Sharing Instructional Materials

In a recent thread on Mastodon I was talking with Ben Leis and Tim Ricchuiti about instructional materials and I mentioned that I basically create everything I need from scratch rather than use materials that already exist. The conversation got me thinking about the challenge of creating instructional materials that can be shared.

It certainly does require a lot of work to create my own instructional materials, but it’s work I enjoy. And it really doesn’t occur to me to do it any other way. No instructional materials exist that can properly leverage the collective strengths of our classroom, so I just create materials that do.

As a result, these materials work very well for me but wouldn’t necessarily work well for others. For example, a recent lesson I wrote starts with the following question for students: “What does a b mean?” I know exactly what I want to happen as a result of that question. I have a sense of how student discourse and collaboration will unfold, and I know how the answer (and the work leading up to it) fits in the development of ideas from intuitive notions of “infinitesimally small” which arose the first day of class to the notion of “arbitrarily close” and the epsilon-delta definition of limit. And as a teacher I know how to manage the action and close the gaps when necessary.

But I doubt that same question (and the same supporting lesson materials) would work for another teacher. Of course anyone can teach this idea in this way, but the instructional design is so tailored to my context that I’m not sure how useful my materials would be to someone else.

You can see the entire thread on Mathstodon here.

Jaipur Literature Festival New York

I’m thrilled to be a part of the upcoming Jaipur Literature Festival in New York City, where I’ll be in conversation with mathematician and novelist Manil Suri. Manil’s latest book, The Big Bang of Numbers, is a tour of mathematics from the ground up, allowing the reader to the experience of the power of mathematical creation as Manil constructs the universe using only math. It is a fun, friendly, and one-of-a-kind book.

In our JLF session A Universe Built on Math, Manil and I will be talking about math, writing, teaching, and everything in between. The talk is happening on September 13th at 4:30 pm at the Asia Society. All the details can be found here.

Math Patterns That Go On Forever but Never Repeat — Quanta Magazine

I wrote a column for Quanta Magazine on the recently discovered “hat tile”, the first ever aperiodic monotile!

Have you ever admired how the slats of a hardwood floor fit together so cleanly, or how the hexagons underneath your bathroom rug perfectly meet up? These are examples of geometric tilings, arrangements of shapes that fit snugly together while filling up space. Two-dimensional tilings are admired all around the world, both for their beauty — as seen in the artistry of mosaics in cathedrals and mosques around the world — and for their utility, in walls and floors everywhere.

In math, tilings are often appreciated for their regular patterns. But mathematicians also find beauty in irregularity. It’s this kind of beauty that a retired print technician was seeking when he recently discovered the first “aperiodic monotile”— a single tile that fills up the plane in a non-repeating pattern. To get a handle on this big discovery, let’s start by thinking about a simpler problem: how to tile a line.

You can read the full article for free here.


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