This all came about the other day when some of Brian Lawler's credential students were in observing my 10th grade class working on "Consecutive Sums." Basically, the prompt is: "explore consecutive sums and see what you discover" (where equations such as 1+2+3=6 and 7+8=15 are considered consecutive sums). Eventually, the conversation turned into trying to figure out which numbers can (or cannot) be written as consecutive sums. I put a table up on the board with the numbers 1-25 on it and asked groups to send people up to fill in the chart once they had found one. What ended up happening is that about 5 students dominated this part of the lesson while others sat and watched. I know there are plenty of suggestions about better ways to handle this particular part of the lesson, but I think the implications are greater than that.
I have read several articles and books for my action research (a couple good ones if you are interested) that outline an amazing vision for a classroom community in which students present ideas, challenge each other, and construct meaning together. Most times when I try this, one of two things happens:
1. I select and sequence student share outs so that certain voices are heard that are usually silenced. Mostly, because I have created the conversation, there isn't much to talk about and students seem disinterested. They aren't debating anything; they aren't solving things collaboratively. OR...
2. I'll select one or two pieces of work to get a conversation started and then step out of the way. This usually gets students talking and debating. The only problem is, it's usually no more than 10 students out of a class of 20-30.
I'm not sure I have any answers to this yet, or even that an answer exists that will work for all groups of students. But, I am really interested by the intricacies of teaching...by the tasks we choose, by how we set up those tasks, by how we get students talking about those tasks, by how we conclude those tasks, and, especially, how ALL of those moves inevitably make a difference in what students are learning about themselves as capable mathematicians. This last bit, to me, is far more important than the "mathematics" that they learn.