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

Coding Math at a Distance — #NCTM100

I’m excited to be co-presenting “Coding Math at a Distance” this week as part of NCTM’s 100 Days of Professional Learning webinar series.

I’ll be working with Mike Larson and Ashley Goetz, the teachers who co-founded CSandMath.org, and our webinar focuses on simple ways teachers can use computer science to enrich math learning. Mike, Ashley, and I have all been involved in this work for many years, and we’re excited to share both big ideas and classroom-ready resources for teachers.

We’ll pay particular attention to the ways in which integrating CS and math makes sense for remote and hybrid learning environments. We know teachers are looking for new approaches to engagement, assessment, and collaboration in this era of remote learning, and integrated math and CS projects offer lots of exciting opportunities, for both teachers and students.

The webinar is free and part of NCTM’s centennial celebration. You can find out more, and register, here. You can also access resources from our session: Our takeaway document; a Scratch studio that includes code examples; and a set of function-based extension projects.

UPDATE: The full webinar has been posted on the NCTM website.

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By MrHonner, ago

AMS Math in the Media — Interview

I was recently interviewed for the American Mathematical Society’s Math in the Media column, in which I answer some questions my Quanta Magazine column and about writing about math for the public. I was asked specifically about my column on the universal covering problem.

Why did you recently choose to write about the universal covering problem?
It’s such a fun mathematical story to tell, with meaningful connections to high school geometry. And there’s something uniquely mathematical about studying a shape for a hundred years and still not knowing exactly what it looks like. I enjoy bringing those experiences to others.

The rest of the short interview can be found here.

By MrHonner, ago
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