Mr Honner

Connecting Classroom Math to AI — NCTM New Orleans

I’m excited to be presenting Connecting Classroom Math to AI at the upcoming NCTM meeting in New Orleans. I think math teachers are uniquely positioned to help students develop healthy, productive, and realistic attitudes toward artificial intelligence tools by making that these tools are understood as applications of mathematics.

Here’s the session description:

Artificial Intelligence tools are everywhere and are likely to affect our lives in profound and lasting ways. To help prepare our students for an AI-driven future, let’s make sure they recognize that these tools are fundamentally applications of mathematics. In this session, we’ll see how topics from the MS/HS curriculum lead directly to the math that underlies technologies like LLMs, chatbots, and more, and we’ll discuss how to make these connections clear and compelling for our students.

You can find all the session details here.

Math Photo — Snow Array

A snow day snow array! I thought of punching out that one stubborn entry, but let it be in the spirit of wabi-sabi. It’s like the Great British Baking Show’s missing raspberry.

Geometry Numbers Teaching

Angle Sums and Pythagorean Triples

I’ve always found it cool that if you double the smaller acute angle in a 3-4-5 triangle you get the larger acute angle in a 7-24-25 right triangle. You can see this as a consequence of the double angle formula for sine. If $\alpha$ is the smaller acute angle in a 3-4-5 triangle, then

$\sin (2\alpha) = 2\sin\alpha\cos\alpha=2\frac{3}{5}\frac{4}{5}=\frac{24}{25}$

In fact, if the sine and cosine of an angle are both rational, then so will be the sine and cosine of twice that angle. This gives a way to turn Pythagorean triples into new Pythagorean triples!

For example, suppose $\alpha$ is an acute angle in a right triangle with $a^2 + b^2 = c^2$ . Then

$\sin 2\alpha = \frac{2ab}{c^2}$
$\cos 2 \alpha = \frac{a^2-b^2}{c^2}$

By the Pythagorean identity

$\left(\frac{2ab}{c^2} \right)^2 + \left(\frac{a^2-b^2}{c^2} \right)^2 = 1$

And so

$\left(2ab \right)^2 + \left(a^2-b^2 \right)^2 = \left(c^2\right)^2$

which of course also follows directly from algebra.

For example, using this process

$(3,4,5) \mapsto (7,24,25) \mapsto(336,527,625)$

Originally posted on Mastodon.

Resources Teaching

2025 — Year in Review

Here are some highlights from what has been another busy professional year.

In September I published a new series in the New York Times that turns Steven Strogatz’s wonderful “Math, Revealed” essays into teaching and learning resources. I got to write about favorite topics like taxicab geometry, triangular numbers, the golden ratio, and packing problems. Best of all, I got to collaborate directly with Strogatz himself! It was an honor to work with him, even if this doesn’t officially make my Erdős number four.

I’ve been thinking and writing about AI in education and math this year. I wrote about how students are using AI, how it is impacting the college admissions process, about experts calling AI-errors “sophisticated”, and how it’s affecting me as a book author. I’ve been through a few hype-bubbles in my time, and am generally skeptical by nature, but there’s no denying the impact these technologies will have in how we learn, teach, and even do math.

I’m wrapping up my 20th, and final, year as a Math for America Master Teacher, and I was proud to run one more workshop for teachers through MfA. “A One-Problem Tour of Statistics” was the story of what I learned by writing Painless Statistics, but also an homage to the kinds of math problems that you keep going back to. It was a fun and satisfying end to a string of nearly 30 workshops I’ve run in my time at MfA.

The applied mathematics and modeling program I run at my school had unprecedented success in 2025. We had a team win the NCTM Award in the 2024 High School Mathematical Contest in Modeling (HiMCM) and finish in the top ten worldwide in the 2025 International Mathematical Modeling Challenge (IMMC). Another team won the MAA Award in the 2025 MCM, finishing among the top of over 12,000 entries worldwide, nearly all of which were college teams! We also had a team earn an “Outstanding” designation — the highest honor — in the 2025 SCUDEM competition, a college-level differential equations modeling competition. I was very proud to be profiled on the COMAP website for “teaching, modeling, and mentoring at the highest level”!

This past summer I was invited to present to the Alliance for Decision Education on my work with student forecasting, after our students made impressive showings in two individual forecasting competitions in 2024 and 2025. I also appeared on MoMath’s QED and spoke with mathematician-in-residence David Reimann about math and math education.

It’s been a good year professionally, and I’m looking forward to more to look back on in 2026!

Writing

The Best Advice I Got in 2025

Draw the lines you see.

I enjoy drawing, and I’m pretty good at drawing mathy things — like surfaces and shapes and diagrams — but beyond that I really have no idea what I’m doing. I’ve always wanted to improve, so when I saw a “Drawing for Teachers” course in the Math for America catalog I was excited to sign up.

The course was terrific. It was facilitated by three teachers, each with different backgrounds in art and different experiences teaching non-art subjects. Each session was filled with theory, history, exercises, and happily, lots of time to draw. It was the best kind of learning experience, one that affects you in many ways. I left with techniques to help me practice, fun activities to try at home, connections that inspire my teaching, and ideas to think deeply about.

But I keep coming back to one particular piece of advice I got from the facilitators. “Draw the lines you see.” I’ve said this to myself many times over past few months as I sit down to sketch. Doing so accomplishes two important things.

First, it centers a basic principle of drawing: everything is made of lines. I suppose this is the kind of observation that is obvious when you know what you’re doing, but as a novice it’s both helpful and practical to be reminded of. That moment I pick up a pencil and commit to trying to draw an object is often overwhelming and intimidating. There’s always a part of me asking “How am I ever going to draw this?” Now I have an answer. Draw the lines you see.

Second, this advice warns me about the common trap I never knew I was falling into. I often draw what I think I see, rather than what I actually see. I think I know what a bird looks like, so after I start drawing it, I stop looking at the bird in front of me and draw the bird I’m thinking of. The problem is I don’t really know what a bird looks like, at least not in enough detail to draw it accurately. My brain dutifully fills in the gaps, and before I know it my bird looks like a flying shark. “You draw with your eyes” was another good piece of related advice from the facilitators.

As eminently practical as this advice has been for drawing, I find it guiding me in other ways. The other day my son politely asked me to try playing the piano accompaniment as it sounds in the recording, not in the bouncy, internal rhythm that I naturally bend all music to. And when reading a book on physics and for the millionth time drifting away from what was written because I’d heard it all before and it didn’t make sense to me, I paused a moment, re-focused on the author’s words, and surprise! It made sense.

Draw the lines you see. Play the music you hear. Think on the words you read. All obvious in retrospect, I suppose, but maybe that’s just the nature of good advice.

Connecting Classroom Math to AI — NCTM New Orleans

Math Photo — Snow Array

Angle Sums and Pythagorean Triples

2025 — Year in Review

The Best Advice I Got in 2025

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