Two weeks ago, I suggested a discussion of a constructivist approach to teaching a math METHODS class, and last week I provided both an update on the replies from both listservs as well as cross-postings. Recent postings on NCTM-l suggest that a discussion of "constructivism in teaching mathematics to K-12 students" is the direction that listserv wishes to take (see Sherbine, Watanabe, and Martin). I think that is a good idea because it actually returns to a strand initially proposed by Brady and Watanabe in mid-June. Perhaps Sherbine's "Constructivism Redux" is the appropriate heading to use for that discussion. So, I am going to recommend shifting the discussion of the math METHODS class approach SOLELY to the AMTE listserv (where it probably logically belongs, anyway) and will no longer do cross-postings.
On the AMTE there has been only one additional posting since the last update. Kepner suggested that we look at "contexts of topics" for a 'methods' type course. In particular, he mentioned cooperative learning and classroom management. However, as of today, no one has responded to his suggestion.
Therefore, to try to prompt additional input from AMTE members, I will ask a few more questions and offer still other topics in the spirit of Kepner's suggestion:
1. Suppose you are convinced that a constructivist approach is the way to go in teaching mathematics content. Does it necessarily follow that a constructivist approach is also what is required in a math methods class? Or is it illogical to even ask such a question;that is, if people learn by constructing their own knowledge, then that's the way to approach the learning (teaching) of anything--including math methods?
2. For many years I followed a "role model" approach to math methods. Namely, if I wanted preservice teachers to learn how to ask good questions, employ alternative assessment, use "wait time" properly, utilize manipulatives or models in their teaching, make technology accessible to their students, and so on, then I tried to model all those things in my methods class--assuming that they would then also do all these things. But in recent years, especially in reading about constructivism, I felt that such an approach was not sufficient. Is role modeling passe? Or does it still have a place? Or should we be role modeling a constructivist approach to learning (teaching)? :)
3. A number of readers agreed that a constructivist approach should be taken to the "content of a math methods class";however, there was really not consensus on what that content should be. Should that be a part of the discussion? Do we need to discuss the content of the Professional Standards in this regard, at least the "Standards for the Professional Development of Teachers of Mathematics" part of the larger document?
4. To follow up on Kepner's suggestion, what TASKS do you find successful in encouraging your methods students to REFLECT on the following (possible) math method content areas?
A. What it means to teach mathematics? [What is mathematics? What does it mean to "know" or to "do" mathematics?] B The current revolution in math education--NCTM Standards--what is valued? C. What will the world be like 13 years from now when today's Kindergarten student graduates from high school? D. The instructional power of technology? E. What is the difference between conceptual and procedural knowledge? F. What is "understanding"? G. What is reflective thinking? How do you promote it? H. What is the purpose (role) of a manuipulative (model)? I. What types of "problems" [translation, process, project, e.g.] are appropriate for what purposes? J. New ways of assessment in various areas of the mathematics curriculum? K. Lesson planning? L. Selecting worthwhile mathematics tasks? M. Promoting discourse? N. Establishing a learning environment? O. How students learn? P. Knowing mathematics pedagogy?
I know there are many others--which other listserv members can no doubt add--but perhaps this list, in addition to the two mentioned by Kepner [cooperative learning and classroom management], might encourage others to share their tasks with us all.
Ron Ward/Western Washington U/Bellingham, WA 98225 firstname.lastname@example.org