Editor’s Note: Chapter 20, the last chapter, will be out this Friday! This is Chapter 19 in a soon-to-be-ended 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. With the series almost over, the paparazzi are following me, so I’m probably looking forward to its end more than you are.” 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, and Chapter 18.
Chapter 19: An Evaluation, the Red Book, and Checking for Understanding
Marianne, the principal at St. Stevens, would occasionally do informal observations of teachers without notice. I had such an observation about the second week of the school year during my Math 7 class. As she got seated at the desk she was greeted by John, one of my students hiding underneath.
“Sometimes they like to hide from me and surprise me,” I said.
This sufficed as an explanation and gave her a window into how I run my classes. It was a good lesson and on the Data Walk-Through form she was very positive about what she saw. She didn’t mention John’s hiding underneath the desk, but later in the day a teacher told me he heard about it, so apparently word gets around quickly.
A more formal evaluation occurred later in the school year. Prior to the event, I had to fill out a form outlining my plan, stating what standards would be the focus of the lesson, and how I would “differentiate the lesson to meet the needs of all learners”. I had said that I would give the stronger students more complex problems to do. I wasn’t sure whether that would occur in class or part of their homework, but I felt my answer was good enough.
The observation occurred in my algebra class, on graphing quadratic functions. The students in that class were a noisy bunch and quite spontaneous. Earlier that year during a sudden downpour the class cheered and before I could stop them, ran outside to get soaked in the rain, including Lucy my recalcitrant student.
There was nothing to worry about for my evaluation; the students were well-behaved. I had students come up and do graphing at the board as part of the lesson, I asked questions and called on those I knew would have answers, and then called on weaker students who, I was glad to see, were able to answer as well.
After going through the lesson, I then assigned students to small groups. I did this to act in the manner that I assumed was expected of teachers aligned with the educational party line. I paired strong students with weaker ones, and gave each group an equation to graph. I circulated around to answer questions and inspect what was done.
About a week later, I met with Marianne in her office, to go over her observations of that particular lesson. She handed me her written comments while she talked to me about her observation of my class.
“I really thought that was a good lesson,” she said. “They followed the explanations, they were engaged, it was well-scaffolded, and it’s clear that they really like you.”
She offered me more praise and it was obvious from this and previous conversations with her that she thought well of what I was doing. But evaluations being what they are she then brought up her concerns.
“I notice that the textbook wasn’t used in this lesson. How are you using it? Do you use it for homework?”
I wasn’t sure whether she was asking about my use of Dolciani’s textbook or the official textbook. So I proceeded cautiously. “The lesson was actually taken from the blue textbook,” I said. (This is the official one). “I incorporate problems from the book into my lesson and yes, the homework is generally taken from the book.”
I could see that she was concerned over whether we were adhering to the Common Core standards as did public schools. I understood this—it would be bad for business if students graduating from St. Stevens would be at a disadvantage in public high schools. In her mind, sticking to the official textbook meant compliance with Common Core.
And while I had mentioned in my initial interview my extensive use of the Dolciani book in teaching algebra, I discerned that such information had not stuck with her. So I offered further clarification.
“I primarily use the book by Dolciani.”
“That’s the red book I’ve seen students with?”
“Yes. I dislike the blue book; I think Dolciani is much better.”
“But you do use the blue book?”
“Yes; to cover what isn’t addressed in Dolciani—like the lesson you saw, and pretty soon exponential functions.”
“So you’re saying you use the red book as a supplement?” she asked.
I said “Yes” even though I believe we both knew that “supplant” would have been more accurate. But people hear what they want or need to hear.
Our conference ended positively and afterward I read her written notes. She questioned how I checked for understanding, noting that I paired weaker students with stronger in my small groups. How I would assess whether the weaker could have completed the lesson without the stronger?
Excellent question; I had to agree. In acting the way I thought I was expected to act I hadn’t considered that perhaps Marianne disliked small groups as much as I do. In fact, I hate small groups. I took her question as a sign that perhaps Marianne hated them as much as I do. As far as how one checks for understanding, there are many ways. I’ve made a note that next time I’m asked, I will rely upon the ed school catechism that formative assessment is a process not an event.
She also noted that I did not do what I said I would in the pre-observation form; namely give challenging problems to the stronger students. Her recommendation: “More intentionality to provide challenge to those students that need it.” To be honest I forgot that I said I would do that.
She reiterated her concern about the textbook and recommended “Intentional correlation between lesson and text to ensure Common Core standards need for Algebra 1 mastery are adequately covered.” I’m always a bit confused about the word “intentional” as used in education. But I think I assured her that my use of text (both “red” and “blue”) was not by accident.