By Patrick Honner, @MrHonner

It’s October, and I have no idea what I’m doing.

Students are logged into my Zoom meeting. I can see some faces, some avatars, some dark, blank rectangles. The problem set is posted in Google Classroom: transformations of functions, composition, domain and range. They’re good problems, a nice mix of review and preview, and I’ve used them at the start of calculus every year. Of course, this year is different.

The delayed school opening gave us two weeks to figure out how to turn ourselves into online teachers, but I get the feeling it’s going to take a lot longer than that. How am I going to fulfill the complex conditions of teaching math over a livestream? Sure, I can explain things, but teaching is much more than explaining.

At least students are working on the problems now. Well, I think they are. But I don’t really know. How am I going to do this? In a classroom I would be walking among the groups, peeking over shoulders, eavesdropping on conversations, asking provocative questions. But right now I have no idea what my students are thinking. And that’s what scares me: If I can’t access their thinking, how am I going to teach them?

At the end of class we review the challenge problem: Given the graph of y = f(x), what does the graph of y= f(x)/f(x) look like? Many students get it wrong. A few get it right. We talk and argue about it, just like we normally would. Maybe things will be ok.

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It’s December, and Tony is wearing a mask, which is surprising because he’s at home, like he always is during class. I can see the bunk bed behind him.

He seems a bit agitated today. Tony used to be the first one to arrive and one of the few students willing to unmute and say hi before class. He’s been doing that less lately. The quality of his work has declined, too. It’s been on my mind for a couple of weeks, one of a thousand different things I’m worried about.

I pop into his breakout room, where he and his classmates are discussing a proof. I’m listening in, trying to get a sense of what makes sense to them, of what they are struggling with. I watch Tony turn away from his computer. He’s gesturing with his hands, frustrated, upset. He hasn’t muted himself, but fortunately we can’t hear what the argument is about. “I have to step away for a minute to deal with something,” he says abruptly, and his screen goes dark. It stays that way for the rest of class.

Later I learn that Tony, like many of my students, has been living with extended family during the pandemic, and one has tested positive for COVID. “He’s dealing with some additional stressors at home” says the email, which is undoubtedly true about Tony but could have been written about any of us by our guidance counselors this year.

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Teaching and learning are tests of resilience. This is especially true in math, which at times can be joyful and elegant and satisfying, and at others mysterious and intimidating and painful. There is a natural tension that exists between teacher and student and mathematics, and it takes time and resilience to resolve it. How will you react when you’ve taught, but your students haven’t learned? How will you react when you thought you understood, but then realize you didn’t?

Facing these questions is challenging enough under the best of circumstances, and these have not been the best of circumstances. The pandemic brought unprecedented professional challenges and personal loss to our shared experiences, and then turned a webcam on all of it. We see each other in our bedrooms, in our kitchens, in our cars, or not at all. We see the struggles of others. And they see ours.

Getting through this past year has required resilience we rarely witness in our classrooms, and empathy we rarely offer to each other. Then again, people are always struggling. Maybe the only difference now is that it’s harder to hide those struggles when they’re being captured on a livestream.

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It’s May, and I’m back in the school building, on call to supervise the students here for hybrid instruction. Whenever I come in, I try to see as many students as I can face-to-face. I hear from their parents that it means a lot to them. It means a lot to me, too.

I missed connecting with Adrian in the morning, so I hustle up the stairs after my last class to catch him before he leaves. When I reach the fifth floor I see about twenty 9th graders congregating in the hallway. They are leaning against walls, sharing earbuds, gossiping, staring at each other’s phones. It all seems so normal. Only the masks give it away. I see Adrian and quietly wave hello in passing, not wanting to interrupt this unusually normal teenage moment.

These moments of success, of normalcy, of hope, come with a little more frequency as summer nears. Adrian brags about his unexpectedly rich pandemic social life. Tony rebounds and finishes the year strong, earning good grades and resuming his morning greetings. I even start feeling like a teacher again, eventually.

There was an additional excitement to saying goodbye to this year. We did it, and we won’t have to do it again. And although we are all looking forward to putting this year behind us, we can do better than just getting back to normal. In a year that reminded us how challenging teaching always is, we found new ways to connect with students and connect them with mathematics. In a year of heightened awareness to our collective health, we cared more for each other as people, not just as students and colleagues. The pandemic may be receding, but the challenges and struggles won’t disappear: They’ll just be harder to see, or maybe just easier to ignore. As much as we want to forget this past year, let’s remember the resilience and empathy that got us through it all, even after the webcams have been turned off for good.

Patrick Honner has been teaching mathematics and computer science in New York City public high schools for nearly 20 years. He is a recipient of the Presidential Award for Excellence in Mathematics and Science teaching, and his writing appears in the New York Times, Quanta Magazine, and The Best Writing on Mathematics.