Here is a proposal for the coming year that I hope you will think seriously about.

Invite someone other than an evaluator to observe one of your classes. Invite yourself to observe someone else's class. Depending on how it goes, do it again, with the same person or a different person. Be creative or not depending on how comfortable you are with this idea.

If you are a new teacher and suspect that you may have a few things to polish, ask a veteran teacher to visit your class and share any observations or thoughts. If you are a veteran teacher, if you think you have it down cold, ask a new teacher to observe your class. Tell the teacher you are looking for new ideas and that you are interested in a fresh look at what you are doing. In both cases, the teacher probably will have some unexpected comments, and in both cases the teacher will probably get a few ideas from the visit. Follow up by asking for a return visit to that teacher's classroom.

The teacher you invite need not be a math teacher. I learned some very interesting things one year when I visited two English teachers, an American history teacher, and a physics teacher. My goal that year was to learn how to get my students more involved in discussing what they were thinking about. I asked students and other teachers who in the school was particularly good at fostering class discussion, and I came up with four names. All four teachers did things I didn't expect; all four classes were thoroughly enjoyable; all four had totally different styles of teaching. One of the English teachers had a chair with wheels, and he scooted around the room and sat directly in front of the student who was speaking, as though it were a private conversation between him and the student. Another teacher had students sitting in rows while he stayed in the front of the room. The students seemed to be enthralled with the class, as was I.

The teacher you invite need not be a math teacher. I learned some very interesting things one year when I visited two English teachers, an American history teacher, and a physics teacher. My goal that year was to learn how to get my students more involved in discussing what they were thinking about. I asked students and other teachers who in the school was particularly good at fostering class discussion, and I came up with four names. All four teachers did things I didn't expect; all four classes were thoroughly enjoyable; all four had totally different styles of teaching. One of the English teachers had a chair with wheels, and he scooted around the room and sat directly in front of the student who was speaking, as though it were a private conversation between him and the student. Another teacher had students sitting in rows while he stayed in the front of the room. The students seemed to be enthralled with the class, as was I.

I took ideas from these four teachers and incorporated them into my style. I learned a lot from these visits. I also became closer friends with all four teachers.

Visiting math classes also taught me approaches to students as well as approaches to mathematics. Interesting conversations followed about things like why it was important to distinguish between the function f and the value of the function at a number x, f(x).

Try it. Not only will you learn some things about teaching and learning, but you will share some things you know. Furthermore, you will open a dialogue about teaching and learning that will make your school a better place to be. Perhaps the idea will grow, and soon there will be an open door policy with teachers coming and going into each other's classes on a regular basis. At the very least, people will begin to understand that teaching is a very personal activity, and while there are best practices, there is no single best way to teach. One size does not fit all.

Have a great year.