# Problem Posing: Reflections and Applications

# Problem Posing: Reflections and Applications

## Synopsis

*The Art Of Problem Posing*-- which related problem posing strategies to the already popular activity of problem solving. It took the concept of problem posing and created strategies for engaging in that activity as a central theme in mathematics education.

Based in part upon that work and also upon a number of articles by its authors, other members of the mathematics education community began to apply and expand upon their ideas. This collection of thirty readings is a testimony to the power of the ideas that originally appeared. In addition to reproducing relevant materials, the editors of this book of readings have included a considerable amount of interpretive text which places the articles in the context of problem solving. While the preponderance of essays focus upon mathematics and mathematics education, some of them point to the relevance of problem posing to other fields such as biology or psychology. In the interpretive text that accompanies each chapter, they indicate how ideas expressed for one audience may be revisited or transformed in order to ready them for a variety of audiences.

## Excerpt

Since the late 1960's, both of us have been heavily engaged in efforts to place problem posing as a central theme in mathematics education. We have published articles in professional journals, taught graduate and undergraduate courses on the topic at a number of institutions, and have lectured and given workshops at professional meetings in the United States and abroad. Much of our thinking on the topic culminated in our book, *The Art of Problem Posing* -- published originally by the Franklin Institute Press in 1983, then by Lawrence Erlbaum Associates with a revised edition published in 1990 (Brown & Walter, 1990).

It was our hope that the book as well as other articles and activities of ours would influence colleagues to (1) further explore the connections between problem posing and solving; (2) further examine the educational values of problem posing; (3) expand upon strategies for problem posing that derive from our schemes, and (4) employ these strategies in situations that we had not previously explored.

Many of our colleagues did in fact take up the challenge. Articles have appeared in professional journals; talks have been given at professional meetings and bits and pieces of problem posing curriculum began to appear in several texts for students.

As we promised in the 1990 edition of *The Art of Problem Posing*, we have created a collection of readings based upon the work of our colleagues in applying and extending the ideas that have occupied a large part of our professional lives for the past quarter of a century. We are grateful to them for having enriched the field so much more than we have dreamed when we first ventured into it.