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. In the updated third edition, the authors specifically: (1) address the role of problem posing in the NCTM Standards; (2) elaborate on the concept of student as author and critic; (3) include discussion of computer applications to illustrate the potential of technology to enhance problem posing in the classroom; (4) expand the section on diversity/multiculturalism; and (5) broaden discussion of writing as a classroom enterprise. This book offers present and future teachers at the middle school, secondary school, and higher education levels ideas to enrich their teaching and suggestions for how to incorporate problem posing into a standard mathematics curriculum. Following an introduction, this book presents: (1) Two Problem Posing Perspectives: Accepting and Challenging; (2) The First Phase of Problem Posing: Accepting; (3) The Second Phase of Problem Posing: "What-If-Not"; (4) The "What-If-Not" Strategy in Action; (5) Some Natural Links between Problem Posing and Problem Solving; (6) Writing for Journals of Editorial Boards: Student as Author and Critic; and (7) Conclusion. [For the 1983 edition of "The Art of Problem Posing," see ED251290.]