# A Book and Partitions

1. 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.
2. 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!

3. 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.)
4. 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.