I am a compulsive problem poser. When presented with a mathematical context, I have an incredible amount of difficulty leaving it alone. My teacher instinct is to push, prod, tinker, and/or alter it in someway. As I do so, I wonder what students might do and what new actions might be sponsored by any changes.
Problems are sandboxes and playing in them is a sort of imagination fuel for teaching.
There was an era when I spent a great deal of time documenting the activities of my practice on this blog. My students sponsored many an inspiration and innovation as I learned (and re-learned, and re–re-learned) how to teach mathematics. Times have changed globally (the math teacher blogging community has largely disbanded) and locally (my young family keeps me busier than ever), but my students continue to notice interesting things and make meaning in innovative ways–I swear. I’ve been chewing on one such occasion for a month now and decided to use this space to get it off my chest.
It all began in the same way that most interesting observations begin–during a lesson on simplifying rational expressions.
When I was a first year teacher, the teachers in my province went on strike for two days. It was on the first of those two days that I signed up for Twitter in order to follow public opinion on the job action. It was only days later that–by accident–I found math teacher Twitter, and the Math-Twitter Blog-O-Sphere (or MTBoS, for short) quickly became the self-organized space filled with ideas, insight, resources, and support that set the trajectory for my career.
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.
NatBanting
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 …
Ordered my Team Inclusion T-Shirt (and a few others) this morning.
What team are you on @NatBanting @MaryBourassa? https://t.co/HYVh3kVT0Y
— Jamie Mitchell (@realJ_Mitchell) October 11, 2021
**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.
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.
**This post contains the materials and advice you’ll need to run a distanced math tournament with your district, division, school, province, state, classroom, family, coworkers, neighbours, etc., etc., etc.**
Honestly, the more math love, the better! (IMHO)
In mid-October, I designed a math provincial math tournament open to all middle school teachers in my home province of Saskatchewan, Canada. After writing up a blog post that served as a formal invitation, the tournament (which I affectionately called the Saskatchewan Mathematics Invitational Tournament–or #SMIT2020 for short) has been running for just over a month with over 80 classrooms from across the province playing Federico Chialvo’s delightful game MULTI. (see here for more information).
“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 tweeps1 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.
My mind has been wandering back to the math class lately. I’ve missed it, and, given the current health concerns associated with the re-opening of schools, I may not be getting it back anytime soon. (At least in the form that I feel the most comfortable operating in). Perhaps it is the pendulum between anticipation and dread that has teaching and learning at the forefront of my awareness lately. Although this is not uncommon for me, absence does, as they say, make the heart grow fonder. It is, therefore, possible that this post represents my final descent into pandemic-induced psychosis; maybe this strained analogy symbolizes just how much I need the classroom back, and serves as a sort of Warshak test–math education style–where ink blot after ink blot of everyday experience suddenly holds latent lessons about the mathematics classroom. Maybe it’s just a way to air my dirty laundry2, to simply stop some thoughts from rattling around in my skull by writing them down. Tabling the discussion of my sanity for the time being, what follows is a quick story about my Saturday afternoon.