On June 16, Cathy Brady and Tad Watanabe tried to interest the NCTM-l subscribers in a discussion of a "constructivist" approach. There weren't many takers. Perhaps folks were already clear in their minds about what such an approach to teaching mathematics content meant. But a related subject--and one which might be more appropriate for the AMTE Listserv--is a constructivist approach to math METHODS. What we do in our preservice classes. Is there any interest in discussing such a topic on either listserv? I'll try to kick things off and see if this goes anywhere. This is not my area of expertise, so I really am interested in learning about this and would appreciate it if those who are knowledgeable would jump in right away!
As a STARTING POINT on this topic:
1. If constructing knowledge in any subject is a "highly active endeavor on the part of the student," which requires "making connections between old and new ideas,"
[And if making such connections requires REFLECTIVE thought];
2. If networks of ideas that presently exist in the learner's mind [cognitive schema] are "the principal determining factors in how an idea will be constructed,"
[And, if fitting an idea into such schema (assimilation) or modifying such schema (accomodation) requires REFLECTIVE thought];
3. Then, would you agree that our job as math educators in facilitating a constructivist approach to a math METHODS class is to involve our students in tasks which encourage REFLECTIVE thought about the CONCEPTS AND PROCEDURES OF MATH INSTRUCTION--whatever they are?
Ron Ward/Western Washington U/Bellingham, WA 98225 email@example.com
PS Quotations above are from Van De Walle [Longman, 1994]