When I think about my growth as a teacher, it’s easy to focus on concrete changes in my practice — standards-based grading, visibly random groupings, a problem-based approach to introducing new content. For an observer walking into my classroom today, comparing with my classroom a few years ago, those might be the more visible changes But I think that the biggest drivers of my improvement in the classroom have been incremental changes to some of the fundamental elements of my teaching.
Of course I have to have goals, and everyone has an opinion about what they should look like – EUs, SWBAT, learning intentions, or something else. But the form matters a lot less than spending time thinking carefully about what, exactly, I want students to learn that day, and finding the best ways to get there. And then coming back to a lesson I’ve taught before and felt good about at the time, realizing that an activity is actually not as tightly connected to my goal as it could be, and adapting or replacing it. Beyond tying my teaching carefully to my goals, I’m constantly expanding the scope of my goals for students. Content, mathematical habits of mind, skills of collaboration and communication with their peers, and positive beliefs and dispositions toward math are a few of those, but I’m always expanding and re-conceptualizing what I want students to get out of my class, and changing how I teach accordingly.
The problems I put in front of students are the heart of my teaching. No matter how well I facilitate a problem, no matter how much students practice, if they aren’t doing worthwhile mathematics they aren’t learning very much. I am constantly finding new, more conceptually rich problems to better probe and push student thinking. I model problems to share a strategy or make a connection explicit, use problems as anchors while exploring new topics to link what students are learning with what they already know, and assemble challenging, varied practice that keeps students thinking and applying what they know in different ways while keeping the math accessible and scaffolding success as much as possible. As I assemble and write better and better problems, I expand my vision of what I want for students, and I provide them new opportunities to think deeply about the math we’re learning.
I remember, during student teaching in college, having to fill out a box for “differentiation” in a lesson plan. I wrote that I would walk around the room while students practiced several problems to see if they had questions. At the time, I thought that differentiation in math class was easy. I just give students some problems, see if they can do them, and then answer questions. I’m in awe looking back at the complexity I didn’t appreciate in teaching a range of students, how many other great ways there are to probe what students know, and how hard it is to actually uncover student understanding and adjust a lesson on the fly. I am always developing new strategies to figure out what students know and don’t know and becoming more adept at changing plans, circling back to a tough concept, or leading a discussion targeted at a particular preconception. But most of all, I am always getting better at looking at a piece of student work and, in a split second, figuring out what they know and don’t know and how I can respond in a way that moves their thinking forward while valuing them as an individual.
I feel like I write something like this every year or two, but I also think it’s one of the more important insights I’ve had into my teaching. Getting better at teaching isn’t always a flashy new pedagogy, it’s just as much the small things that add up over time, the small things that I try to practice deliberately every day but always fall a little short of where I want to be. But this stuff is powerful, and it’s iterative. As I set more ambitious goals, I write and seek out richer tasks to move students toward those goals, and I see student thinking in new ways that teaches me to adjust my teaching in new ways. I find new ways to probe what students know and don’t know, realize that I haven’t actually reached the goals I set for students, and design a new task to fill in that gap. This is teaching, for me. This is the little stuff that I love, day after day, week after week. This is what makes teaching such a great profession to spend a career getting better at.