Editor’s note: This is the fifth piece 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, Nonpartisan Education Review, 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.” The previous chapters can be found here: Chapter 1 , Chapter 2 , Chapter 3, Chapter 4.
Ch 5. The Rituals of School, an Unusual Communion, and the Vast Wasteland of Math 8
Each day at St. Stevens starts out with the entire school of 200 students, plus teachers, gathered around the flagpole to say one or two prayers, and the Pledge of Allegiance. I enjoy the ritual, particularly seeing everyone—first graders through eighth—cross themselves in unison. Before I started at St. Stevens, a friend asked me if knew how to cross myself. “Yes,” I said. “But at this point it’s procedural; I think the understanding will come later.”
My days are built on a set of procedures resulting in an ever-changing understanding of where I am. After “flag”, came a quick walk to my classroom, walking fast to stay ahead of the rapidly dispersing horde of students. I call my classroom The Batcave, partly because my classroom is out of the way and cavelike. I have come to love the room and wouldn’t change it for the world.
It appears to have been a storage closet in a former life and is right next door to the gym. It has a door to the gym which sometimes gets bumped by stray basketballs and other objects. Then there is the music that is played during exercises or dance which usually elicits conversation among my students about the songs being played. I squeezed eight desks in the room to accommodate the students in Math 7 and 8.
The Math 8 class was segmented from the rest of the eighth graders who were in the eighth grade algebra class. During the first week, a rather stubborn and outspoken student, Lou, stated what the rest of the class was feeling. “It’s obvious we’re not too good at math which is why they put us in this class.”
I had heard something similar at my previous school from my seventh graders. In neither case did I respond by talking about “growth mindset”. It was the first time I had taught Math 8 and I was rapidly discovering that the course was a vast wasteland of disparate topics that did little or nothing to prepare them for algebra in the ninth grade.
After my Math 7 and 8 classes, came my algebra class—held in Katherine’s classroom since there were sixteen students. Like most of the algebra classes I’ve taught, this one was full of energetic and motivated students. They were also quite noisy and extremely competitive. Unlike the Math 8 class, they had both confidence and curiosity. The difference between the two classes was never more obvious than when I showed a magic trick to both classes.
It was on a day in which school was dismissed at noon (another cherished tradition in which one’s best plans and schedules written over the summer start to resemble a game of Battleship—a day you thought you’d have for a complicated lesson turns out to be a short one). I had performed this trick many times over the years, starting when I was a sub.
Given the following five cards, someone picks a number from 1 through 31, writes the number on the board and erases it after everyone has seen it so everyone but me knows the number.
I then ask what cards the person sees their number on. I immediately tell them the number. The trick is based on the binary number system. One student in the algebra class who is interested in computers knew how it was done so he kept quiet.
I embellished the presentation for the algebra class by having them help me construct a table of binary numbers from 1 through 31, and then transfer the information onto the five mini whiteboards to make the five magic cards.
“You can fill this table out by looking at the patterns,” I said, realizing that any onlooker who happened to poke their head in to my class would think “Oh, good, Mr. Garelick is teaching them that math is about patterns!”—a characterization that I dislike for reasons I won’t get into here.
I started filling out the first four rows; once I got to the fifth row, they started to see the pattern.
“Oh, it just keeps repeating itself: 01, 10, 11, and 100,” a boy said.
“What do the numbers mean?” someone else asked.
“They correspond to the numbers on the left.”
I tried to explain, showing that you’re adding powers of 2 just as in base 10 the number 11 is (1 x 10) + (1 x 1). Some students understood, but most didn’t.
I then said “Just keep filling out the table. It doesn’t matter right now whether you understand what the binary numbers mean.” If the same onlooker who liked my comment about patterns was looking in again, the reaction would probably be “Oh wait; he’s having them ‘do’ math without ‘knowing’ math”. Or some equivalent bromide.
Once all 31 rows were filled, I had five students transfer the numbers to five mini whiteboards. I then proceeded to do my magic trick. The first time I got the number the entire class shouted.
“Do it again!” I did, and got it right again. Each time I revealed their number they were now screaming. “He’s a wizard!” a boy named Sam shouted out.
I finally revealed the trick: “I look at the first number on each card you told me contained your number and then added them up.” I showed them that for the number seven, the first numbers on those cards are 1, 2 and 4, which sum to seven.
There was a collective “Oh, that’s how!” Their excitement was in stark contrast to the Math 8 class who, although curious and amused, took it in stride as just one more thing that didn’t concern them. I had sets of magic cards that I printed up and asked if anyone wanted them. No one in my Math 8 class had wanted them, but the algebra class immediately surrounded me, some with hands cupped as if receiving communion.
During the prayer before dismissing for lunch (“Bless us, Oh Lord, and these thy gifts…”) I realized I had to do something to fill in the vast wasteland of the Math 8 course. I wondered if perhaps I could sneak in more algebra. And for an extra challenge, doing so without the ritual of “growth mindset”.