“Mathematics is equipment for thinking”

Francis Su,Mathematics for Human Flourishing, p. 110.

The sun sets around 5:30PM this time of year in my little prairie slice of paradise. Yesterday, well after dark, there was a ring of the doorbell and a package delivery: My copy of *Building Thinking Classrooms* by Peter Liljedahl. Over the last couple weeks, I have watched as tweeps^{1} sent messages of exhilaration having received their own copies. The, now familiar, orange cover adorned with the beautiful illustrations of Laura Wheeler is a welcomed sight on my Twitter feed, each time accompanied with excited messages you’d expect to hear from children anticipating a visit from the Tooth Fairy.

Honestly, holding the book felt weird. I say that as a testament to Peter’s work: It draws you into participation to the point where it feels like it’s a part of your history. In my case, that’s because this book *is* a part of my history. Receiving the book sponsored a sort of nostalgia, as I’m sure it did for so many who have followed the ideas as they’ve developed over the years. This feeling surprised me, because, despite the real feeling of connection to the physical copy of the book and the brand of teaching it represents:

*I don’t run a Thinking Classroom. *

That statement comes with three qualifications.

First, I attempt to forefront student knowing in my classroom *at. all. times*. However, I don’t employ–with persistency–all fourteen practices that are detailed in the book. Sometimes the structures catalogued in the book are employed, sometimes tweaked, and sometimes deliberately abandoned. Some of them (vertical non-permanent surfaces (VNPS) and visibly random groups (VRG), for example), I experimented with as a young teacher unaware that Peter was systematically doing the same a few provinces westward. The fact that we arrived independently at similar conclusions about their impact on student action speaks to their effectiveness.

Second, too often I’ve seen the complexity and nuance of a “Thinking Classroom” simplified into: any class with students standing at whiteboards in random groups. (Both pieces of what Peter calls, “Toolkit #1”). This reduction misses the potency of Peter’s work, and somehow belittles the art of teaching Peter so masterfully espouses. Sure, these practices stick out like sore thumbs from the expectation of neat rows of desks, piles of note packages, and graffitied textbooks; they can even be disorienting when first encountered^{2}. However, those structures do not teach; they amplify potential teaching moments. We, as teachers, still need to harness them, and *Peter develops many ways to do so in the sections of the book*. And so when it is proposed that I run a “Thinking Classroom,” I am always careful to interrogate what the proposer has in mind, because I think we have the responsibility to ensure that the term “Thinking Classroom” doesn’t strictly refer to the structure(s) of VNPS and VRG and leave the *teaching* behind.

Third, Peter encourages this teacher autonomy.

“This is not to say that you must implement each optimal practice exactly as stipulated in the chapter. These practices are a framework that is meant to come alongside your current teaching experience.”

Building Thinking Classrooms, p. 17

As mentioned previously, the ability to welcome us into the work is one of its major strengths. This post is not designed to denigrate the colossal importance of the work. *Here, I want to think deeper about why the work is so important*–why holding the book sponsored the reaction it did. In a way, it is to expand on my heartfelt recommendation of the work, which was published just inside the front cover^{3}.

And so, if you’ll permit me to diarize for a moment, let me tell you about the first time I met Peter…

I was a zeroth year teacher, just finished my degrees in mathematics and education from the University of Saskatchewan, and had yet to teach a day, save for my experiences during my extended practicum. Peter came to Saskatchewan to speak at the Saskatchewan Understands Mathematics Conference, and he had us work on a task called “Race Around the World,” which you can find on his website.

At one point, he approached my work. He questioned the times I’d recorded in a fictitious itinerary, and then asked for clarification about a specific flight I had booked over the International Date Line. I responded that for the people on the plane, time was experienced as normal, but time was frozen for everyone else. He responded: *What was everyone else doing on the day when time froze?*

*I was hooked*.

It took one sentence, but I had never been more conflicted. I *knew* my thinking was solid, but also *knew* that it could not be the case that earth-dwellers ceased to function during that 24-hour leap in time. All these years later, and I still distinctly remember that one moment–a moment when I was thinking mathematically. Worth noting: I was working horizontally, by myself, on a pad of paper that was woefully permanent. But it didn’t matter. Peter got me thinking, and it has, arguably, continued ever since. Years later, I still look to this moment as one with the formative capacity to shape my career. It may very well have been this moment where I became obsessed with anticipating, inviting, observing, impacting, and assessing the mathematical actions of youngsters. Such is my connection to Peter and his work.

Since this interaction, I have been incredibly lucky to call Peter a friend. I have followed the development of the Thinking Classroom while, at the same time, becoming infatuated with facets of the teaching of mathematics that are not explicitly addressed Peter’s work. I think that’s why receiving the book elicited the response it did: In many ways I grew up with these ideas.

Please read them, and think on them deeply. Dwell in the cracks and pull at the edges of your practice in order to forefront student knowing–always. If that means you build a Thinking Classroom, great. Peter has roadmapped this beautifully. If that means you develop some hybrid, that’s great too, because this book is not about providing a recipe.

This book is the culmination of a relentless pursuit of student thinking, and that’s what makes it particularly impactful. It’s simple to get caught up in a checklist of stages and lose sight that each of the fourteen actionable pieces of the framework gain their potency because they are saturated with this pursuit. The pages provide a model of how to fervently seek student thinking, and I consider that model to be the lasting impact of Peter’s work–work that has already impacted so many teachers and learners, and, heaven knows, has made a lasting impact on me.

NatBanting

- A “tweep” is simply defined as “one who uses Twitter”.
- Fittingly, this is a major theme of the book: Disrupting our expected norms in math classrooms to generate spaces for student thinking.
- My recommendation reads as follows: “
*Building Thinking Classrooms*prompts us to reflect on the potential of mathematics classrooms, teachers, and learners. Supported by numerous stories from classrooms, Peter methodically exposes the familiar structures of school mathematics that suppress the potential of learners, then carefully outlines a set of opportunities around which teachers of mathematics can organize a dynamic and responsive classroom. – Nat Banting”.

## One reply on “Thoughts on Thinking Classrooms”

Thanks for writing this! I too hear many people say they are “doing thinking classrooms” or they call it “vertical spaces”, but this doesn’t guarantee thinking is occurring. I agree there are different ways of creating these thinking spaces- but I do believe it does require to have some core beliefs that regardless of the way I teach- my values….my beliefs…stay solid. One of the beliefs I see so deeply rooted in Peter and his work is an unwavering belief in students as capable- and I’m not sure anything works if we don’t truly believe that. We can say it, but walking those beliefs isn’t as easy. I have had the pleasure of hosting Peter’s sessions, and have never seen secondary math teachers embrace anything as quickly as many have with this work. And that is exciting to see an educator get a taste of what a different approach in teaching can look like, and it begin a change in them. Thanks for your wise words.