I feel I am long overdue to write this blog post. In part, this is due to, you know, life getting in the way. In part it is because I have about three posts swirling around in my head right now. Next week our students are taking term finals so I will have a little more unstructured time and I may finally get around to writing more. That is, if I get around to writing plans for the short stint between thanksgiving and winter holidays.
Today, I am going to try and make sense of a fantastic post by Mark Chubb (@MarkChubb3) that can be found here. In the post (which you DEFINITELY should read) Mark raises important questions about the questions we ask our students AND the purpose, the goal, of those questions. I often tell a story about a student who graduated back in 1993 named Ashley. I had the privilege of teaching Ashley for four years in a row up through Calculus BC. The week before her AP exam I asked her how she was feeling. She told me that she was not worried at all because she knew that if she got stuck on a problem she would hear my voice in her head asking her what that problem reminded her of or what have we done in the past when we have seen this. I was flattered that she had internalized some of the strategies we had worked on together and I felt good that she felt comfort in my leading questions that I had been asking her over the years. She was also a tremendous student who was in a group of talented kids who pushed each other over that four year span. Since then, however, I have begun to question myself about the sort of questions I pose. I still believe that most of my students would be able to effectively work through problems they are presented if they can have an internal monologue that is similar to the conversations we have as a group. What I worry about is whether my guided questions are taking away their agency, their ability to discern what they think is important in a problem. I made it through high school math pretty successfully and I have confidence that I can guide students through this journey. But posts like Mark’s, and conversations I have had through this blog, in conferences, through twitter all push me in the direction of making my voice less central in my class. I have taken great strides in this direction in the past few years, but I still feel that I talk too much, that I initiate conversations and lines of questioning too often. That I impose my sensibilities about what to notice and what to wonder about on my students. The trouble is that many of them are happy to have me, and their other teachers, take on this burden. It is easier, it feels more stable and safe to hear the expert in the room direct the conversation. I know that this is not the best strategy but I too often fall into this trap.
I am going to lift a portion of Mark’s post here to draw attention to the central question about questions that I think he was trying to raise.
Funneling vs. Focusing Questions
As part of my own learning, I have really started to notice the types of questions I ask. There is a really big difference here between funneling and focusingquestions:
Think about this from the students’ perspective. What happens when we start to question them?
After reading this and playing back a number of classes in my head, classes that I was really proud of, classes where I felt that my students had made some major breakthroughs, I realized that I do FAR too much funneling and not enough focusing. An easy excuse is that my students struggle in metacognitive processes, so it is more painful and time-consuming to do this. And, just like my students want the more comforting path of me telling them what is important, I am prone to take the comforting role of the guiding questioner. But my students are not going to get better at monitoring and understanding their own thinking this way. They are not going to take ownership of what they feel is important in a problem this way. They can get to be better mathematicians and be more successful at high school math, but I fear that I am training students to be mini mrdardys instead of being better high school mathematicians as themselves.
Our school is moving to a new schedule model next year. We will be on a seven day cycle where in each rotation we meet four times for 50 minutes and one time for 90 minutes. This will force us to re-examine how we run our classes, how we will value and plan for our time together with students. There are many layers of what we will have to examine but for myself, I think that I will be going back to Mark’s post over and over, I’ll be looking at a few classes that I have had videotaped and I will be working out how to hand ownership of ideas to my students. I will be working on how to make sure that the classroom and the class time we spend together is not so dependent on my point of view and my insights into problems. I want my students to leave my class better high school mathematicians, that is absolutely true. But I want them to be better models of themselves as high school mathematicians, not imitations of me. As Ben Folds sang once, I do the best imitation of myself. I don’t need my students to be imitations of me.