I had two interesting moments in my professional learning this year.
The first was this ignite talk by Grace Kelemanik. It illuminated what it means to reason abstractly and quantitatively, look for and make use of structure, and look for and express regularity in repeated reasoning — practice standards that I didn’t understand very well before. It gave me some new insights into how the different practice standards fit together, and some concrete implications for the classroom. It also helped to spur a project at PCMI on mathematical structure that has helped me to learn an enormous amount about that practice standard, and have continued working on since then.
I don’t want to get too deep into how this talk changed my thinking. What is particularly remarkable is that I was in the room when Grace gave her talk at NCTM this spring. And I forget every word she said within about three minutes. There were other great talks, and hers just didn’t click for me at that time. It wasn’t until I read this great blog post by Dan Goldner, about a month later, that Grace’s ideas started a cascade of insights into my teaching. For some reason, the way Dan framed the talk, the space I was in when I read his post, and my current thinking, set me up for learning — but I wasn’t ready just a month before, with Grace speaking at PCMI. I’m not sure I can articulate exactly why, but that seems to say something important about learning — and in particular, about learning a difficult but extremely important concept.
The second interesting moment happened after PCMI. 75 minutes each day were dedicated to “Reflecting on Practice”, and the theme this summer was formative assessment. I had some conceptions of what formative assessment meant coming in. I had read Dylan Wiliam’s Embedded Formative Assessment over a year prior, and had spent plenty of time reading blog posts about formative assessment, even writing a few myself. But the space at PCMI, the time we had to dive into the topic, and the thoughts of my peers all pushed me to think much more deeply about my practice.
Again, I don’t want to get too deep into how PCMI changed my thinking. After all that, I picked up Embedded Formative Assessment for the first time in over a year, and realized that I literally remembered nothing of what I had learned the first time I read it. And it seemed like every other page, I found some profound insight, clarifying something I had struggled with at PCMI, or furthering my thinking with a pithy idea that synthesized challenging concepts.
In both of these situations, I encountered a resource for learning — some profound wisdom about the teaching of math (or at least that’s my perspective right now). And it just passed me by, leaving nothing of substance behind. What was it about that moment that prevented real learning?
I’ve been rereading another great book recently called Darwin on Man: A Psychological Study of Scientific Creativity. The premise of the book is that the discovery of natural selection was one of the most creative insights in human history, and Charles Darwin’s extensive journals and notebooks provide a unique opportunity to see what was happening in his brain during that time.
It’s a great read, and I’d highly recommend it. My big takeaway from the book is about how, exactly, Darwin came to the realization of the process of natural selection. There was no huge insight, or magic moment. Instead, he started with a great deal of accumulated knowledge, much of it from Robert Malthus. Then he inched his way toward his realization. Reading his thinking over the years he reflected on his trip to the Galapagos Islands, it’s honestly hard to watch — from the perspective of the reader, you know where he’s going, but it seems like he’s taking forever to get there, and building his ideas in tiny pieces and over a ton of time, tiptoeing around what seems obvious to the reader but was clearly an arduous piece of mental work for Darwin.
What Does This Mean For Learning?
It seems to me that the way that most real learning about things that matter happens is extremely slowly, and build up over a long period of time. It’s sure the way most of my ideas about teaching have developed.
I have two questions here:
What are the implications for my students’ learning?
What are the implications for my professional learning.