I have enjoyed the discussion about cooperative learning, lecturing, etc. However, "cooperative learning" is too all inclusive and even "lecturing" is not clear. Here are a few quick comments.
I appreciated the "6 minutes" message (sorry I don't remember who wrote it). I said in my message that I lecture (and when I say lecture I mean that I am talking with an occasion student question about clarity) for 5 to 10 minutes at a time and the rest of the time the students are working on their own. I use these short lectures to help break up the students' work although I don't schedule the short lectures regularly.
There are so many different types of cooperative learning being mentioned: peer instruction, in class peer review, cooperative class work in conjuction with discovery learning, cooperative class work without discovery learning, etc. There are also many different versions of lecturing. Maybe each of us should be more specific about the type of instruction we are talking about.
My major concern about lecturing (with its many variations) is the ability for insecure students to express their ideas. When I have students do work together in class (they are doing some predetermined task (like graphing functions using the derivatives)) I move from group to group to see what progress or difficulties has occurred. In this way I get to speack to each student sometime during the class and am able to elicit responses for all students. The students feel more free to express their ideas within the bubble of a private conversation with me rather than in class during a "lecture."
Finally, I also appreciate references made to the literature available on cooperative learning (again, I apologize for not knowing the name(s) of the sources of these references). If anyone else have a particular good resource, I would like to see it posted.
Thanks again for the ongoing discussion.
--------------------- Murphy Waggoner Department of Mathematics Simpson College 701 North C Street Indianola, IA 50125 firstname.lastname@example.org ---------------------