CBMS Issues in Mathematics Education
Volume 7, 1998
Teaching Mathematical Problem
Solving: An Analysis of an
Emergent Classroom Community
Toward the end of the semester I assigned the following ... . As usual,
the class broke into groups to work on the problem. One group became
the staunch defenders of one conjecture, while a second group lobbied for
another. The two groups argued somewhat heatedly, with the rest of the
class following the discussion. Finally, one group prevailed, on what struck
me as solid mathematical grounds. As is my habit, I did not reveal this
but made my usual comment: "OK, you seem to have done as much with
this as you can. Shall I try to pull things together?" One of the students
replied, "Don't bother. We got it." The class agreed. (Schoenfeld, 1994,
pp. 63-64)
This paper is the product of a long and enjoyable collaboration that began in 1990, in
Berkeley, California, and continued over six years and four continents (thanks to e-mail). Each
major section was individually developed and thus has a single author, though all of us critiqued
each section. The Introduction and the Concluding Discussion reflect our shared views, and
each of us had some part in writing them. However, Abraham Arcavi, Luciano Meira, and Jack
Smith would like to thank Cathy Kessel who composed these sections with unusual editorial
care and wisdom.
The authors thank the editors, Ed Dubinsky and Jim Kaput; the reviewers, Barbara Pence,
Beth Warren, and one anonymous reviewer; and members of the Functions Group, liana Horn,
Andrew Iszak, Sue Magidson, and Natasha Speer, for their help in improving the successive
versions of this article.
We owe special thanks to Alan Schoenfeld. This article would not have been possible
without his cooperation. It is not easy to be the subject of any analysis, let alone one so
prolonged. Schoenfeld not only cooperated with us, but did so with grace, tolerance, and
© 1998 American Mathematical Society
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