Teaching

Last year my calculus students worked on creative projects at the end of the term. They submitted videos, podcasts, and art projects related to their favorite topics from the year. Two students wrote and hosted an integration bee. Another baked and decorated a four-layer “Washers Method” cake. We didn’t do that this year.

My geometry students wrote short papers on their favorite topics at the end of last year. They built interactive Geogebra demonstrations to accompany those papers. We didn’t do that, either.

With just a few weeks left in the school year the overwhelming feeling is relief. I’ve made it. I wasn’t sure I would. At the start of the year I often felt like a first-year teacher. I wasn’t sure I could do my job at all, much less at the level I expect. Just making it to this point is an accomplishment.

But the end of the school year is a time for reflection, and it’s hard not to look back and see everything I didn’t do. I didn’t have my students write enough, or take as many photographs, or experiment with computing. These are staples of my classroom, but in a year where just covering the curriculum was a cause for celebration, I simply didn’t have the time or energy or opportunity to get us there.

It’s unusual for me to feel this much regret at the end of the year. But it’s been an unusual year. Thankfully, the end of the school year is also a time to look ahead. And although new challenges certainly lie ahead of us next fall, I’ll be excited to face them.

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Monday was my day to be in the building. Before teaching remotely from my empty classroom, I walked upstairs to the gym to say hi to the students who physically came to school. I saw a few kids quietly standing near the ping pong table that had been set up for socially distanced socializing.

One of my calculus students was with them, so I challenged him to a game of ping pong. They didn’t have any ping pong balls, so we searched the empty lockers and he found a fist-sized green squishy ball. He held it up as if to ask “Want to give this a shot?” and I nodded. After about 45 awkward seconds we succeeded in inventing some kind of paddle-ball game. As we played we talked about infinite series, differential equations, and the BC exam. After a few minutes a dozen students were watching. I handed off the paddle and said goodbye, and headed upstairs.

Outside the cafeteria I saw a student standing by himself at another ping pong table. I realized it was a 9th grader I’d been teaching all year but never met in person. I grabbed a paddle and we started playing, chit chatting for the first time after working together for 8 months. A few other students gathered, including one of his classmates. It was 10 o’clock and I had to get back to my empty classroom to teach their class, so I handed off the paddle again. I grabbed an extra ping pong ball and headed back downstairs. Paddle-ball was in full swing, which made me think twice about giving them the ping pong ball I’d snatched for them.

Back near my classroom I noticed a familiar face in the distance. It was a student of mine from last year. He and a few friends had set up an unofficial pod in the lobby and were quietly working at an out of the way table. I took a quick detour to catch up — How’s your year going? How’s Algebra 2? Any plans this summer? — and then hustled back for the start of class.

I love teaching and I love math, but I love this part of my job, too. I love being a small part of the small moments of the daily lives of students. Sharing a smile or a laugh or a serious thought before school. Silently saying hi in the hallway in between classes. Catching up years later, seeing how students have changed and grown, listening to how they remember our shared experience. I figured out the teaching and the math this year, but not this other part. I’ve really missed it.

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I taught a bad lesson this week. It’s not unusual. I teach hundreds of lessons every year: Some go very well, most are just fine, a few go poorly. A successful school year has its ups and downs, for students and for teachers, and you take the bad days with the good.

This week was the area of a circle. It’s always a challenge teaching a topic that students already know: It can be hard to get students to engage deeply with an essential question like “How do you conceive of the area of curved things when your notion of area is based on straight things?” when they’ve been using since 6th grade.

I took a standard approach and had students explore area relationships between a circle of radius 1 and various inscribed and circumscribed polygons. The goal was for students to engage with the essential question while sharpening their area-computing skills and previewing some important arguments they’ll see again in calculus.

Usually this lesson works just fine, with occasional moments of greatness. But this year I had to trim the area unit a bit to accommodate the schedule, so prior to this lesson we just hadn’t done enough with polygon area. As a result, the conversation bogged down in the early stages of the exploration and it was hard to get unstuck. And because the remaining schedule is so tightly packed, there really wasn’t really time to stop and regroup. We just had push through.

It wasn’t a disaster: We did math together, students grappled with and argued about important ideas, connections were made. But the lesson didn’t go as I’d hoped, and that was a downer. On the other hand, it was comforting to realize that this lesson went bad for some very normal reasons. It didn’t fall flat because my wifi went out or because I couldn’t share my screen or because I had no idea how to access student thinking on a computer. The lesson didn’t work for the same reasons most lessons don’t work: I misjudged prior knowledge and tried to execute a plan that was too ambitious and too rigid. It might have been a bad lesson, but it also might have been the most normal lesson I taught all year.

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I’m proud I covered the curriculum this year.

“Covering the curriculum” is one of those phrases that’s been around so long everyone in education has turned against it. Curriculum coverage has become synonymous with prioritizing the delivery of content over student success, or fixating on what the teacher presents rather than what the students learn. “You shouldn’t cover the curriculum. You should uncover it!” says the education influencer, getting 1K retweets every time.

Of course curriculum planning should center student experience. But it should also embody a clearly defined set of concepts and tools. Covering the curriculum should mean delivering that full set of ideas to students in a coherent and meaningful way. And covering the curriculum was not easy this year.

In September I had to plan for a year of unknown unknowns. Our restructured school schedule included a switch to block periods and a 33% overall reduction in instructional time. Double periods are not as simple as teaching two lessons back-to-back. Losing a third of my class time was going to have a substantial impact on what we could do. There was a lot of uncertainty about what the courses I’d taught so many times before would look like. More fundamentally, there was a lot of uncertainty about what each day of class would look like. I had no experience with live remote instruction, and I had no idea what could be accomplished in a 55-minute Zoom class.

Putting together a pacing guide in September was flying blind. Our Geometry team worked together to streamline the sequence and differentiate core concepts from peripheral ones. I consolidated units in my combined pre-calculus / calculus course hoping for more efficiency. I made my best educated guesses based on my 20+ years as a teacher, but I really had no idea how the courses would unfold.

As unusual as the year was, one thing was the same: Like every year, I tried things, I got feedback, I learned, and I adjusted. I slowly got a feel for pacing and a feel for the day-to-day. And quite remarkably, as we face down the last month of school, I can say that the plan worked. It wasn’t easy, but I taught the courses I set out to teach. Students learned what they needed to learn, and they will be ready for what comes next. I covered the curriculum. And I’m proud of it.

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I keep a Word document open on my computer that serves as my planner. Inside is a table I use as a calendar, and I look ahead as many weeks as rows can fit on the page. It’s crude and dependable, like many systems that stick around.

I update the calendar, and the file name, as weeks and months pass. A recent update to May Plan.docx put the final instructional day on my calendar. Visualizing that day was a powerful moment.

Eight months ago it wasn’t clear how even the most basic elements of school would function. How was “hybrid” instruction going to work? How many students would be in the building? How many teachers? Which courses would be taught, and which dropped? Visualizing the last day of instruction would have been impossible then.

Even after the basic elements were set, it took me months to feel even slightly competent at my job, and months more to feel like I was starting to be effective. Now I’ve figured some things out, and I’m having enough day-to-day success to feel like a teacher again. And as I plan for the end, I realize that, for the most part, I’ve successfully executed the curricular plan I put in place in September, when I had virtually no idea what lay ahead. Being able to imagine the final day of instruction at all feels like an achievement, and to see it as the end of something successful feels a bit like a miracle.

The stretch run to the final day is always an exciting and challenging time. Usually it’s a time for me to experiment, but since everything’s been an experiment this year, I’ll be content with my small successes, delivering the courses I set out to deliver, and deleting the final row from June Plan.docx.

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