Editor’s Note: This is Chapter 17 in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California. He has written articles on math education that have appeared in The Atlantic, Education Next, Education News and AMS Notices. He is also the author of three books on math education. Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd. Thanks to my faithful readers for hanging on. There are only three more chapters to go until the end.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 , Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12, Chapter 13, Chapter 14, Chapter 15 and Chapter 16.
Chapter 17: “Math Talk”, Stalin’s Hemorrhoids, and Murder of Crows
The energy that accompanies the start of the school year begins to dwindle noticeably around Thanksgiving, continuing through the approach of Christmas. It starts up again for a short time in January. Around February or March, when the rains bring tree frogs, students (and teachers) start to sense that spring break is near with summer vacation soon following.
Seventh graders are growing and starting to look like eighth graders. And eighth graders are now looking ahead and becoming nostalgic for what will soon be a big part of their past. It is a nostalgia in advance—a holding on to the familiar at the same time as saying goodbye.
In my Math 8 class at St. Stevens, the holding on to the familiar manifested itself in even more conversations than normal. The literature on math education does not talk much about eighth graders’ conversations. I recently saw an article claiming that “research shows” that students who talk about their math thinking are motivated to learn. In addition, this “math talk” is viewed as a form of formative assessment giving teachers a peek into student thinking and where they need help.
I believe that motivation comes from proper instruction which allows students to carry out the tasks and achieve success. “Math talk” is an effective tool only if the instruction they received allows them to make use of it. Otherwise, it is like children dressing up in their parents’ clothes to play “grownups”.
As far as a peek into student thinking, sometimes the conversations pertained to the math problems they were working on—and sometimes not. But as long as they were working on math, I didn’t mind. Shortly after the tree frog incident when Jared tried unsuccessfully to find the loud croaker, I was putting my plan to teach them more algebra into high gear. I had introduced some simple factoring exercises which Jared found these fun and even said “Invigorating!” as he did them.
We were making fairly good progress with factoring, but when we got to algebraic fractions they got a bit bogged down. I had to continually remind them to factor in order to simplify.
“I don’t like factoring,” Jared said.
“Why? You told me they were invigorating a few weeks ago.”
“That was before they got complicated,” he said.
His friend Kevin chimed in. “Factoring messes things up,” he said.
“Look at it this way,” I said. “When you take algebra next year in high school, you will have seen all this already. You’ll be wondering why you thought this was difficult.”
Mary and Valerie had their own private conversations which would often merge with the others’. One particular conversation and its tributaries comes to mind. Valerie, avoiding saying the word “hell” said “H, E, double hockey sticks.”
Lou reacted to this. “There’s nothing wrong with saying the word ‘hell’. It’s a place,” he said. Discussion followed about when “hell” was permissible to say and when it was not.
“I don’t see the big deal,” Lou said.
“You would if you were Catholic,” Valerie said.
“OK, I’m not Catholic, but I believe in Jesus. I just think Catholics are too strict about some things.”
Kevin chimed in “Well, this is a Catholic school so there are certain things you have to go along with.”
“Hell shouldn’t be one of them,” Lou said though it was unclear whether he meant the concept of hell itself or about saying the word.
Kevin then asked me how to find the lowest common denominator of two algebraic fractions. As I was showing him, Mary, who clearly did not want to do any more work asked, “Lou, if I died would you cry at my funeral?”
“Well, I would be sad,” he said. “But I don’t cry easily.”
“What would it take to get you to cry?” she asked.
He appeared to be in thought. “I don’t know. When my grandmother died I didn’t cry, but when my dog died, I did. I don’t understand why.”
I had finished helping Kevin with his problem, and thought I might help Lou with his. “You don’t always cry when someone dies,” I said. “When my mother died last summer I was sad but I didn’t cry.”
“Sorry about your mom,” Valerie said.
The room grew suddenly quiet; students are listening when you least expect it.
“But then I had a dream about her one night,” I said. “And when I was telling someone about the dream, I started crying.”
“You probably cried because you knew you were saying goodbye,” she said.
Which, unbelievably was what the dream was about. I had to go somewhere but couldn’t take my mother with me so I had to say goodbye. There was no need to mention that so I didn’t and conversations returned to less somber topics—in particular, the history paper Lou was writing about Stalin. “Stalin died from hemorrhoids,” he said.
“How can you die from hemorrhoids?” I asked.
“I assume that will not be covered in your history paper,” I said, but his answer was drowned out by a noisy chorus of crows in the tree outside.
“Can I chase the crows away?” Jared asked.
“Stay seated,” I said and shut the door to the classroom.
“The door won’t block out the sound,” Jared said.
I shut the door and the crowing stopped. I said “Do you hear them now?”
Never at a loss for a rejoinder, Jared said “The motion of the door scared them away.”
“Do you have proof of that?” I asked.
He didn’t answer.
“I’ll take that as a no,” I said.
“Can we play hangman?” Jared asked.
“If you’re all finished with your math problems.”
“There’s only two minutes left of class,” he said.
I gave the go-ahead, and Lou and Jared jumped up to put their hangman challenge on the board. I realized at that moment that I had grown quite fond of this class, and that our little rituals were starting to feel like we were saying goodbye.