Give this a try this year, if you haven't already

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.

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.

Two things for (from) your first day...

Today was the first day back for my school, and for many others.  Leading up to it, and reflecting on the drive home, I had two thoughts about what makes for a good year teaching and learning.

First, micro: do actual math on the first day.  It's easy to get caught up in going over rules, procedures, grading standards, etc.  But why do we implement those systems in the first place?  For the most part, the point is to ensure that our students do, actually, learn some math.  How ironic to then spend the first day not doing math in order to communicate that math is the main thing!  Much better is to communicate that math is the main thing by actually spending a chunk of the period doing math!

(For the record, I doubt that going over lists of rules or procedures is even helpful. I myself have a personal capacity of learning about five rules, procedures, or standards at a time--tops--and maybe ten per day.  I doubt most students are much better.  Even at just two rules per period, the students are effectively done by lunchtime.  So there's no point in going through every detail; instead, provide a handout with the fine print, mention the big picture, and make sure to go over rules as (just before) they come up.)

This math doesn't have to be hard.  In Geometry, we go through a sequence of folds on a circle and talk about angles, symmetry, terminology, etc.  It's a great pre-assessment of what kids know coming in, and it allows us to "get through" a lot of vocabulary in a context where that vocabulary is meaningful.  In Calculus, we watched a video of a speedometer:

 and a video of my dog's ability to do calculus while fetching a ball--which wouldn't upload, so here's the original "Dogs know Calculus" video.

Both videos generated lots of mathematical discussion, and allowed me to preview the main ideas of the course.  And the students were engaged--doing math.  How excited can a kid get about the details of a quiz makeup policy?

Second, macro: do something new.  Obviously (?) do NEW math with the class on the first day: spending several weeks "just reviewing", as far as I can tell, only communicates to kids that it doesn't really matter whether they learn it the first time around.  But mostly I'm talking about you, the teacher.  Try something new this year.  Change your grading system.  (My department did: regular nightly homework, as such, is no longer counted towards student grades; instead, we'll quiz more often, and assign more interesting out-of-class work that we can collect and grade thoughtfully.)  Or change your pedagogy:

• use videos (á la Dan Meyer), or
• incorporate more formative data into your lesson planning, or
• plan quizzes and tests collaboratively, or
• create tiered work on which students can select for themselves the appropriate level of challenge (aka Challenge by Choice), or
• design (or borrow) writing prompts that get students to think mathematically, or
• anything else you haven't done very well before, like in that cool presentation you heard at last spring's conference.

It doesn't have to be a complete overhaul.  But if you don't set your sights on growing at the start of the year, you're not going to be able to when you can't even see above the stack of exams you need to grade.  Pick something and try it.  And if it doesn't work so great, well, as we Chicagoans know all too well, there's always next year.

Good luck, and do some great math!  In the comments: what math did you do on the first day?

== pjk