In my last post, I shared a question posed to me by a student. Essentially, it boiled down to: can we algebraically prove that the following will always be an integer? I shared it with two friends in my department because they both really love combinatorics like me. One gave me some really nice ways ..read more

Today in class, a student asked a question that stumped me. I haven’t yet given myself a lot of time to think about it, but I went into the city after school for something and on the subway ride home I had my audiobook on and I basically didn’t “hear” anything because my mind kept ..read more

On Thursday, after school, I hopped in an Uber to the airport. I was flying to a conference, the “Teaching Contemporary Mathematics” conference (TCM) held at the North Carolina School of Science and Mathematics. I think I’ve been at least twice over my career, maybe three times, and always found it to be a really solid conference. The big sell for me is that it’s primarily high school math-focused, and most of the sessions are given by actual math teachers about their own teaching practice. And more importantly, it’s felt like forever since I just got to geek out with other math teachers. A fe ..read more

I had a thought that just occurred to me and I wanted to archive it before I forgot it. I’ll probably forget that it is even here at all, and nothing will come of it, but I had a thought about developing a new one-semester course for juniors and seniors at my school. It would be called something like “Reading and Writing about Mathematics.” I’ve always been obsessed with reading books that aren’t textbooks about mathematics. I have almost half a bookshelf filled with these books. I love (when I have time) reading articles about modern mathematics in Quanta magazine. I’ve sometimes formally inc ..read more

For a month this summer, I paid $30 to get an Alamo Drafthouse Movie Pass. Alamo is a movie theater that allow serves food and drinks. What the Movie Pass allows you to do is watch a movie every day (and you only pay a $1.89 service fee). It is summer and I figured why not? I could take good advantage of this deal. I had never gone to the movies alone before, but this past month I realized I really enjoy it! The movies I saw using the pass: Mission: Impossible – Dead Reckoning Part One The Lesson Oppenheimer Past Lives Indiana Jones and the Dial of Destiny Shortcomings Joy Ride Haunted Mansio ..read more

Throughout the month of July 2023, I participated in a PD experience that was unique to me. Justin Lanier, a former math teacher turned professional mathematician, held a PD he developed called “21st Century Mathematics” and the ultimate goal was “To grow as mathematicians, both for our own enjoyment and for the benefit of our students.” Each week in July, he provided problem sets for us to work on. Justin kindly allowed me to share these: week 1 problems, week 2 problems, and week 3 problems. Each week’s problems were related to a chapter in the book that formed the backbone of the course: Th ..read more

This is a continuation of the previous post. My goal here is to connect this up to calculus. Below is a graph of stitches I need to make to create any given row. So for example in Row 16 and Row 17, I have to make 45 stitches. So to find the total number of stitches from row 1 to row n, I have to take the integral of this function. So to find the total number of stitches in the entire shawl, I’ll take the integral from 0 to 168. And two things become apparent. First, we get the answer we expected from the calculations in the previous post: 30,072 stitches. Second, we have a Riemann Sum that ..read more

Last summer, my friend and math teacher extraordinaire Peg Cagle started teaching me to knit. It’s been wonderful — something I can do while listening to audiobooks. I’ve been trying to push myself a little bit each time I pick a new project [1]. I’m now working on something called the Boneyard Shawl by Stephen West (who is one of my favorite knitting designers). This is what the final shawl looks like: Now I was at the library knitting, after writing a college recommendation and needing a breather… and I started wondering seeing some nice math in what I was doing. So I wanted to recreate som ..read more

I got an email from a college friend about their kid Sam… Ahoy Big Sam! I have a question regarding Lil Sam.  He’s big on math.  Like big big.  Do your colleagues in the lower school / primary school have a list of resources for self-directed math exploration for the youth? Or even applied math via games etc so its more play / exploration vs workbooks? It got to the point that he was asking us to come up with math questions that we just bought a stack of workbooks but those feel like work and less development of interest and joy.  Now I don’t know anything about little ki ..read more

One way I start my Advanced Precalculus classes is by having them thinking about n-dimensional cubes. We get there by first exploring the “Painted Block Problem“. First I have kids look at one of these blocks (I think I give a 5x5x5 block) and have them notice and wonder. Eventually kids wonder what’s on the inside, why different parts are painted different colors, etc. And after some drama, we open up the block, and kids see the new color inside. The question they then are tasked with are how many mini-cubes of each color exist in an n x n x n block. To be clear, green blocks have 0 exposed ..read more