# Killer Class

In Advanced Precalculus, my kids were working on something I call “The Arrow.” It’s new this year — something my co-teacher and I dreamed up to make combinatorics make sense. It’s incredible. My co-teacher told me today “I’ve had so many amazing insightful conversations around combinatorics this year, I feel like I have had more than I deserve in my teaching career.” (Or something like that.) I agreed, saying it was an “embarrassment of riches.” The kids — on their own — have come up with a formula for combinations and permutations (they don’t know it yet… we haven’t given names to them yet). And in doing so, they actually derived the binomial expansion. No Pascal’s Triangle. (That comes later, as a consequence of everything that we’re doing.) They spent 30-40 minutes persevering and had so many gaspable moments.

They had insights about tree diagrams, connected them to “tile problems” (the structure we dreamed up), kept on asking why instead of moving forward just to move forward. It was the most beautiful noise. I wish I had a videotape of this class — so I could show it to future classes so they could see what my ideal class looks like.

It was the best.

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In my 90 minute Precalculus class today, I took my kids to the math-art gallery that I helped curate. I was nervous about it. This is my tiny, quiet class. But because I had a great structure to facilitate the visit (given to me by my partner-in-crime Brendan), the visit went well. They kids for the most part found pieces they were fascinated by. And I heard some interesting conversations.

***

I bought a game (we didn’t playtest this at allrecently, but hadn’t opened it. It’s a 1-5 minute game. I broke it out in our math office, and we played a few times. I love that my office has quirky teachers that enjoy being quirky. After this, we played a game where everyone got a slip of paper, and we had to write our names and a counting number on it. Then we gathered the papers, and the person with the lowest unique number wins. (So if the papers had 1, 1, 2, 3, 7 on them, the person who wrote 2 wins! And if the papers had 2, 3, 4, 4, 8 on them, the person who wrote the 2 wins!) I don’t know why but we totally geeked out about this too. (As a side note, I had a multivariable calculus student do an interesting final project on this problem a few years ago… and how it relates to the Nash Equilibrium… she’s now at MIT!)

***

We had a firedrill and it was beautiful weather outside. So although my class was interrupted, it was worth it for the moment of zen. Especially since today I taught all of my classes — and one of them was the 90 minute block. On a Friday before a long weekend.

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I have a teacher friend who had a medical issue this summer, and so things have been hard for her this year physically. I hadn’t seen much of her, except in passing in the halls. But I happily got a text from her asking if I was free for dinner — so I went to meet up with her in Park Slope and get some delish thai food. It was great catching up with her!

## 3 thoughts on “Killer Class”

1. suevanhattum

Will you share “The Arrow”? I am right now teaching combinatorics in my CC Statistics course.

• I just emailed you some files. I’m afraid that without me blogging them extensively, the files aren’t going to be much use (and I don’t have time to blog right now) 😦 But maybe you can figure them out? I will say that teaching combinatorics this year has totally opened my eyes to the subject in a new way. It’s pretty amazing!

• suevanhattum

So generous! Thank you. I will be eager to read anything you have time to write on this topic.