A particularly soothing art deco facade in Miami Beach, both because of its curves and its blues.
Resources
The Math of Social Distancing is a Lesson in Geometry — Quanta Magazine
My latest column for Quanta Magazine connects the geometry of social distancing, a topic on everyone’s mind right now, with sphere packing, a problem mathematicians have been working on for hundreds of years.
Determining how to safely reopen buildings and public spaces under social distancing is in part an exercise in geometry: If each person must keep six feet away from everyone else, then figuring out how many people can sit in a classroom or a dining room is a question about packing non-overlapping circles into floor plans.
In two dimensions, the sphere packing problem is really the circle packing problem, and the best way to pack circles in the plane is known. But it was only recently that mathematicians settled the question about how to most efficiently pack spheres in dimensions 8 and 24. And there are still many open questions in other dimensions!
You can read the entire article here.
Geometry Photography
Math Photo — Parallel Paths
I like the parallel paths traveling across the surface of this lampshade. I can’t recall ever seeing this irregular polyhedron before, with its equatorial belt of alternating isosceles triangles and trapezoids at the top and bottom.
Teaching
Remote Learning — Week 14
Everything has changed, so they say. The end of the school year is usually a time of great relief and satisfaction, but there’s something anticlimactic about this transition to summer. Usually it’s accompanied by a comforting sense of resolution. Not this year.
My department spent its final days trying to talk about the fall. What if we see students every other day? What if we only see them every five days? What if we’re entirely remote at the start? Can adjusting our course sequences help? How do we approach assessment? Participation? Collaboration? In a way it’s fitting that we end with as many questions as when we started. Maybe more.
I’ve heard people say remote learning made them feel like they were first-year teachers again. I wouldn’t go quite that far, but rethinking everything from instruction to engagement to assessment definitely brought back memories of my early career, when everything I did seemed like an experiment on the brink of failure.
Navigating Emergency Remote Learning as a teacher has been an unique professional challenge. I’m thankful that I didn’t have to face it alone: I learned alongside many great teachers in New York City and across the country. And I’m lucky that my students were ready to adapt, learn, and succeed, as they always are.
And so ends fourteen weeks of reacting and adapting. I’m glad I made time for these reflections: They’ve helped these past few months, and they’ll help in the fall. But first, I’ll give the comfort of summer a few more chances to sink in.
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Teaching
Remote Learning — Week 13
As part of their end-of-year portfolios, students completed a survey reflecting on their remote learning experiences. I asked questions about the workload, the resources they found most helpful, and what was missing. Overall I got lots of great feedback, both on things I knew about and things I didn’t.
But the feedback also demonstrates why it can be so difficult to think and talk about education at scale. Take these two responses, sitting right next to each other in my spreadsheet.
“I think that you should consider doing more whole class meetings.”
“I would say to avoid class-wide calls for Remote Learning.”
To me, this exemplifies the core challenge of the practice of teaching: What works for one student may not work for another. What works for one teacher may not work for another. What works today may not work tomorrow.
The fundamental unit of teaching is person-to-person interaction, and those individual interactions are subject to great variation. Of course there are general trends in what the students said in their surveys, and there are general approaches to teaching that work better than others. But to teach all students we need to listen to all students. And we must always be mindful that each experiences instruction in their own way.
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