- In one classroom, the teacher drove the direction and flow of the class period by telling students which problems to put on the board and offering extensions and generalizations wherever possible. Students critiqued one another's responses, and asked questions like "would that still work if it were negative?" or "what if you used this form instead?"
- In another classroom, the teacher did much more of the work; students explained their work but often faltered and looked to the teacher for affirmation or to catch errors, and the teacher asked almost all of the questions. Students mostly spoke up when they were confused or needed help.
- In a third classroom, the teacher spoke only three times in the entire class period: once, to introduce us as the visitors, and twice to pause the conversation (she literally just said "wait--") until a student picked up on what she wanted them to talk more about and restarted the conversation. In this class, students not only continually pushed the mathematics forward, but also pushed each other to explain better or differently, to consider an alternative, or to make sure the whole class was on board.
|What STUDENTS do||What TEACHERS do|
I'm not pretending this is a complete list, but it was a really helpful exercise to do this inductively, while sitting in the back of classrooms, rather than deductively, particularly since it gave me concrete examples that I didn't have to make up. Old hat to you? Any surprises? Now, to figure out what (if anything) I should do with this table... any ideas?