Brown S., Walter M. The Art of Problem Posing 2005

Textbook in PDF format

The new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. The Art of Problem Posing, Third Edition encourages readers to shift their thinking about problem posing (such as where problems come from, what to do with them, and the like) from the "other" to themselves and offers a broader conception of what can be done with problems. Special features include: an exploration of the logical relationship between problem posing and problem solving; sketches, drawings, and diagrams that illustrate the schemes proposed; and a special section on writing in mathematics.
The Art of Problem Posing is a great book. The authors provide a step by step method for learning about and solving problems in mathematics. Written at an elementary level, but the insights are fantastic. I don't know if the mathematically astute think analogously to the manner taught in this book, but it seems there would be something here for everyone. Also, the book is so short that it can be read (and re-read if need be) speedily until the strategies are second nature. I was as excited reading this as I was Polya's series -- but the two cover different aspects of mathematical investigation. I'm glad this book was written and that I found it!
Best Sellers Rank: #188 in Mathematics Study & Teaching (Books)
#433 in Psychology (Books)
#502 in Math Teaching Materials
Introduction
Two Problem-Posing Perspectives: Accepting and Challenging
The First Phase of Problem Posing: Accepting
The Second Phase of Problem Posing: "What-If-Not"
The "What-If-Not" Strategy in Action
Some Natural Links Between Problem Posing and Problem Solving
Writing for Journals of Editorial Boards: Student as Author and Critic
Conclusion