PCMI 2021

I’m excited to be a part of the Park City Math Institute’s 2021 upcoming summer program!

PCMI provides immersive mathematical experiences for scientists, students, and educators through their summer programs. This year, I’ll be running a week-long session for PCMI’s Teacher Leadership Program titled Complex Geometry Made Simple. Here’s the course description:

The complex numbers are one of the great achievements of algebra, but their geometry may be even more compelling. Join us as we explore the complex connections between elementary geometry, inversion, rotations, functions, and more! The shortest path to real truth may involve a detour through the complex plane, but in this course we’ll be sure to take time to enjoy the journey.

PCMI’s Teacher Leadership program runs July 12 — 30 and includes courses on Fibonacci Recurrences, led by Daryl Yong and Bowen Kerins, and Hands on Combinatorics, led by Brian Hopkins. You can find out more information on the programs, including how to apply, here.

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Some Things Work Better Remotely

It’s natural to focus on what’s missing in remote teaching, but some things do work better remotely.

For example, this week I introduced reflections in my Geometry class. I began by having every student sketch the reflection of a quadrilateral.

I watched every student sketch this in real time and confirmed that they all had a good intuitive understanding of what reflection meant. Then I gave them two triangles and asked them to work together to devise a mathematical strategy for determining if two objects were indeed reflections of each other.

Dashboards, like in Geogebra Classroom and Desmos Activity Builder, have solved the biggest pedagogical problem I’ve faced in remote teaching: They give me access to student thinking. Here I can see that students already have the core ideas of the lesson — congruence and constructing the line of reflection — on their minds.

Usually I’d gain this insight by walking around, looking over a few shoulders, eavesdropping on a few conversations, asking questions. Though it’s not quite the same, dashboards like this give me efficient access to much more individual student thinking. And it’s especially nice, and easy, to just share this screen with the class and show them all that thinking. We can debrief their strategies, honor student creativity and ingenuity, and extract the ideas we need to move forward.

Efficient access to student thinking makes formative assessment easier, too. Here I’ve asked students to sketch an object such that r_l(P)=P for exactly five points P.

In just a few moments I can see that the class generally gets the idea, publicly praise students 5 and 3 for their degenerate-case thinking, and offer student 4’s response for further consideration.

Like everyone else I’m looking forward to mingling in classrooms and looking over shoulders again. But with a return to schools on the horizon, I’ll also be thinking about what’s worked well in remote teaching, and I’ll try to bring that back with me when I return.

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Back to School

New York City is moving toward reopening high schools. We’ve been fully remote since November, but reopening dates are being floated and rumors are circulating, as has become common in this era of crisis mismanagement.

The lack of consensus is another common feature. Some believe that schools must reopen for the good of the community. Others feel that we still aren’t ready to confront the realities of face-to-face teaching in the pandemic, even now, nearly a year into it.

I don’t have any deep or important thoughts about reopening high schools. I know there are students, and families, who are not succeeding right now. And I know there are schools that still aren’t prepared to properly handle in-person schooling. Like all complex issues, there’s truth on both sides. And like all issues in education, the public conversation takes form as a high-level policy debate, while the reality of the situation exists at the complex and diverse level of the individual. This is another reason it’s hard to think about education broadly.

When school began in the fall I was reporting to the building. I appreciated the opportunity to see some students and interact with some colleagues. After early challenges, I found a rhythm and a style that was starting to work for me. I was concerned when we went fully remote, worried about trading in that rhythm for a full house and an over-taxed wifi.

Three months later and now I’m used to working from home. I’ve found a rhythm and a style here, and a set up and routine that works. Now I’m worried about going back to school, disrupting that routine, losing what’s working once again.

But I look forward to going back and seeing some students and some colleagues. And offering some small hope that we all might be back to normal someday soon.

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Getting Ahead

I noticed something unusual recently: I was a full two weeks ahead in preparing my classes.

I should say very unusual. Even that might not be strong enough. In nearly 20 years of teaching high school I can’t actually remember ever having two full weeks of lessons completely planned ahead of time.

I always have a plan that includes what I expect to teach on certain days, and for courses I’ve taught before I have materials to draw on to build those lessons when the time comes. But that time rarely comes two weeks in advance. There are too many ways a rigid plan can be disrupted: A group that needs an extra day with an important concept; an unexpected administrative interruption; a fire drill that ruins a three-lesson flow. It usually just doesn’t make sense to try to plan in detail so far ahead of time.

Yet I’m doing it this year. It’s a consequence of having to explicitly prepare more in advance of remote teaching, as well as the block schedule we adopted to better serve the uncertainties of hybrid learning. As a result, I’m teaching fewer, but longer, classes and I have to prepare much more material ahead of time for them.

It’s taken me a while to figure out how to design a remote class that works for me and my students, but now that I’ve started to get the hang of it I find I’m able to plan detailed lessons further ahead than I have in the past. Which is a bit of a surprise, given than I started the year having virtually no idea how to plan a remote lesson. But being this far ahead in planning is a nice feeling, and it’s something I hope to bring back to normal schooling someday. At least until the first fire drill.

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“I can’t put my finger on it.”

In our course team meeting this week a colleague was discussing intervention attempts with a student who was resisting offers of support. “Why do you think the student won’t accept tutoring?” I asked. It’s a question I should probably be asking myself about some of my own students.

My colleague wasn’t sure. The student was exhibiting a pattern of odd behavior: Unexplained tardiness; unexpected evasiveness; non-responsiveness. “There’s something going on,” my colleague said. “But I can’t put my finger on it.”

My colleague did put a finger on how I’ve been feeling. There are things going on with some of my students behind their zoom avatars, their emails, their chat messages, but it’s hard to know exactly what. So much harder to know than when you’re standing next to someone, when you can ask them to look you in the eye, when you can pull them out into the hallway for a quick check in.

Before I began teaching a mentor offered some powerful advice in the form of a warning: You never know what someone is going through. It’s good advice in life, and even better advice in teaching. And right now it’s harder than ever to know.

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