Each year, the California Mathematics Council hosts a NorCal conference for Math teachers at Asilomar, near Monterey, CA. It’s a stunningly beautiful place to nerd out with hundreds of other Math teachers for the weekend. This was my third time attending the conference, but my first since 2019, so I want to take a moment to share a few reflections.

First of all, there are a lot of people who not only love teaching Math, but also love talking about teaching Math. There were dozens of sessions and only six time slots, so it was really hard to pick just one place to go. Talks I attended ranged from the hyper-specific (such as methods for teaching equivalence to English Language Learners), to the esoteric and philosophical (such as a defense of Algebra II’s role in the curriculum).

Probably my favorite session was on the Math of music, where Zeke from The Exploratorium talked about how ratios between different pitches and harmonics lead to consonance and dissonance in music. This is something I have been exploring personally for a couple of years, and it was like one of the youtube videos I’ve watched was coming to life. It was the final session of a long day of reflecting on my teaching practice and networking with other teachers, and it was so much fun.

Second, I doubled-down on my love of problem- and project-based learning. The stars of the show this weekend were the folks behind Building Thinking Classrooms. Equal parts inspirational and practical, BTC is hands-down my favorite book on teaching. I even wrote a bit about it here. The author was the keynote speaker, and a number of sessions centered on their classroom practices. My key takeaway here was that engaging students with good problems is the best way to help them develop as mathematicians.

And speaking of good problems, that brings me to my final takeaway from Asilomar. I just love a good Math problem. Every time I’ve attended this conference, the best part has been the problems I come home with. I’ll share one that I discovered during a session by the folks at Innovamat:

How many different quadrilaterals can you make on a 3×3 grid?

I showed up to this session late because I knew my colleague was there and would give me the notes. Instead, I opted to check out the exhibition floor and see if I could win a free calculator (I didn’t). When I got to the session, everyone was already working on this problem and I dove right in. It’s so simple, yet leads to so much complexity. Used in the classroom, it’s a great vehicle for introducing concepts in geometry such as types of quadrilaterals, their perimeters and areas, as well as similarity and congruence. It leads to debates, such as what it means for two shapes to be different, or what it means to be “on the grid.” And on top of all of that, it’s the perfect low-floor, high-ceiling task that can meet every learner where they are. My next mystery here is to find how many quadrilaterals you can make on a 4×4 grid, and see if there’s a pattern. Methinks there is…