Pedestrian Algorithms

…17…16…15…

I’m not going to make it. I’m about 75 feet away from where the crosswalk begins, and it’s a boulevard. Plus my back is already damp from commuting with this backpack and shoulder bag. An 18-second trot will only make things worse.

I slow down, but eye the corner. I do have to go north: Should I make the turn? If I do, I run the risk getting caught at the the next light. What’s the right move? Let’s do the math.

If I wait it out here, I’ll be stuck at a newly green light staring at the “DON’T WALK” sign for the maximum possible duration. If I make the turn, there’s no guarantee that I won’t get stuck at the next light, but that’s no worse than what I’m facing now. And there’s a good chance I’ll arrive in the middle of the cycle somewhere and be spared the maximum delay. That would get me to the opposite vertex of my rectangle in less total time than if I stop and wait it out now.

I make the turn. And await the next opportunity to optimize my commute.

Beyond My Control

Teachers have great power to impact their students, yet so much depends on factors beyond their control. This is one of the many tensions of teaching.

In my first year as a teacher I noticed some students didn’t bring pencils to class. I was dumbfounded. “How are you going to do math without something to write with?” was my naive reaction. Later I realized the more pressing question was “How am I going to teach math if I can’t rely on kids bringing pencils?”

As a public school teacher you become acutely aware of what you rely on. Even the best schools I’ve worked at would run out of paper, or chalk, or chairs. Working hard only to have your plans derailed by something beyond your control really stings.

All of this has shaped my approach to teaching with technology. In many ways I’m a very technology-positive teacher: I was an early adopter of tools like Desmos, Geogebra, and Scratch. But I’ve been reluctant to grow too dependent on technology in my teaching. I’ve had Smartboards for years, but never prepared slides; I’ve had laptop carts, but designed lessons that required internet access sparingly. It’s a very real possibility that I’ll show up to school and the Smartboard or wifi just won’t work. With so much beyond my control, it’s often easier to just avoid the risk.

One of my frustrations in the current remote/hybrid landscape is that I can no longer avoid that risk. Every single moment of my teaching now depends on multiple technologies functioning properly. And teaching well requires not only that they function, but that they and I function together smoothly. Now I find myself depending on a Smartboard and Google Classroom and Zoom and so much more. And I have to learn them all while trying to figure out how to turn a video conference into math class. It’s a bit overwhelming on the best of days. And then my laptop speakers decide to stop working.

There’s a minimalism to teaching and learning math that I’ve always loved. With just a pencil and paper I can become a mathematician. With just one good question I can launch a math class. But now there’s a lot more I have to rely on, and plan for. And it’s all beyond my control.

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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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