2023 — Year in Review

As I reflect on my professional 2023 I keep coming back to the line “Normal is normal again.” Not the world, certainly, and not for everyone, but since changing schools nearly five years ago this is the first year when being in the classroom hasn’t felt extraordinary for extraordinary reasons.

Still, it’s been a mix of the new and the old. In addition to my normal lineup of geometry, calculus, and linear algebra courses, I’ve been doing more mathematical modeling with students this year. In the spring we had a team of modelers invited to compete in the International Mathematical Modeling Contest (IM2C), thanks to their excellent work on last year’s High School Mathematical Contest in Modeling (HiMCM), and I’ve been working to expand the program at school. This year interest was high enough to have eight teams compete in the HiMCM, and we’re looking forward to new modeling opportunities this spring. In addition, a colleague and I mentored around 70 students who competed in a national forecasting tournament inspired by the Good Judgement project, and our teams took first and second place!

An extracurricular highlight this year was interviewing mathematician and author Manil Suri for the Jaipur Literature Festival. We had a lively talk about his excellent new book, The Big Bang of Numbers, and also about math, writing, and teaching, and the Asia Society of New York made the entire video of our conversation available here.

As usual, I continued to design and run workshops for teachers this year, including a new entry in my ongoing linear algebra series titled Learning to Love Row Reduction. I also gave two talks at this year’s NCTM Annual Meeting: So, You’re Teaching Pre-Calculus, and A Case for Linear Algebra. I’m already looking ahead to new talks this coming year, including an upcoming workshop on the geometry of linear regression I’ll be presenting in February.

Writing my column for Quanta Magazine was as challenging, and fulfilling, as ever, with pieces aimed at bridging the gap between classroom and research math focused on the newly discovered aperiodic monotile, the algebra of secret codes, graph theory and cliques, a high school student’s amazing proof, and what three-point turns tell us about a hundred-year-old geometry problem.

And with the landscape of social media continuing to change, I’ve been enjoying my time on Mastodon more and more in 2023.

Platforms based on decentralization, user autonomy, and interoperability definitely seem like the right way forward. And I’ve been trying to do a better job of archiving what I write by cross-posting some of my social media posts here on my blog.

It’s been a good 2023, and here’s hoping for another good, and relatively normal, 2024!

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ChatGPT in Geometry Class

I gave my geometry students some ChatGPT-generated “proofs” this week to review. There were several examples, each designed to illustrate a different point. One was a “proof” that the diagonals of a rectangle are congruent, which contained several errors. I was proud that several students immediately identified how dangerous it was: “It sounds like it is correct, until you look more closely at it.”

Originally posted on Mastodon.

Pierre de Fermat’s Link to a High School Student’s Prime Math Proof — Quanta Magazine

My latest column for Quanta Magazine tells the mathematical story of the incredible high school student who proved a result about not-quite prime numbers that had eluded mathematicians for decades.

[Daniel] Larsen was a high school student in 2022 when he proved a result about a certain kind of number that had eluded mathematicians for decades. He proved that Carmichael numbers — a curious kind of not-quite-prime number — could be found more frequently than was previously known, establishing a new theorem that will forever be associated with his work. So, what are Carmichael numbers? To answer that, we need to go back in time.

You can read the full article for free here.

NCTM 2023

I’ll be in Washington, DC later this week for the National Council of Teachers of Mathematics (NCTM) Annual Meeting, where I will be giving two talks.

On Thursday, Gary Rubinstein and I will be presenting “So, You’re Teaching Precalculus”.

With the College Board’s new Advanced Placement Precalculus course on the horizon, a lot of math teachers will be teaching a brand new course in 2023. What are the big ideas in AP Precalculus? And how might AP Precalculus differ from the courses already taught at your school? In this session we’ll look at the themes that define the AP Precalculus framework and how they link important ideas in algebra, geometry, and trigonometry to what lies ahead in a calculus course.

And on Friday, I’ll be making “A Case for Linear Algebra”.

Students need as many pathways to mathematical success as we can give them, and linear algebra offers a flexible and versatile course option that can fit alongside an established sequence or help define a new one. Come learn about the whys and the hows of teaching linear algebra, and see where the core ideas pop up in the classes you already teach.

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This Student Gets Me

Student: “The distance to the far end of the circle is three.”
Me, skeptically: “Where is the ‘far end’ of the circle?”
Student, gesturing: “On the far left side.”
Me, intentionally choosing a point on the left that is close to, but clearly not, the farthest left: “Oh, you mean here?”
Student pauses: “I understand what you are trying to do. But I don’t know how to be clearer.”
Me, surprised: “What am I trying to do?”
Student: “You are trying to force me to be more precise in my statements.”

I’m impressed at how thoroughly this student understands me after only four days of class.

[Originally posted on Mastodon.]

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