classroom structure factors routine tasks theory

Going with Your Gut

I teach university courses in mathematical problem solving at St. Francis Xavier University during my Summer break. The classes involve initiating numerous problem solving episodes and then interrogating and filtering our collective experience through the lens of current theory in the field. This structure provides plenty of opportunity to workshop new ways to launch tasks, and this year, I began experimenting with a new sort of launch routine that had pleasant results. This post is an attempt to reflect on why that may have been the case.

First, however, you must indulge me by responding to a prompt in five seconds or less.

assessment classroom structure

The Interview Quiz

I love creating curious tasks for my students. I love anticipating their thinking, observing their milestones of thought, and then posing new, interesting wrinkles to sustain their problem solving. It really is what fuels my practice. Honestly, interacting with students keeps me coming back for more–day in and day out. It’s what I enjoy most about the job.

I think that’s why I’ve always hated assessment events. They always seemed disconnected from the students.

reflection theory

NCTM LA Ignite!

I was one of eight educators invited to give an Ignite! talk at the 2022 NCTM Annual Meeting in Los Angeles. I want to thank the program committee (specifically, Aleda Klassen) for the invite, while, at the same time, express just how terrifying the entire experience was–in a good way.

There was no official recording of the event (like previous years), but a fellow Saskatchewan educator, Kirsten Dyck, managed to bootleg us a copy! The videography gives a nice sense of the energy in the room.

The content of the talk expresses the very root of my work in mathematics education–work that I’ve shared freely across digital platforms, and work that I would happily continue with ambitious teachers and districts. Questions, clarifications, and objections can be directed to @NatBanting (on Twitter) or get in contact via the Contact Form on this website.


factors pattern polynomial tasks

Trinomial Factoring Match

Fractions, factors, and functions.

A large portion of my career to date has been spent musing over how to engineer classroom environments that infuse meaning into these three mathematical structures. When it comes to polynomial factoring, the area model has provided the most success. After connecting 2-digit by 2-digit multiplication, the area model becomes a beautiful visual to make sense of the “adds to ___; multiplies to ___” phrase that echoes around the room.

But we don’t keep the area model around forever. Once we’ve used the model to build meaning, we mobilize that understanding in more symbolic situations in a careful, deliberate march toward mathematical abstraction.

geometry reflection

Triangles and Trapezoids

Debating definitions has long been one of the favourite pastimes of math teacher Twitter. (see, for example, #sandwichchat or #vehiclechat). Recently, and in a move of pedagogical brilliance, the collegial tone of such debates was soured by an ongoing feud between Shelby Strong and Zak Champagne.

The object under debate: The trapezoid.

Both teams made their case and canvassed for support. Shelby argued for an inclusive definition, Zak argued for an exclusive one, and math teachers aligned themselves in one camp or the other: #TeamInclusive or #TeamExclusive. (You can pledge your allegiance in apparel form here or here.)

I was more than happy to take my place on the sidelines, just hoping both teams had fun, until …

reflection routine theory

Oops, I forgot: Productive forgetting and convenient remembering

**My good friend Joce Dagenais has translated portions of this post into French here.**

In 2018, I made the cross-country trip to attend and present at the OAME Annual conference in Toronto. The session was attended by a particularly boisterous group of math teachers–all of whom I adore. Emerging as the ringleader of this rag-tag group of pedagogical hooligans was Fawn Nguyen, who, in her notorious brilliance, later distilled the ideas into a classroom routine by the name “Oops, I forgot…“–OIF, for short. This post is in response to requests to elaborate a touch on the idea and provide more support for teachers thinking about implementing it in their practice.

functions graphing quadratics

Introducing Quadratics

Quadratics feel important. This impression is no doubt influenced by the boated importance placed on calculus in secondary school. They represent the giant leap from linearity and pave the way for more elaborate functions; therefore, I often find myself musing on ways to have students meaningfully interact with the topic. Once the structure of the function is established, I’ve played around with interesting ways to help students visualize quadratic growth, connect that growth to the Cartesian plane, and build these functions to specifications; however, my introduction to quadratics in vertex-graphing form has always been a series of “What happens to the graph when I change the ___ value?” questions. These aren’t bad questions (and a quick setup of Desmos sliders helps visualize the effects), but they don’t exactly build up understanding from experience. Such was my introductory quadratics lesson for years, lukewarm but lacking the epiphany to address it.

“If you want to kill flies, you don’t need bazookas”

– Ben Orlin, Math with Bad Drawings, p. 44
data analysis estimation fractions play reflection

COVID Math Fair

In 2015, my students and I founded an annual math fair in my school division. Inspired by mathematical play, the fair grew from humble beginnings into a staple of my mathematical calendar. Like nearly everything about this school year, the fair was jeopardized by the pandemic; however, with a touch of innovation and the ongoing support from my school administration, the teams of educators in our five feeder elementary schools, our trustee, and the school community council, I managed to pull together three math invitation carts that could be disassembled, transported, and reassembled in the elementary schools.

integers technology visual

The Bucket of Zero

Over the last year, Dr. Lisa Lunney Borden and I have been working on a model for integer operations that she introduced me to a while back. Our goal is to amplify her research for classroom mathematics teachers. Right now, the idea consists of three pieces, each at varying stages of development.

  • A paper
  • A platform
  • A set of plans
quadratics technology vine

Animating Quadratic Patterns

My first attempt at animating patterns was published on this blog in 2013. I suppose you can consider this post a long-overdue extension of the thinking there, however with a much-needed bump in production quality. In those old days, I hunched over a whiteboard with a collection of square tiles, creating six-second loops on the (now defunct) social media platform, Vine. Now, thanks largely to Berkeley Everett and his crash course on how to make animations in Keynote, the process has become much more streamlined.