Teaching

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.

By MrHonner, ago

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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By MrHonner, ago

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.]

By MrHonner, ago

Math that Moves the Needle — Quanta Magazine

My latest column for Quanta Magazine explores a century-old geometry problem that anyone who’s ever performed a three-point turn can appreciate.

Imagine you’re rolling down the street in a driverless car when you see a problem ahead. An Amazon delivery driver got their van halfway past a double-parked UPS truck before realizing they couldn’t make it through. Now they’re stuck. And so are you.

There’s a fun math problem here about how much space you need to turn your car around, and mathematicians have been working on an idealized version of it for over 100 years. It started in 1917 when the Japanese mathematician Sōichi Kakeya posed a problem that sounds a little like our traffic jam. Suppose you’ve got an infinitely thin needle of length 1. What’s the area of the smallest region in which you can turn the needle 180 degrees and return it to its original position? This is known as Kakeya’s needle problem, and mathematicians are still studying variations of it. Let’s take a look at the simple geometry that makes Kakeya’s needle problem so interesting and surprising.

You can read all about the surprising resolution of Kakeya’s needle problem in my full column for Quanta Magazine.

By MrHonner, ago
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