- Today I had two kids linger at the end of our multivariable calculus class. I wasn’t sure why, so I asked them what was up. They had gone to the school book fair, and saw Ian Stewart’s
*Flatterland*for sale there, and bought it for me! (Earlier in the year, we read*Flatland*for class.) It was so incredibly sweet. I asked them to inscribe their names into the book, so I could always remember it came from that. I’m going to miss the kids in this class when they go off to college next year. - At the start of each class, kids push the tables so they can seat five groups. I have folders for each group, and I throw the folders on different tables each day (so kids aren’t always sitting in the same place). Today three students were helping me by rearranging the tables, so I told the kids they could place the folders and choose who sat where. I had five folders and three students. So my mind wandered:
I could give two students two folders and one student one folder. 2+2+1. Or 3+1+1. Or 3+2 (one student would get no folders). Or 5.

I enjoyed thinking about this, so instead of starting class, I introduced the notion of

*partitions*with my kids. We generated p(1), p(2), p(3), p(4), and p(5). I had kids come up with p(6) and p(7). We compared our answers to the list on the Wikipedia page I pulled up. We saw how quickly the values of the function grew. I then showed kids the trailer to the movie involving G.H. Hardy and S. Ramanujan (which I watched this weekend):Why? Because the partition function was an important part of the movie! I told them go to see it! Then somehow we started talking about other weird things in math, and although I didn’t get to spend much time before being forced to move forward, it was great because it reminded me:

**go on tangents in math class because it piques students’ interests and I can capitalize on that! It feels different and weird, and interesting!** - Without giving too much context, I got an incredibly thoughtful email from a student which — in essence — centered around the idea of ethics/morality. It reminded me that kids sometimes can and do think deeply about their actions. (Although it sounds like this was about cheating, it wasn’t.)
- I had a nice conceptual insight that made me so happy. A multivariable calculus student was having trouble getting the right answer to a problem… his answer was off by a factor of 4. I eventually figured out what his error was and emailed it to him. I did it algebraically. But then I asked myself “why? why did the algebra work out as such?” and I felt
*awesome*when I figured it out conceptually/visually/geometrically. It wasn’t deep, but I was proud of (a) asking the question and (b) answering the question.

# A Book and Partitions

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