One of my favorite things about mathematics is how cooperative it is. With few exceptions, math is done by teams of people, not by individuals. They work together, build off each other's strengths, and solve together what none could alone. Even the loners of math history like Newton, or Andrew Wiles more recently, have been standing on the shoulders of giants. So why then does most classroom math focus on keeping your eyes on your own paper, so to speak? Why the emphasis on individual work, when professional mathematicians don't work like that?
I have often thought that I would prefer to organize my class into several small groups. This will allow them to challenge one another, and uses their natural social structure to improve learning. It also effectively means that instead of teaching 30-40 separate students, I will be teaching 5-7 teams. I have recently read about creative math teachers using this approach with much success. I'm not saying that it's a revolutionary idea or anything, and I'm sure it's been done before. It is certainly the exception, rather than the rule. I would like to read some case studies on the subject. There are many variables that concern me. For example, I'm not sure yet whether I want to choose the groups myself or allow the students to do it themselves. The first way allows me to group quick-learners with struggling ones, but the second will better guarantee a positive group dynamic.
Regardless of the details, I am sure this will be a major element to my classroom structure. Whether its a few round tables or a bunch of desks shoved together, my students will be working in groups.