In a recent post, Ilana Horn offers this food for much thought:
I still wonder if it’s possible to adequately capture teaching practice –– in the broad meaning of the word that I know my colleagues intend — through the specification of routine activities.
Once upon a time I had a student tell me, “I want to study enough so that I don’t have to think during the exam.” I responded that my goal in writing each exam is to find out how students think; if they’re not thinking during the exam I haven’t written it well. More broadly, one of my teaching objectives is to move students away from the misconception that mathematics is merely a set of routine activities, to be memorized and then mindlessly executed.
When we talk about the habits of mind that we want our students to develop, can we also consider what habits of mind we value in teachers? For example, how might the CCSSM Standards for Mathematical Practice inform our thinking about the practice of teaching? (Stay with me here — I know this might be a stretch.) Don’t we want teachers to “Use appropriate tools strategically” in their classrooms? This is what I see in the wonderful example of “contextuality” at the end of Ilana Horn’s post. I wish I had a recipe for responding to calculus students with weak algebra skills, but each underprepared student is underprepared in his or her own way, and each set of students is different. I’ve developed a toolbox through practice and reading and consultation with colleagues and so on, but in the end I have to decide which approaches to use and how, depending on the context, adjusting as I get more data.
When I was writing my latest post for the AMS blog, our excellent Editor-in-Chief Ben Braun suggested a few titles. I used one of his suggestions there and another here (thanks, Ben!). It’s not that methods and plans and instructional activities aren’t important; they are necessary. But they are not sufficient on their own, as I tried to argue in my contribution to a New York Times dialog on “scripted teaching.” As many have pointed out, a teacher makes many decisions in the course of a single day. To suggest that all or even most of those decisions could be decided ahead of time is to misunderstand the complexity of the work. Given that we (with the notable exception of, for example, some school board members in Colorado) want to help our students become critical thinkers and flexible problem-solvers, it seems worth considering how teachers manage to balance technique and improvisation in their approaches to the “cultivation of learning” problem.