Teaching

Remote Learning — Week 2

May you live in interesting times, so the blessing / curse goes. These are certainly interesting times to be a teacher.

Mandatory remote learning has given the entire teaching community a common challenge to face, one that most teachers have no experience with. Effective teachers are problem solvers by nature — with hundreds of little issues to deal with each day, we must be — so it’s no surprise that teachers are largely rising to the occasion. But in observing teachers navigate this challenge, I’ve noticed very different approaches.

I mentioned this the other day.

A lot of teachers are looking to recreate the experience of their classroom, with mandatory Zoom meetings, roll call, video-proctored exams, and other synchronous activities. My approach has been to recreate the workflow of our classroom: presentation of key ideas followed by low-stakes formative assessment followed by a work-feedback-revision cycle, all happening asynchronously. With this basic framework in place I’ve only recently begun to consider how live sessions can fit in. I see their value, if for no other reason than to connect with each other, but so far students have expressed mixed feedback about their importance.

As I said in my tweet, this is all observation, not judgment. Like everyone else I’m just trying to figure out what works for me and my students. And things will change, as they so quickly do these days. But I hope we take advantage of these new challenges and new technologies to rethink what we do, rather than simply figure out ways to replicate what we’ve always done.

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By MrHonner, ago

Remote Learning — Week 1

The COVID-19 pandemic closed New York City schools down two weeks ago. After a week of preparation, we officially transitioned to remote learning on March 23rd. Having just completed our first week, I asked for feedback from my students. I wasn’t sure what to expect.

In the thread that follows the above tweet, I share some things students say are working for them. One of those is flexible scheduling: All of the required work is asynchronous, which allows students to figure out for themselves the best time to get work done. A recurring sentiment in the feedback is the value of learning at my own pace:

“I could actually take my time to comprehend the lesson plan on my own pace.”

“That I could do work mostly when I felt like it, instead of being stuck to doing it between 8:45 and 10:15.”

“I was able to finish all my work in my own time without having to catch up to anyone in class”

“There are times I get stuck on a math problem and I would just put it aside and have it at the back of my mind while I do something else and come back to it at a later time.”

A lot will have changed by the time the coronavirus has passed. As we start our journey into remote learning, I wonder how my teaching will change. It seems I’ll have plenty to think about.

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By MrHonner, ago

NPR — Teaching Math Using the Coronavirus

I make a brief appearance in this NPR story about teaching using the coronavirus. In “Teacher Uses Coronavirus for Math Lessons”, reporter Emily Files profiles a teacher in Wisconsin who is using the coronavirus epidemic to get his middle school math students thinking about data and rates of change. Files interviewed me a about the lesson I wrote for the New York Times Learning Network on “Dangerous Numbers” (available here).

By MrHonner, ago

How Rational Math Catches Slippery Irrational Numbers — Quanta Magazine

My latest column for Quanta Magazine is about a clever technique for finding rational approximations to irrational numbers. The technique, developed by the German mathematician Gustav Dirichlet, works by covering the number line with tiny intervals centered at certain rational numbers.

But Dirichlet did better. He improved this method by figuring out how to shrink the intervals around their centers while still keeping the entire number line covered. As the intervals shrink, so does the distance to any irrational number we are trying to approximate. This means we’ll get better and better rational approximations, even using relatively small denominators. But we can’t shrink the intervals too quickly: Even though there are infinitely many of them, if the intervals get too small too fast they won’t cover the entire number line. In the battle between the infinitely large and the infinitely small, Dirichlet had to find the right balance to prevent some irrationals from slipping through the cracks.

Dirichlet’s technique explains why we can always find good rational approximations to irrational numbers using small denominators, like \pi \approx \frac{22}{7}. Developed nearly 200 years ago, this technique ultimately led to the proposal of the Duffin-Schaeffer conjecture which was finally proved this past year.

You can read the full article here.

By MrHonner, ago

What Makes a Great Teacher?

great teacher - patrick

I’m honored to be featured in Ben Orlin’s post “What Makes a Great Teacher?”

Ben, the author of “Math With Bad Drawings“ and “Change is the Only Constant” (one of the books I read in 2019) asked four teachers to respond to a fan’s inquiry. Here’s what I had to say.

I’m reluctant to use the phrase “Bad Teacher.” Faced with hundreds of interactions and decisions every day, we all have good and bad moments. Those moments accumulate over a semester, a year, a career, and in most cases yield a net positive result I’d say.


But you can tell a lot about a teacher by how they respond when students don’t succeed. Some will say, “What’s wrong with you?” Others will ask, “What’s wrong with me?”

I really enjoyed thinking about the question, and the different and diverse insights of Fawn Nguyen, Jo Morgan, and Marian Dingle were wonderful. As were Ben’s trademark illustrations of our responses! He nailed mine. Be sure to check out the entire post for yourself at Ben’s blog.

By MrHonner, ago
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