So I took them up yesterday, and surprisingly, solved both without a terrible amount of trouble or time. I could chalk this up to simply taking a break and seeing the problem in a different light - which has worked for before - but I think it's more than that. Teaching high school mathematics has made me a much, much better mathematician.
While this certainly gives me a personal sense of accomplishment, I'm more interested in the specific things that have made me a better mathematician and how I could use these in my teaching. Reflecting on my work yesterday, there were a few significant changes in the way I was working:
- Make big problems small
- My go-to approach is to plug some stuff in a small example, see how it works, and look for some kind of pattern.
- Slowing down
- I was solving for slowly - once I had an idea that I thought might work, I took the time to think/write out my reasoning before getting started on the solution.
- Starting over
- I was much more ok with completely scrapping something and starting in a new direction.
These are nothing revolutionary. Far from it. They are things I've heard and read before, and things I (sometimes) try to incorporate into my teaching. But there is something about experiencing this first-hand that really drives it home.
What's my take away? This needs to be a more conscious part of my teaching. It's not going to change a student in a day. It might now show up on a test. But at the end of the year, if I've done my job right, there will be a whole new level of problems that a student will now have the ability to take on. The process is slow, but without fruit.
I also need to keep doing mathematics. Whether it's inside the classroom or out, it's not an indulgence - it's a professional development necessity.