A New Unit
As a geometry teacher I rely heavily on compass and straightedge constructions. My course usually begins by establishing the basic construction results and developing facility with the technology, and those ideas are then woven into topics throughout the year. We’ll pull out our compasses to explore triangle congruence, review parallelogram theorems, understand concurrency, and more.
I worried about my ability to efficiently assess the hands-on construction skills of 34 Zoom boxes every class every day, so I took a different approach this year. I de-emphasized compass and straightedge constructions, and instead relied on Geogebra as a construction and exploration tool. Geogebra has generally been a terrific substitute: In most cases, we now just pull out Geogebra when we would have pulled out our compasses. The underlying thread of construction has been disrupted a bit, but the course has still flowed in the way I wanted.
Until we hit transformations. My approach to teaching reflections, rotations, and translations is deeply embedded in the theory, and the inherent constraints, of compass and straightedge construction. Out of necessity my approach this year has revolved around finding ways to make existing materials work, but this was a unit where simply swapping Geogebra into my existing materials wouldn’t cut it. Too much of the development of the ideas required a fluency with geometric construction that my students just didn’t have.
I’ve reached the point where I’ve started developing new lessons for remote instruction, but I hadn’t yet had to re-design an entire unit. That’s what I had to do with transformations. Luckily I no longer feel lost as a remote teacher. I’ve started to develop a sense of what works for me and my students, and I have a set of tools I can use to deliver instruction and gain access to student thinking. I redesigned my transformations unit around simple prompts like intuitively identify the center of rotation:
And simple tasks, like sketching transformations and investigating whether or not two objects could be images of each other.
In the end, I was happy with the way the unit worked. Ideas flowed differently, but they flowed, and well enough so that when I’m planning my transformations unit next year, for a (hopefully) normal classroom, I’ll be thinking about what I did remotely.