Editor’s Note: At long last!! This is Chapter 20, the last chapter in this 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: “I thank all my faithful readers for staying with this til the end. The book will be out in the fall. That said, there will be no book tour.” 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, Chapter 18, and Chapter 19.
Chapter 20 Out on Good Behavior, and a Final Narrative
My meetings with Diane during my second year at Cypress had taken place once a week, initially at a coffee shop near the school. When that proved to be too noisy we moved to my classroom. The day finally came when all electronic checklists had been filled out and discussions ended.
The potential for ending our discussions reminded me of a conversation I had in the Math 7 class regarding how you cannot divide by zero, nor zero by zero. I asked about the latter. Someone said “It’s zero”. I said, “Yes, that would be an answer.” Someone else said “two”, another said “seven” and others threw out numbers until I said “There are lots of answers which is why we call it indeterminate.” I overheard Jimmy whispering to a classmate: “We could have kept this going for a long time.”
This struck me as a fitting description of my talks—first with Ellen and then Diane—which, like the mathematical concept of zero divided by zero, seemed to be indeterminate. On the one hand they were meant to help me be a better teacher. On the other the discussions were often fueled by a chain of misconceptions and ideologies built on the magical thinking found in most ed schools. And they could go on for a long time.
But all that was ending at long last. The principal joined our final meeting which Diane started by saying “This has been quite a year for you. The seventh grade class really gave you some challenges.”
“Yes, they did,” I said. “You can lead a horse to water, as they say. But I think some of them drank it.”
“You weren’t just leading them—you dragged them to the water. Kicking and screaming,” she said. This was an exaggeration of course, but it was in my favor so I let it go.
“Any words of wisdom for us on the mentoring process?” she asked.
I’ve had the “any words of wisdom” question asked of me by HR people as part of exit interviews at other jobs I’ve had. It’s one of those questions where they want to hear good things, but are willing to take their lumps.
“I know we didn’t always agree on things,” I said.
“Yes,” she said. “It’s been interesting You’re certainly not what I expected when we first met.”
Which was probably true. I’m definitely not someone in their twenties right out of ed school. And while I had successfully avoided getting into knock-down drag outs about things like “productive struggle” and “differentiated instruction”, I did feel bad about some of our disagreements and how I had expressed them.
“In any teaching situation there are going to be people we don’t agree with,” I said with a bit of hesitation. I wasn’t sure where this was going to end up—a not unfamiliar feeling for some of my math lessons.
“Maybe we don’t agree with the way they teach or their philosophies about education. But somehow we all have to get along—we have to make it work,” I went on. “And even though I disagreed with you on some things, there were things that I did agree with and which were helpful. So that’s what I’m taking away from this.”
I don’t know if she viewed this as an apology, but I intended it as one. I could tell she meant well for me, and she had a good heart. She seemed pleased with what I said.
We then moved on to other business, signing papers, and getting instructions on how to retrieve my final teaching certificate from a certain website. And then a picture of me holding my certificate of completion.
And that was that. I was now out on good behavior as a fully credentialed teacher, free to continue putting into practice my ideas about teaching math. Free, that is, to the extent possible with having to attend PD sessions that are about engagement but pretend to be about instruction. Or hearing teachers talk about particular students’ learning styles. Or having discussions about how to instill students with a growth mindset, or being asked how I differentiate instruction in my classes, or being exhorted to engage students in productive struggle and, of course, having to be intentional. And above all: getting along with others.
I’ve been out on good behavior for over a year now and am tremendously happy at St. Stevens. As of this writing, I just completed my second year there. In keeping with my “We all have to get along” apology to Diane, I keep my views to myself.
There is the occasional PD that I have to attend, but nothing as bad as what I’ve had to endure in the past. I hear teachers talk about blended learning and intentionality and growth mindsets now and then, but we all get along. And based on my evaluation from the principal, they’re willing to look the other way.
I’m also pleased to say that Lucy, my algebra student, took algebra again in high school and got A’s all the way through. I recall during the final exam in my algebra class, she asked me for help on a point slope problem. It asked for the equation of a line passing through a point, and perpendicular to a specific line.
“I don’t know how to do this,” she said. I allowed them to have a cheat sheet and I pointed to the point slope formula that was on her cheat sheet. It was clear that my lesson deriving that formula didn’t stick with her.
A few minutes later I came back to see how she was doing. She was crying.
“Oh, you’re upset,” I said. “What’s the matter?”
She pointed to her answer to the problem.
I looked at her work. “It’s correct! You got it right.”
“But it doesn’t make sense,” she said.
I’m fairly sure she thought the problem was asking for an ordered pair of numbers. Getting an equation for an answer – well, it didn’t fit her narrative, so to speak.
And as long as we’re on the topic of “narrative”, and also in the spirit of getting along with others, I offer my readers a choice of narratives that this episode represents, with varying nuance:
1) Understanding always trumps procedures.
2) It’s all part of formative assessment.
3) At the novice level students focus on the procedure. Sometimes the understanding will come later. And for some, never.
4) Teach understanding as best as you can but don’t obsess over it.
There are probably other narratives, but I’m somewhat new at this and therefore take a rather narrow and un-nuanced view of the world. So I will leave it to my faithful readers to add their own. Just don’t tell me about them. I’m happy in my ignorance and from what I hear, doing just fine with what I know.