapping.”

I turned back toward the screen with the equations and the graphs.

“So. Where were we?”

It was a good Friday.

As Trudy tossed and turned in the pre-dawn hours of the morning, as Charlie wandered around the house dazed and confused, as Miss Izzy tried unsuccessfully to sneak outside to bark at the night creatures, as BBC played on the radio, I was repeatedly falling back asleep. Because… well my wheels are weary.

After the sun had risen and Trudy had made coffee, I pulled myself out of bed.  I slipped into my sandals, looked out onto the backyard and announced, “There’s only one thing I’m going to do in the yard today.” (Only one thing, because there are many first-year teacher things to do today, before next week begins.)

I got the pitch fork from the garage, and I went to consolidate our two compost piles into one, both of them having cooked down over the summer to about half their original 3 foot height.

I pitched the decay from one pile into the other, periodically slapping at the fire ants nipping at my toes. We’ve had a lot of rain, lately, and the pile was wonderfully moist, and frankly mostly finished. Still, I tossed fork-load after fork-load onto the other pile… and then stopped. There was something in the original pile.

I bent over and picked up three Giant Stag Beetle grubs. 

I have mentioned these before. The larvae look exactly like a june bug grub but larger — much larger. If you’re not comfortable with bugs and critters, these are the stuff of nightmares: wet-looking, soft, curled up, with wiggling legs and nasty looking mandibles. They fill the palm of your hand.

I set the grubs on a board and I walked to the screen door. Trudy was in our almost-finished kitchen/dining room putting away dishes in the almost-finished cabinets. 

“Hey Trudy?”

“Hey David?”

“Come look at this.” 

She walked to the door and looked out. 

“Wow!” she said.

Trudy is a cheerleader of critters and bugs, and it’s been a few years since we saw evidence of these. So it was indeed a moment to celebrate: we had not just one grub, but three. She went to get her camera and came out to document the occasion.

Meanwhile, I returned to pitching loads of leaves, but progress was slow. With every fork-load, I found two or three more grubs.

As Trudy walked back into the house, I announced, “We have at least a dozen!” Minutes later, it was two dozen. And then it was more than three.

It was a veritable beetle bomb!

1. Scientists and Mathematicians

I write ‘x’ and ‘y’ on the board in blue.

“Scientists,” I say, “care about these x’s and y’s. They care about what they mean. Given the current time (x), how fast is the rocket going (y)? Given the distance downstream from the dam (x), how many fish are in the river (y)? Given the amount of pesticide (x), how many bees are there (y)? To scientists these meanings of ‘x’ and ‘y’ are at the heart of what they do.”

“But mathematicians?” I say, pausing and looking out at the students. “…not so much.”

“Of course, we will have word problems where ‘x’ and ‘y’ have a particular meaning. Of course, the math only matters if we use it. But as mathematicians, we study the relationship between the x’s and y’s without focusing too much on what they mean.”

“Today we’re beginning to look at linearly related x’s and y’s. Soon we’ll have x’s and y’s that are related quadratically and exponentially and logarithmically. For the rest of the year, we’re going to ask, “How is ‘y’ related to ‘x’? And for that, we don’t really need to know what ‘x’ and ‘y’ mean.”

“Scientists, on the other hand, care deeply about what they mean.”

I stop.

“That makes me think of something…”

2. A Video Clip

“The word ‘scientist’ makes me think of ‘laboratories’. And ‘laboratory’ makes me think of Frankenstein.”

I switch the projector from my document camera to my laptop. 

“How many of you have seen the black and white Frankenstein movie?” I ask.

In all of my periods, only one student raised her hand. (When that particular period was over, I heard her explain what the movie was about to one of her friends as they left my classroom.)

I explain how the story was originally a book by Mary Shelley and how it is a story about creation and the meaning of life and what it means to be human. Then I expand Youtube to full screen.

Thunder is crashing. Lightning is flashing. Victor Frankenstein is standing in his lab coat staring at the ceiling where his creature is exposed to the storm. He lowers the gurney back into the laboratory. The camera zooms in on the creature’s hand hanging limply to one side.

A finger moves. I hear my students gasp. If you’ve seen the movie, you know what comes next. 

Dr. Frankenstein stares closely at the moving fingers.

“Look,” he says. “It’s moving,” whispering so quietly that I have to repeat it to the class. (Since my classroom audio isn’t working, I use my laptop audio which is hard to hear.)

“It’s alive,” he says, clenching his fists and shaking with excitement. And then he shouts (and this is the classic part)…

“It’s alive. It’s alive! It’s alive!!”

At that point, I pause the video. I don’t think the students know what to think. 

“This is a classic scene,” I tell them. “You should know it. And better yet, when one of your friends discovers something (maybe in a science project) or gets excited about something new, you can say…”

It’s alive. It’s alive! It’s alive!!

The median score on the first test was not good. It revealed the extent to which many of my students just weren’t getting what I was trying to teach.

I was convinced that I was doing something fundamentally wrong, despite reassurances from all the other math teachers that this is a common reality we are up against, that it wasn’t my teaching. Hearing that helped, but it seemed obvious to me that I had to do something.

So Friday, we didn’t move on to inequalities. Instead, we spent a third day on absolute values — this time, done differently.

“Here’s what we’re going to do today…” I told the kids. I explained how we were going to work problems together as a class, with each of them coming up to the board to contribute.

As you might imagine, they looked at me in horror. Then I told them how we were going to do it. 

We’d start with the last problem on the sheet they had been working on (mostly unsuccessfully) the day before. One by one, we’d set up each of the problems, working backward thru the list. Our focus was going to be on the set-up part of the problem: we weren’t going to completely work them but rather set them up so that the solving part left undone was something they already knew how to do.

I listed the steps in our (new) set-up process on the board. They were tiny steps.

“The first step,” I explained, “is to copy the problem onto the board. One of you will do that. The others should check that they copied it correctly. And that’s it for that step.”

“The next step is to draw a wide horizontal line and a vertical line under it. Someone else will do that — which is kind of like “art”. And that’s it for that step.”

“The next step is to draw a circle…”

“The next step is…”

Then I proceeded to explain the other microscopic steps. I pointed to the list of steps I had written on the board in the morning. I explained how they would help each student at the board, how none of them would be alone when it was their turn, how we would back them up, how this was not a math performance, how it was a group project.

“We are doing this together,” I said.

Then I called on one of them randomly to kick things off. Then another for step two. Then another. And another. Sometimes the students would raise their hands to volunteer (often for the steps that involved drawing lines, but later for more substantial stuff). Sometimes they would call on the next person themselves. And sometimes the student I called on was too shy to come forward, so I just asked them to tell me what to write from their seats.

It worked. Magnificently.

The classroom was loud. The kids laughed. When they volunteered, they jumped out of their seats. Some of them began to work the problems in little groups so they could be ready in case I called on one of them. They got to choose their own whiteboard marker colors. They got to choose how large (or small) to write. They got to turn and ask for help.

And in each of the six periods that day, with only a few exceptions, every student came to the board (some of them several times) to work on math.

It was a good third day of absolute values.