## Saturday, June 18, 2011

### Putting myself in my kids' shoes

I always preach mathematical fearlessness to my kids, my colleagues, and just about anyone who will listen. I go on and on about the importance of being able to sit with a new problem for more than 5 minutes, or even 5 days, and mulling it over, poking around, trying whatever you can to solve it without giving up or losing interest or Googling the answer. I always want my students to try something in lieu of just staring, and I am usually stingy with hints.

One thing - quite possibly the only thing - I miss about math grad school is the feeling of sitting down and figuring out a really, really difficult problem. At the time it felt a bit like "intellectual masturbation" because that's all I would do and I felt like I was contributing absolutely nothing to the world, but it definitely helped me develop my mathematical fearlessness. Since I started teaching it is rare that I actually sit down with a truly challenging problem and force myself to think it through from start to finish. So much of what I do is in a rush - I don't have time to really think about a problem because I am trying to plan two lessons for the next day, so instead I think about it for 5 minutes and then look at how someone else did it. Shameful, I know. The question presented itself to me: Can I actually practice what I preach? Am I still mathematically fearless?

My office-mate presented me with this problem about a week ago: You have a square dartboard. What is the probability that a randomly-thrown dart will land closer to the center of the dartboard than to an edge?

I sat down to solve it and was absolutely stumped. I had no idea where to start besides drawing a little picture. Said office-mate told me that he had banged his head against the wall and couldn't figure it out, which made me a little disheartened because I consider him to be a much more clever problem solver than I am. [Lesson one about how my kids feel: It's difficult for them to actually believe in their abilities when they look around and see classmates who they consider to be "smarter" who are also struggling with the problem.]

I took the problem home and presented it to my boyfriend, who really is the smartest math guy I know. He struggled with it for a little bit, went inside the bedroom, and came out about 30 minutes later announcing that he had solved it and that he would not tell me how he did it. Fine. Be that way. At that point I was still really struggling; I didn't even feel like I had a solid starting point. I went into the bedroom and I have to admit that I glanced over at his clipboard where he had solved the problem and saw some nasty math that I didn't like. My heart sunk even more. [Lesson 2 about how my kids feel: When they see another student's solution and don't immediately understand it - and how could you really immediately understand someone else's solution to a problem? - they tend to give up because they think that they could never think of that solution. The thought doesn't even cross their mind that maybe they can come up with another way to solve the problem.]