## Weaving Classes into Courses

I’ve heard veteran teachers say that this new era of hybrid and remote learning has them feeling like first-year teachers again. In some ways I feel it too. Seven days into to fully remote instruction and I’m still figuring out how much I can reasonably expect to accomplish in a 55-minute Zoom meeting, how I can most effectively present ideas, how I can best get students interacting with mathematics and each other.

Like in my first year of teaching, I find myself focused on very short-term goals: Getting through today’s class; getting students to engage with a single concept; getting them to demonstrate mastery of one unadorned procedure.

I’m generally energized by the challenges of teaching, but it’s difficult going back. After 20+ years in classrooms I’m used to thinking in terms of threads that weave classes into courses, the small details that bind together a year’s worth of conversations and explorations. It’s hard to get there when you’re unsure about executing the daily details that make class run.

I did it once, and I can do it again. I just hope it doesn’t take me as long this second time.

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## The Simple Math Problem We Still Can’t Solve — Quanta Magazine

My latest column for Quanta Magazine explores a simple math problem that no one should try to solve. Even though everyone has probably tried to!

This column comes with a warning: Do not try to solve this math problem.

You will be tempted. This problem is simply stated, easily understood, and all too inviting. Just pick a number, any number: If the number is even, cut it in half; if it’s odd, triple it and add 1. Take that new number and repeat the process, again and again. If you keep this up, you’ll eventually get stuck in a loop. At least, that’s what we think will happen.

The infamous Collatz conjecture has been capturing the attention of mathematicians and recreational problem solvers since it was first introduced in 1937. It seems so simple, yet no one has been able to prove it. Recent progress has been made, however, by none other than Terry Tao, one of the world’s great mathematicians.

You can learn more about Collatz conjecture in my column. Just don’t try to solve it! You’ve been warned.

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