Categories
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 …

Categories
reflection routine theory

Oops, I forgot…

**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.

Categories
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.

Categories
classroom structure factors games play projects reflection technology

Report on a Math Tournament

**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).

Categories
reflection whiteboards

Thoughts on Thinking Classrooms

“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.

Categories
reflection

A Lesson from a Washing Machine

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 laundry1, 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.

Categories
area games geometry investigation pattern reflection scale

Upscale Pattern Blocks

[Updated April 9th, 2020]

First off, I hope you are well. This post represents a portion of my attempt to remain “well enough” in the midst of tremendous uncertainty. Most of my time is spent talking about the teaching and learning of mathematics, something that seems to have ground to a necessary halt in recent days. Given our collective circumstance, the time feels as good as ever to talk about a little project I’ve been working on, and ask for a smidge of help.

The Blocks

Recent access to a laser cutter and a kindergartener got me wondering. I began to play with a few possibilities. One of the fun things that fell out was a set of scaled pattern blocks I’m calling, “Upscale Pattern Blocks”. Essentially, they are pattern blocks scaled in three different sizes. The sizes interacted in some very interesting ways, and after some test cutting and multiple trips to the craft supply store, I ended up with a really fun result.

Categories
geometry reflection

On Scalene Triangles

[Update Nov 4th, 2021: Since this initial post, I have intentionally backgrounded the term “#FreeScalene” because I am now at a place where I feel that facetiously couching a classroom activity in this language treats the work of important social movements with too little respect. I leave this post here (complete with this addendum) because this blog is a place to archive my professional trajectory, and I feel this update is an important piece of that growth.

If you want to read my thoughts on the merits of debating geometric definitions (especially triangles), portions of this post are expanded upon here.]


[Original Post: Published March 2020]

This past weekend I was invited to Toronto to give the 2019 Margaret Sinclair Memorial Award Lecture at the Fields Math Ed. Forum at the Fields Institute for Research in Mathematical Sciences. While the layers of the organizational hierarchy can be a mouthful, the bottom line is that I was given the great honour of presenting my thoughts on the teaching and learning of mathematics–as they are formulated at this time of writing. I broke the day into three distinct sections: The recipient’s lecture, a poetic provocation about hotdogs and mathematics education, and a gallery walk composed of some of my favourite invitations from my career to date.

(Link to the video archive of the invited lecture.)

Categories
probability reflection

An Improbable Run at the Rosenthal Prize

In early December, I found out that my submission had been selected as the winner of the 2019 Rosenthal Prize for Inspiration and Innovation in Math Teaching. At the time, I had zero reference point to understand what that meant, but have since experienced first hand the hospitality of the international math education community. This post is not a summary of the winning submission; that detailed lesson plan has been posted on the MoMath website. [UPDATE April 2021: Rachel Welbourn a gracieusement traduit les documents de la tâche en français.] Here, I want to take the time to reflect aloud on how this whole thing happened–a process, I think, might be of value for math teachers. I’ve attempted to distill my take-aways into four categories, but, in actuality, they still exist (for me) as a tangled heap composed of equal parts disbelief, gratitude, and empowerment to pursue the next challenge.

Categories
reflection theory

Thirteen Days

A huge piece of my identity is invested in being a mathematics teacher.1 This week I began a new and interesting challenge as a university faculty member preparing pre-service elementary and secondary mathematics teachers. This provides me more time to think deeply and openly about the entirety of the mathematics education enterprise, and put some of those ideas into public circulation through speaking and writing opportunities. I am really looking forward to that.

It also means that I am charged with orchestrating the formative experiences with mathematics teaching for about half of my province’s new teachers. That fact is terrifying. I am given just thirteen days in each course with which to shape the impressions, experiences, and ambitions of the future teachers of my province, city, school division, and (quite possibly) my own children. Thirteen days.