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.
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.
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.
Related Posts
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.]
Trying to get the timing right was a nice little diversion at the bottom of this beautiful crater lake.