A Critical Lens On Teaching

It’s been a great summer of travel, relaxation, and a lot of thinking about math. Park City Math Institute, Twitter Math Camp, and lots of time to blab over here about whatever is on my mind at the moment. I’ve spent time puzzling over problem solving, differentiation, standards-based grading, formative assessment, and much more. And in my reading this summer, one quote keeps coming back to me.

First, the students at Christopher Wren School and North Westminster Community School in London taught me most of what I know about learning. The research I have read and carried out since then has done little more than help me make sense of what I learned there.

-Dylan Wiliam, Embedded Formative Assessment (Acknowledgments)

This really resonates with me. I love talking about teaching, and figuring out new ways of thinking about teaching. But I love doing this thinking because of how much I enjoy being in the classroom and putting it into practice. But being in the classroom is often pretty distant from what I talk about on this blog.

Something I’ve been thinking about this summer is the difference between getting better at talking about teaching, and actually getting better at teaching. This connection is what I want to focus some energy on this school year — bridging the research-y world of math blogs and Twitter, and see how I can use it to impact the quality of my teaching.

“My students were really engaged by Conic Cards.”
This activity is the best way to introduce the Pythagorean Theorem.”
Visual Patterns is amazing.”

I don’t disagree with any of these — but it’s easy to get lost in the sauce of “here’s this awesome resource” or “that stinks” — especially when the conversations are detached from the classroom. What I’m interested in is using a lens to look at what is happening in my classroom, and how I can apply that principle again in the future.

Screenshot 2015-08-20 at 9.52.17 PM

This is the bridge between talking about teaching and actually teaching, and bridging those two without getting lost in generalizations. And this is my goal for the school year — to spend less time blabbing about what I think is good or bad, and instead come to a better understanding and formulation of some big ideas that I can apply in my classroom.

Some Examples

Formative Assessment
I spent a ton of time this summer thinking about formative assessment. My current definition of formative assessment is how I figure out what to do next in my instruction. I can use that lens both to plan my lessons, as well as to say, “hey, that didn’t go well. I need to use better formative assessment to make sure I know what I’m doing.” At the same time, as I put this into practice, I come to a better understanding of what formative assessment means — different types of formative assessment, and better tools to do it with.

Low-Floor, High-Ceiling Tasks
This is a bit less research-y, but it’s a favorite of mine. It’s a great step to take in my planning — to ask myself, “how can I lower the floor on this task?” Then, in the classroom, I can work to recognize when a task needs a lower floor or a higher ceiling, and use that to inform my teaching. And at the same time, I am hopefully coming to a better understanding of the ways to create a low-floor task, what types of tasks fit different situations, and what principles I can apply across a variety of lessons.

Pyramid of Abstraction
Here’s something I threw out a few weeks ago. I felt like I had an idea that brought together some useful principles. It made sense to me, but between comments and conversation on Twitter, I realized that while I knew what I was talking about, different people reading it had vastly different perceptions of what I meant and what the idea could be used for. Maybe it’s not totally useless — but the process of formulating my idea and getting feedback on it taught me a ton about my teaching.

High Cognitive Demand Tasks
This isn’t an original idea, but it’s something I’m still struggling to formulate clearly, and I think has a ton of potential. It’s one of the lenses that I will be working to flesh out this year — to try this approach to teaching in the classroom, reflect, iterate, trying again, and keep reflecting and iterating.


At Twitter Math Camp, Christopher Danielson reminded us — “Find what you love. Do more of that.” This is the process I love. Clarifying or putting forward a critical lens on my teaching, and hashing out exactly what it means and how it can be used to teach a little bit better tomorrow. Some of my ideas will be half-baked, or fizzle out. I’ll misinterpret research, make mistakes, and backtrack. But all of that is necessary to take this talk, and turn it into action.

My goal for this year is to make these connections. To take the high-falutin teaching theory, and see how it can influence my teaching. And see how the realities of my classroom can help me to better understand the broader principles of teaching.

This feels like a pretty big goal. It also feels like a great challenge, and one I’m looking forward to diving into. Summer is ending, bring on the school year!

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