Teaching

I stopped asking “What did I do last year?” months ago. In some ways it’s true that good teaching is just good teaching, regardless of the circumstances. But designing remote instruction is so fundamentally new to me that, as I’ve slowly figured out what I’m doing, it’s been easier to start from square one when planning a lesson.

This has required a lot of work. It’s been a long time since I’ve had to worry about every single lesson I teach. It’s not an unfamiliar feeling: Throughout my career I’ve always taken on the challenges of teaching and creating new courses. But creating a mathematical computing course from scratch is easier when the geometry and calculus courses I also have to teach are already in good shape.

But a month ago we passed the one year mark of remote learning in NYC, which means the answer to “What did I do last year?” is suddenly relevant. Last year I made short videos explaining key concepts. I created auto-graded quizzes to use as formative assessment. I wrote documents that placed essential course content into the context of our year-long conversation. These are all resources I can plug into what I’m doing right now, usually with only minor changes.

The ability to use pre-existing materials as is has provided some much needed relief. There’s still so much to do each day and week, but every resource I can reuse amounts to a small reduction in the stress and burden of planning everything anew. And with the home stretch ahead of us, every little bit helps.

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I was at school twice this week: First to proctor the SAT, then on my rotation day (The school is required to have a certain number of teachers in the building every day, so available staff rotates through the responsibility.)

It was nice to be around students, even if it was just proctoring an exam with nine kids in a room, or walking around the cafeteria, smiling and saying hi as they worked on their laptops.

There was an especially nice moment at the end of the day. About twenty 9th graders gathered in the halls after the final bell rang. They were talking, laughing, making plans, looking at their phones. Apart from the masks, it all seemed so normal. Like a time not too long ago, or a time not too far in the future.

I have been moved by the resilience of students throughout my career. When the world disappoints them, they figure out how to move forward. When I disappoint them, they give me another chance. I often find strength in their strength.

Students have suffered greatly this past year. I’ve seen it. I’m seeing it. But I’ve also seen their resilience. It will carry them. And maybe us, too.

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Students sit in groups of four in my classroom. The arrangement creates opportunities to collaborate, argue, and socialize around mathematics. It’s essential to how I design instruction.

This wasn’t a common approach when I first started teaching high school. But 20 years later the practice is so common there are different schools of thought about how to assign students to groups: homogeneous grouping (students at similar levels), heterogeneous grouping (students at different levels), visibly random grouping. Like most ideas in education, each approach has its proponents and detractors. And like most ideas in education, each approach can cycle from preferred to discouraged as it gains and loses favor in the spirit of the times.

I’ve always used a variety of strategies in assigning students to groups. As a mathematician I appreciate the benefits of randomization, but as a teacher I want to leverage my knowledge of my students in designing experiences that serve them best. Sometimes I want advanced students working with advanced students. Sometimes I want gregarious students working with quiet students. Sometimes I want Jane to work with Julie because they think in similar ways and I want them to share ideas. Sometimes I want to place students in groups based on who they are, hoping that they will enjoy themselves and learn and grow.

Like many teachers engaged in remote instruction I’ve been using breakout rooms to try to replicate some of the student-to-student interaction that comes from sitting together in small groups. It has been a challenge. Sitting in a zoom breakout room is not the same as sitting in a chair next to someone. The social dynamics are dramatically different. I’ve had some success, but I have not figured out how to make breakout rooms work the way I want them to.

Part of that may be because I just don’t know my students as well as I would under normal circumstances. I’ve felt this in many different ways throughout the year: When I can’t remember which student observed that congruence is a kind of similarity two days ago; when I’m trying to write a recommendation for a student I’ve taught only remotely; when I realize that I might not recognize John when I pass him in the hall next year.

When I recently changed group assignments for my classes, I felt this again. Because for the first time all year I was comfortable assigning students to groups based on who they are. It felt so normal, so satisfying. And then I realized that it’s April. It took me nearly all school year to reach this point. Better late than never, I suppose. It’s been a year of celebrating small successes, and I’ll take this one. And it will make reaching this point next November something to celebrate, too.

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The week started out with a few empty chairs in class. My attendance is usually 100%, so even a couple of absences is noticeable. Especially when it happens every period. By Friday there were 7 or 8 students out in every class. The DOE wasn’t acting as fast as parents were, but the shutdown was inevitable.

I knew things had gotten real when the NBA suspended its season in of the middle of the game I was watching. I remember telling students closure was imminent. We probably won’t be back before Spring Break, I told them, maybe not even by end of the year. I said we might be dealing with this for the next two years, somewhat prophetically.

Teachers had started to stay home, too, which made it easier for me to book a computer lab for the Thursday and Friday of that week. I brought my geometry students in for a crash course in Geogebra. I had a feeling it would come in handy.

They closed the schools the next week. For students. Staff still had to report, though more were calling out. In an email the Chancellor of NYC Schools spelled it out for us: “By Monday, March 23, we expect all students and teachers to begin engaging in remote learning in all grades.” I had one week to figure out how to turn myself into a remote teacher.

One year later, I’m still figuring it out. This is the 40th entry about my transition from experienced classroom teacher to novice remote teacher. I’m glad this series is nearing its end, but I’m also glad I kept a record of where we started and how far we’ve come.

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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:

100 student responses. What was the prompt?#math #mathchat #geomchat pic.twitter.com/CVAbFXQYTg

— Patrick Honner (@MrHonner) March 18, 2021

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.

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