CBMS Issues in Mathematics Education

Volume 7, 1998

Teaching Mathematical Problem

Solving: An Analysis of an

Emergent Classroom Community

ABRAHAM ARCAVI, CATHY KESSEL,

LUCIANO MEIRA, AND JOHN P. SMITH III

INTRODUCTION

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

generosity.

© 1998 American Mathematical Society

1

http://dx.doi.org/10.1090/cbmath/007/01