Editor’s note: This is the fourth 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.
4. The Parole Officer’s Check List, the Dielectic of Competition, and Gnarly Problems
Upon starting at St. Stevens, I had completed my two years compulsory Teacher Induction Program (TIP) under two different parole officers, otherwise known as mentors. The TIP process consisted of discussions, observations, and the mentors/parole officers having to fill out an online checklist of items which would serve as the final authentication of having gone through the induction.
My first mentor (who I will call Ellen) told me that she would be making suggestions and giving me ideas, but I was under no obligation to follow any of them. This was good because she had no shortage of dubious ideas and quickly learned that I was going to do things my way. At one point early in our meetings, having determined that I didn’t assign group work and rarely had activities, Ellen asked “What are you going to do about Common Core, which requires activities and group work in teaching math?”
“The Common Core standards do not prescribe such pedagogy,” I said and pointed out that the website for Common Core states clearly that the standards do not mandate pedagogical approaches. I expected an argument, but instead she quickly moved on to other business. The mentors are used to teachers fresh out of ed school who are in their twenties and believe whatever they’ve been told about how to teach and what Common Core requires. In any event that was one response she did not expect that remained unrecorded on the online checklist.
My second mentor, who I will call Diane, was assigned during the second year of my induction. Like Ellen, Diane also had teaching experience—second grade mostly—and was now in charge of the mentor/parole program for the county in which I teach. Like Ellen, she would make suggestions that I could either follow or ignore. She would occasionally evince educational group-think that passed as sound advice.
Our first meeting took place in my classroom. “Tell me about your classes,” she said.
I had two that year: a seventh grade math class (non-accelerated), and eighth grade algebra—the latter made up of students I had taught the previous year.
“My seventh grade math class had a rough year last year so they’re coming in with an ‘I can’t do math’ attitude right at the start,” I said.
“That’s never a good thing,” she said.
“And on top of that, they have significant deficits. Like not knowing their multiplication facts.”
Her eyes widened. “Really? How can that be?”
Actually, it can be and is in many schools across the US. I wondered how on earth she could not know this, being in education as long as she had.
“So how are you addressing that?” she asked.
“I’ll let you in on a secret,” I said. She looked intrigued.
“I’ve been giving them timed multiplication quizzes every day to start off the class. My principal told me that timed quizzes stress students, but these kids love the competition, plus I show them how their scores are increasing.”
“Of course!” she said. “Kids love to compete.” I was heartened at this for two reasons: she wasn’t against memorizing multiplication facts, and she appeared to be going against the educationist dialectic of “competition is bad”. But then she added, “Of course, it isn’t good to do that in the first and second grades because it can stress kids out, but it’s perfect for seventh graders.” A few minutes later when I told her I posted the top three scores on quizzes or tests, the dialectic clicked in.
“Are you sure that’s a good thing to do? Some of the students who didn’t make the top scores might feel left out,” she said.
“They ask me who got the top scores, and they don’t seem upset when I post them, so I’m assuming it’s OK,” I said. She had no answer to that and looked around the room. “I like the way you’ve set up your classroom.”
Diane liked various quotes I had tacked up on my walls; random things uttered by my students that I felt worthy of posting. Like “I never get used to math; it’s always changing.” and “Variables don’t make sense and make sense at the same time”.
I kept the ones from my previous year’s classes on the wall, as well as those from my current students. “Seeing quotes from previous classes gives students a sense of legacy and tradition,” I said. I remember being intrigued when my seventh grade English teacher would show us examples of work done by her previous classes, and we would see the names of students from years past—some were brothers and sisters of my classmates.
I pointed out one quote from a student named Jimmy in my current seventh grade class. It had emerged from a dialogue I had with him on subtracting negative numbers:
Me: You lose 5 yards on a play. You have to make a first down. How many yards do you have to run?
Jimmy: Couldn’t you just punt it?
Jimmy had had a particularly rough time in math the previous year and had very little confidence. The first time we had a quiz I had made sure that the students would do well, giving them lots of preparation. Jimmy did do well: 97%. When I was handing back the quizzes he kept saying “I know I failed it.” When he saw his quiz he was silent and then asked if anyone in my class last year had failed.
“No,” I said.
“Do you think it’s possible that I’ll pass this class?” he asked.
“Yes, it’s entirely possible,” I said.
I told Diane about this. “Fantastic that he got 97%. How did that happen?”
I explained how I was using JUMP this year and how it breaks things down into manageable chunks of information that students could master. Given where they were coming from I felt that building up their confidence was very much needed.
“Are you planning to go beyond just mastery and give them some gnarly problems?”
I was tempted to ask her to define “gnarly problems”, though I’m fairly sure it had something to do with “If they can’t apply prior knowledge to new problems they haven’t seen before, there is no understanding”. But my answer to her was “Of course”. JUMP does in fact provide “extension” problems in the teacher’s manual. I made a note to self which when roughly translated was something like: “Come up with something.” Given the deck I had been handed with this class, I had other things on my mind besides giving the class gnarly problems, however it was being defined.