With these things in mind, I asked one of my fellow math teachers to observe a class period. Before the observation, I asked him to be mindful of this list of questions and concerns:
- Does Matt display any behaviors that might increase students' math anxiety? (Examples might include expressed frustration at repeated questions, gestures or mannerisms that suggest annoyance, avoidance of certain questions, lack of eye contact, etc.)
- Does Matt do anything that might empower one gender or another to be more or less vocal and participatory during class. (Does he call on one gender more often? Does he not do enough to get responses from a variety of students, allowing two or three to dominate? Does one gender seem to dominate discussion?)
- Do you see anything in general that Matt could improve upon or that he is doing well?
The lesson my friend observed was on graphing rational functions. We were taking generic graphs with asymptotes and intercepts plotted (no scale or numbers) and sketching in the shapes of the graphs following some graphing "rules" that we had discussed for rational functions (for example: the curve can only pass through the x-axis at an x-intercept; the curve cannot pass through a vertical asymptote, but instead must go to positive or negative infinity as it approaches one).
The lesson went well, unusually so. A wider variety of students than usual were volunteering to answer questions than usual, and just about an even balance between male and female students. There was a lot of discussion, and even some arguing about the mathematics. Students were asking insightful questions about the behavior of the graphs and what causes it. It was a fun class period. I was reminded again the next day how well things had gone, because the class seemed kind of flat by comparison.
My friend didn't notice any of the behaviors or tendencies I had listed in my questions for him. He kept a tally of responses from different genders, and again, it was almost an even split. He also noted that my questioning of all students was consistent in difficulty, and that I wasn't guiding with my questions. He said it appeared as if I have great rapport with my students and that they seemed very comfortable with me, asking questions and offering responses. Another thing that he made note of that he liked was that I took students' suggestions of how to sketch a portion of a graph, drew it that way on the board whether it was right or wrong, and then asked the class whether they agreed or disagreed. On some days my class might have gotten frustrated with me for not being direct about right and wrong answers, but on that day they seemed to embrace it and liked the added discussion.
While I was relieved that my friend didn't notice any of the behaviors I was worried about, since things went so well I am left wondering why they did, in hopes that I could have more class discussions like that. I don't know that I can take any credit for how well it went - most of that is probably due to my students and their interest and willingness to discuss - but here are some things that I think may have helped:
- Having another teacher in the room, especially someone who's there just to watch you teach, really makes you bring your "A game", I think. I'm not sure exactly how that affected me, but it probably made me relish the good discussion that was happening, and be more thoughtful about the questions and answers I was offering.
- Rational functions was a new topic for my class, one that they hadn't had much prior exposure to in earlier classes. I think this leveled the playing field a bit and contributed to a wide variety of students taking part in the discussion. The graphing rules that we had may have also empowered them to argue with each other a little more, too, rather than just waiting to see if I said the answers were right or wrong.
- The list of questions I had given my friend to look for was fresh in my mind, and as such I was especially mindful of how I was asking and answering my questions, the tone of voice I was using, and the mix of students I was calling on. I was even thinking about my use of eye contact when I asked questions. I think you can sometimes draw out a response to a question from one student or one section of the room by directing your eye contact at them while you ask, and looking at them during the wait time. Or maybe it just makes them nervous.
- It might have just been one of those days when things are going to go well, and I was lucky enough to have another teacher there to witness the good discussion.
After all, I really appreciated the instructional dialogue process. I think just picking something for one of my peers to look at and thinking about that ahead of time improved my teaching a bit. Having someone else in the room to observe my teaching helped me to remember what my A game looks like, and left me challenged to try to put forth my best effort every day, whether another teacher is watching or not. Even though the lesson that my friend observed went well, his observation notes left me with more to think about and some things to keep working on and building on. I'm hoping I can do more instructional dialogues with my colleagues in the future.