Teaching

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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By MrHonner, ago

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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By MrHonner, ago

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.

By MrHonner, ago

“That’s a good question.”

“That’s a good question.”

I’ve done it a hundred thousand times in my career. A student is trying to solve a problem and calls me over. They ask a question that indicates they are right where they should be. I praise them for asking such a question. And then I walk away.

Some students find it frustrating at first. They expect an answer to their question. Well, they expect a different kind of answer. They will soon understand that I have answered them: I’ve indicated they have asked an important question, and by not answering it, I’ve suggested they are capable of answering it themselves. They learn to recognize it as validation, though it may not offer as much assistance as they hoped for.

It takes time and practice to learn how much validation, and how much assistance, each student needs. I err sometimes, but it’s an important investment in the classroom culture I hope to build each year. It’s such an integral part of my classroom experience that it’s been mentioned in valedictory addresses.

And it feels likes it’s been taken away in remote teaching. So much of that 10-second interaction relies on being there together: the body language that accompanies the question; the glimpse at the paper; the quick read of the group mates; the half smile that gives some warmth to a superficially cold response; the eavesdropping as I walk away to make sure the right message was received. It just doesn’t happen like this in a Zoom meeting. Which is not to say I can’t build this kind of classroom culture remotely. It’s just harder without my familiar tools.

When I wrapped up my emergency remote learning journal last year, I wasn’t expecting to pick it up again this fall. Not because I thought everything would be back to normal, but because professional exhaustion prevented me from thinking about starting a new school year remotely. But we’re here now. And there are still lots of things to think about and adapt to. And new tools to build.

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By MrHonner, ago

MfA Workshop – A Crash Course in Geogebra

Today I’ll be facilitating “A Crash Course in Geogebra” as part of Math for America‘s summer professional development series.

In response to the challenges and uncertainty of the upcoming school year, MfA teachers have been sharing ideas and expertise with the community this summer. My experiences using Geogebra during NYC’s emergency remote learning led me to develop this workshop.

Geogebra is an invaluable tool for doing mathematics under normal circumstances, but its versatility as a mathematics environment, a demonstration tool, and an assessment platform is even more important in this era of remote and hybrid learning. In addition to reviewing the basics of Geogebra in the webinar, I’ll also share specific classroom strategies and student project ideas for implementation in either face-to-face or remote/hybrid learning.

As I said recently, I can’t imagine teaching geometry remotely without Geogebra. And while I can imagine teaching geometry face-to-face without it, I wouldn’t want to!

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By MrHonner, ago
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