I have had an absolutely incredible time at the Park City Mathematics Institute the last three weeks. I will hopefully continue reflecting and have a chance to write more in the future. Today, on the last day of our session “Reflecting on Practice”, on formative assessment, we videochatted with Dylan Wiliam.
He is incredibly insightful about just about everything in education, and we toured through distributed practice, memory, learning styles, rich tasks, rubrics, criteria for success, self assessment, and more. While watching him speak and reflecting on my experience the last few weeks really brought together some of my thinking about my practice, and in particular about my strengths and weaknesses as a teacher.
One of the things I’ve been thinking a great deal about is my experience giving rich formative assessment tasks in my class. I haven’t done it enough, but even so, it has been really difficult for me as a teacher. Almost uniformly, I learn that students who I thought understood very well actually knew far less than I thought, and far more students were completely floundering than I had suspected.
PCMI has felt really similar for me in a lot of ways — it has been endlessly humbling as I have been surrounded by great teachers and great ideas that I have so much to learn from, and constantly exposing myself to new ideas and new perspectives on what great teaching looks like.
For me, one of the fundamental benefits of formative assessment is finding out what students know, really honestly, without skewing the data because I just taught a procedure for that problem, getting deep into understanding, and with as little confirmation bias as possible. This reminder — that as a human being who wants to be a good teacher, I will always be biased around what my students are actually learning, and I need to work constantly to see, from a new perspective, what is happening in my students brains, and what math they can and cannot do. Dylan Wiliam was really articulate about this — and about some of the illusions that fool us into thinking students know when they actually don’t.
I feel like this constantly humbling perspective has been a strength of mine while here at PCMI, really just out of necessity. I have learned so much about mathematics I thought I already understood from Darryl and Bowen’s morning sessions. I have gotten quieter and quieter in Reflecting on Practice as the course moved on, trying to listen more and learn more from those around me, soaking up new ideas and perspectives. In my afternoon working group, I’ve definitely frustrated my partner at times by constantly saying “I put this together, but I don’t like it very much, please change as much as you want” — not that that’s bad, but I think constantly being humbled, and working with an incredibly competent partner, made me think my ideas were less valuable than they were.
Thinking about my takeaways from Reflecting on Practice, it really comes down to one big idea. I want to ask myself, as often as possible and as honestly as possible, what my students actually know. Having the sand to follow through with this — whether I hear what I want to hear from my students or not — is what I need to take with me from PCMI. Everything else is a way to do this better — a perspective on what I can improve about the way I am listening to student ideas, or a tool to get this information quickly and efficiently, or a technique for further probing this student thinking. I am hoping to write more in the coming weeks about some of these tools and perspectives that I hope to come back to over the course of the year, but this, for me, is a concrete goal that I can return to over the course of the year, and make my teaching a little bit better.
This seems simple, but I ignore this information in small ways every day. I don’t look at student work systematically and naturally get a biased view. I don’t give enough tasks that truly elicit this thinking from students in new ways. I give tasks and don’t take the time to look at student work. I call on kids with their hands raised who are more likely to know the answer. I take what a student says and “round up” — deluding myself that they understand when they actually don’t. And I forget that students forget — if they can do it today, that does not mean they will be able to do it tomorrow, or next week, or next month.
To hold myself accountable, I’m setting a reminder for September to give my students something rich and worthwhile that will elicit their thinking, and reflect and write about how it went and what I learned. I hope to make this a habit, but I have so many ideas this summer that I need to focus my attention on some specific, concrete actions I can take that will start to build these skills.