Everybody see that?
You want me to go over that again?
Did I go too fast for you?
Even without context, we recognize these as teacher phrases. These are things well-meaning teachers routinely say to students in an effort to be encouraging and positive about the lesson at hand. There are many more phrases such as these; I am sure you can think of some.
One of my mentors, David R. Johnson from Nicolet High School in suburban Milwaukee, wrote an article, “Every Minute Counts,” and a sequel, “Making Minutes Count Even More.” The articles deal with the nitty-gritty of teaching mathematics. Even the titles embrace an important idea: that good teachers make use of every minute. There is no time to be wasted.
I bring up these articles now because David had considerable insight about these teacher phrases, and I would like to share some of his thoughts with you.
“Everybody see that?” This kind of question is not answerable by a student and teaches them to ignore my questions.
“You want me to go over that again?” They really didn’t want me to go over it the first time.
“Did I go too fast for you? “ No. Faster, faster. Let’s get this done.
“Here’s an easy one.” This comment could be one of the worst things we say. As a student: if I get it right, so what, it was easy; but what if I don’t? Then I know I can’t even do the easy ones.
When I first heard these comments from David, they hit me hard. I recognized the accuracy of his observations. I also recognized these remarks as things I said virtually every day. I tried to change my habits, but it was hard. Gradually, I realized that these bad habits were symptomatic of a larger problem with my teaching. I was still thinking of myself as the person who was explaining math so well that it would be clear to everyone. My classes were still teacher-centered.
It took me a long time, and a lot of trial and error to change what was happening in my class so that students were working on authentic problems that taught them important ideas in a coherent way, while I observed and learned from them how they were thinking and what progress they had made.
The questions that David discusses are all about how well I am doing, not how well my students are doing. I look over these remarks, and it strikes me that all of them assume that it is my job as a teacher to explain, and it is the student’s job to listen and therefore learn. Those job descriptions highlight what is really wrong with these teacher comments. The answers to these questions, these comments, are really meant to reassure me that I am doing well in explaining, which is not the point at all. The real question, every minute of every class, is how well are each and every one of my students doing as they struggle to comprehend the new ideas I have confronted them with today. And the best way for me to measure comprehension is to walk around and listen to what they have to say to each other and look at what they write. Then it is still not my job to explain to them how math works. It is my job to ask interesting questions and then to direct the discussion students are having as they try to figure things out.
A coda: I never would have figured all of this out by myself. We need each other: teachers need students, and teachers need other teachers so that we can all contemplate best models from every angle. I am a pretty good teacher, but only because of the wisdom that has been passed on to me by people like David Johnson.