Day Two: Mr. Feeny

It is nice to see Duncan again.

Duncan is a colleague at my school. He teaches across the hall from me, and I don't think I've ever had a better neighbor. He and I talk for thirty minutes this morning before classes start. I teach him how to use the thermometers I've brought in, and he trades me for a linear equation activity I can do with my classes. “We work together,” he says. “Now I’m hoping you’ll help me out when I have that look in my eyes.” I know the look he means. The shellshocked look. Maybe I don’t look that way, but I certainly feel that way.

Why does anyone think I can teach? Who looks at my resume and my cover letter and says, “yes, that Dudley guy, I think he can do this job. I think he can teach these kids what they need to know.” What sort of process goes into that? Same idea with me and these kids. How can I look at them, barely talk to them, and have them barely answer a few questions, and then say, “yes, these kids can do this. They can learn what I have to teach them.” I suppose education is partially an exercise in blind faith.

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At 11:20, the kids are dying to go to lunch. They are punchy and a bit grumpy. I’ve made them walk around, take measurements, and I’ve introduced them to an ultrasonic motion detector, which determines how far away something is by chirping out a tiny sound wave, waiting for the echo, and recording the time it takes. They had never seen a piece of technology that did what it did; students are shocked to hear that, if you are far enough away, you can hear the echo and the difference in sound. It is especially clear if you're a different distance from the target than the detector is. We have covered systems of linear equations, and everything that leads up to it, in addition to all this playing with the technology. It’s a lot of information to take in if you didn’t know it before, and it’s clear that they did not, except for one.

Student A: she didn’t come yesterday, but she came today, and I can tell she knows a little more than the rest. She has some talent for mathematics, and she also has some of that mental discipline required for the work (attention to detail, perseverance, an eye for little things like the position of an equal sign or crossing sevens and zeroes). Her English is still limited. However, her handwriting is pristine, linear, and predictable. And she is kind. I simply see that she struggles with little mistakes, things that are easy to correct. She shouldn't be here, I think. She's too good at this. I hope in my heart I can help her iron it all out.

At 11:30, I give the kids a system of linear equations to solve. They are struggling, save for A. While I’m showing a couple of students at the end of the circle how to set up the problem, some of the others already have it. A has shown them. Student B, her neighbor, pipes up, “hey, Mister, she showed me too!”. Turns out, she has helped four or five people with the problem.

11:43. Everyone wants to leave for lunch. I tell them, “if I let you leave, you are telling me you’ll be able to do this when we come back.” They say “yes” and walk out the door.

Letting them go: that’s faith.

Before I let A go, I call her attention. “Thank you,” I say. “That was a great thing.” I didn’t need to say any more. The look in her eyes told me she knew exactly what I was talking about. “You’re welcome,” she said, and walked out the door with the others.

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Remember how I told them that I expected them to bring it after lunch?

Well, they brought it. They brought it hard.

I gave the group three problems on chart paper, and assigned them a random problem using a Random Number Generator. My RNGs are ways for students to chat, get up out of their seats, and use math; I get a pretty reliable random assignment out of the deal. Not this time, though. I ask for the students to go shortest to tallest, which they only do moderately well. They did better when I used my hands to clarify what ‘shortest’ and ‘tallest’ meant.

Into random groups they go, with three systems of equations problems I invented at lunch by plotting three points into a line. I did this not by choosing the line first, but by choosing the point of intersection and working backwards by choosing three other collinear points and writing the equations from there. This assured a nice, round, integer solution for the ordered pair. Simple.

Well, not so simple, apparently. The students work in groups and the work is humming. One group finishes early. Very early. They come up with an answer of x = 5/3. “Mister, is right?”

“No, it’s not right,” I say.

“¿Que no?”

“Que no.”

Two of these girls, students C and D, are aghast. “No, Mister, it is right.”

So I check it. And I’ll be damned. They are right! I check it again, and I immediately see the mistake. y = 2x + 2 on the page, when I meant 2x – 2. Ah, well. I immediately get over my pride and default to a Dudley rule: reward good work with harder questions.

“Okay, good, it’s right! Find ‘y’!”

“¡Dios mío!”

My God, indeed. Takes them two minutes.

Meanwhile, at the next group, A and her group are fighting through a problem with an almighty fraction. They know slope. This is not lost on them. However, I taught them what to do with an integer slope (2 = one to the right, two up; one to the left, two down). Using a staircase analogy, I explain that a -1/3 slope is one to the right, three down. This leads to subtracting a fraction from another number, which is another whiteboard explanation in concise English, followed up with a think aloud in Spanish, but eventually arriving at the right answer. I leave them alone.

Finally, at one poster, the group has finished, but one of the group's members has done all the work. I see a solution, but not a graph of their system of equations. I ask for one, and the group member who has done the work is livid. “¡Yo hice todo en trabajo!” I think she says. I repeat the sentiment: “That’s right! She did do all the work. You two do the graphs!” From across the room, two kids look at me with wide eyes, and I say to them, “I learn fast.”

And where does the motion detector fit in? I used it to graph two students walking, and found their speeds using lines of best fit. Then, those two students walked toward one another along a line of meter sticks, and we used a system of equations to predict where they would cross (so long as they walked exactly the same way). Sure enough, they cross just about at the place we predicted. I hear a chorus of "Mister, that was easy." 

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I thought today was going to be rough, but it ended well. My students are learning, and there is proof accumulating on the walls outside the room I am assigned. The proof is student work: problems and the work that goes with them drawn out on chart paper in bright colors. My students sign their names proudly when they are done, and for good reason: they don't want to put it to paper if it's not right.

And you know you’re making it when a student calls you ‘Mr. Feeny’. That is a universal backhanded compliment from students to teachers that has been completely hijacked for good. I was also coerced into buying candy for tomorrow, a request to which I acquiesced because the students making said request knew, for a fact, they did good work. I couldn't say no.