Eileen Schoaff wrote: <<It is hard for teachers to work with students as equals. In cooperative learning we want students to listen to each other. And teachers must also learn to listen to students ideas carefully so as not to squelch ideas just because they don't align with our own thinking. Sometimes kids have great ideas!>>
I agree with you, Eileen. Your comment reminds me of the many lessons I have observed (and unfortunately probably taught) which could be characterized as the "Guess what's in my head" type of lesson in which the teacher, with the admirable desire to elicit mathematics from the students, questions the students until one of them says what it was the teacher was looking for to begin with. It would be easier for the teacher to say what it was s/he was looking for than to go through this procedure of rejecting students' responses until the "right" one came along--for this reason: If you are asking a question, then a person's answer should be respected and considered. Also, the teacher is not the only one who should be considering the answers to questions. Other students in the class should be engaging in the discussion of the validity of the various responses offered to any question. In this way the teacher can gain valuable information about where the students' understanding actually is and can thus formulate questions better suited to fostering the students' growth. If teachers modeled real listening--not a patronizing "That's interesting. Now let's get on with it", then students would be able to imitate the teacher's genuine interest and questioning and thinking procedures. Moreover, the message to the students would be, "I value your thinking ability. You are worth dialoguing with. You can teach me with your questions and ideas and I can teach you from my experience."
Happy Fourth of July!!!!! Lucille Peterson
Lucille L. Peterson Math Leadership Program Bank Street Graduate School of Education Tel: 212-875-4665 610 West 112th Street Fax: 212-875-4753 New York, NY 10025 E-mail: firstname.lastname@example.org