I would like to reinforce the comments made by Cindy Chapman. I suspect lecturing is not really such an awful thing. What is awful is to assume that lecturing is the best way to present all material all the time , and that all students will learn best when the teacher explains it to them. I also suspect that classes that exclusively use cooperative learning are not delivering instruction to all students in the best way all the time. Variety is the best way to reach all of our students, and co-operative learning needs to be part of our strategy, but if it is our only one, I think we are fooling ourselves into thinking we are doing the best we can. Likewise, co-operative learning does not always mean groups of four. Sometimes two is a better number to get a certain task done. We math people talk about alternative approaches all the time, but deep down we want there to be one way to solve all of our problems. There is no such way.
While I am on the soapbox, I think this also relates to previous discussions about discovery learning. I suspect there are some things we ought to expect our students to discover for themselves, and others we need to push them right next to and hope they grab it and still others we need to show them. Think about matrices for example. Most students will conclude all by themseove show to determine if two matrices are equal, and will figure out how to add and subtract them if we just aks what they think instead of showing them how. I suspect few students would guess how to multiply matrices correctly or discover a method of finding the inverse of a matrix, unless they just pushed the right buttons on their calcutator.
At least , that is my humble opinion.
John Benson Evanston Township High School 715 South Boulevard Evanston Illinois 60204 Evanston IL 60202-2907 (708) 492-5848 (708) 492-5848