Emergency Remote Learning, Redux

And we’re back.

Eight months after shutting down for the first time, New York City has once again closed schools due to the pandemic.

A lot has changed in eight months. Last Spring, I was remotely teaching students I already knew well. Those relationships helped us successfully get to the finish line, even as I struggled to figure out what I was doing.

This September I started a new school year teaching live remote classes to students I’d never met. This brought with it an entirely new set of challenges, some I’ve successfully met and others I’m still working on.

While I am anxious about the school closures, I certainly don’t feel as lost as I did eight months ago. I’ve appreciated the opportunity to be in my school building this year, and interacting in person with some colleagues and some students has really helped me get a handle on what I’m doing with my classes. Some things are working, and they’ll continue to work during the shutdown.

But I hope for a quick and safe return to schools. Although I’ve reached the point where I feel like I can teach remotely, I’m still hoping this is just a temporary interruption.

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Some Math Problems Seem Impossible. That Can Be a Good Thing — Quanta Magazine

In my latest column for Quanta Magazine I write about the secret power of impossible math problems.

Construct a convex octagon with four right angles.

It probably says a lot about me as a teacher that I assign problems like this. I watch as students try to arrange the right angles consecutively. When that doesn’t work, some try alternating the right angles. Failing again, they insert them randomly into the polygon. They scribble, erase and argue. The sound of productive struggle is music to a teacher’s ears.

Working on impossible problems has a way of helping us better understand what is possible in math, and the impossible plays an important role in the history of mathematics. In my column I explain using several examples, and include a few extra exercises to play around with. The impossible can be frustrating, but also fun!

The entire article is freely available here.

Forty Phone Calls

Parent-Teacher conferences joined the list of education practices remade by the pandemic this week.

Ours went surprisingly well. Parents signed up in advance, and our administration created a schedule for every teacher detailing whom to call and when. The schedule prioritized students who struggled during the first marking period, which meant conversations that really had to happen were more likely to occur.

Knowing whom I’d be meeting with was very helpful. Usually Parent-Teacher conference night is three hours of pure reaction: A parent walks through the door, I quickly try to identify them, place their child, locate their records, search my mind for what I want to tell them, and then move them along within three minutes because I’ve got 25 other parents waiting in line. This year I was able to prepare talking points and review student work ahead of time. It was much less hectic.

In my conversations I was struck by how grateful parents were. Parents are generally appreciative of the work teachers do, but there was something extra this year. Even though we could speak for only a few minutes, most parents made it a point to explicitly thank me both for what I’m doing in the classroom and for taking the time to call them. In fact, many of these conversations felt like thanking me was itself the point.

I made forty phone calls over the two days. It was exhausting, but worth it: A familiar feeling that made this year’s abnormal Parent-Teacher conferences feel very normal.

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NCTM 2020 Virtual Conference

I’ll be presenting “Bringing Modern Math into the Classroom” as part of the NCTM 2020 Virtual Conference. Here’s the description for my talk:

New mathematics is created and discovered every day, yet the mathematics we teach is hundreds, if not thousands, of years old. How can we build connections for our students between the mathematics we currently teach and the mathematics at the edge of discovery?

The talk is based on my column for Quanta Magazine, where I connect cutting edge research to curricular math. In addition to this talk for NCTM, I’ll be running two workshops on Bringing Modern Math into the Classroom for Math for America this year.

You can find out more about the NCTM 2020 Virtual Conference and register here.

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I Taught a Good Lesson

I taught a good lesson this week. Not considering-the-limitations-of-remote/hybrid-learning good. Just really good.

A lesson where all students hit the checkpoints on schedule. Where small group conversations served their intended purpose with precision. Where the variance of whole class conversation was small enough to keep us focused but large enough to keep it interesting.

The lesson was on the Mean Value Theorem. I’ve taught it many times, and it’s usually very successful. But success is a little harder to come by right now, so it was a welcome surprise to see just how successful this lesson was in remote / hybrid learning.

Early in the lesson every group was able to outline the proof of Rolle’s Theorem via its connection to the Extreme Value Theorem. Later on, every group was able to develop a proof of the Mean Value Theorem based on its connection to Rolle’s Theorem. Our final whole-class discussion of the proof of the MVT was driven by several students who have been fairly quiet in class up to this point, which is always a sign of success.

The success of the lesson wasn’t due to any particular innovation. I simply have a better feel for this kind of teaching now: How to structure tasks, which questions to ask, how long to leave students in small groups, how to organize platforms to serve my instructional goals. And I have a better feel for my students, as well. I know who needs a nudge, and who needs to struggle a little more.

It’s been challenging trying to redevelop my feel for teaching this year. Success has come here and there, in brief moments. But this lesson accomplished exactly what I hoped it would. It feels good to finally be able to say that.

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