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 …

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.

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.)

cylinder geometry surface area tasks visual

Re-Constructing Shapes

For the first time in a decade, I am not reconvening with a high school staff to begin preparations for the school year. (I’m preparing to work with pre-service teachers on a university campus). It feels weird–very weird. It is a day that I look forward to because optimism is a constant across the building. Staff feels fresh, materials are crisp, and possibilities are endless. It sadly belies what’s to come.

Bummer, right?

estimation geometry technology

Estimating with InO-Bot

You can count me among the folk that believe that there is a real possibility to teach mathematics (among many other things) through coding. I do not claim to have any expertise in the area aside from a handful of undergraduate credits and the odd project that has grabbed my attention over the years; however, the intuitive nature of Scratch provides a novice entry point for anyone interested in giving it a shot. This post describes my initial foray into using coding technology in the classroom. Like all things, the structure of school provided certain constraints, but in the end, it was a very positive experiment for both myself and the students.


Constraining the Two-Column Proof

There is no dedicated course for geometry in Saskatchewan’s secondary curriculum. Instead, the topic is splintered amongst several courses. There are advantages and disadvantages to this, neither of which will be the focus of this post. I just thought that, especially for the non-Canadian crowd, a glimpse of context would be helpful.

The notion of a geometric proof only appears in one course. It is presented as a single unit of study during a Grade 11 course and is preceded by a short unit on the difference between inductive and deductive reasoning. I have taught this course a lot over the past few years, and have always had mixed emotions toward this portion. I love the metacognitive analysis students participate in during the inductive v. deductive reasoning unit. It is a (metric) tonne of fun to teach because it largely entails the completion of games, puzzles, or challenges and a subsequent interrogation of our thinking patterns. This could be my favourite week and a half in the course. After we have experienced the difference between induction and deduction, we spend a couple weeks slogging through angle relationships and parallel lines, triangles, and polygons using the ultimate edifice of deductive reason: The two-column proof.