ABSTRACT
During the past few years, I have been struck by certain issues or themes that seemed very important for those of us interested in the teaching of mathematical problem solving but which were not seriously addressed in the literature. Closely connected to these fundamental issues is my assessment of some important directions in which research on problem solving should move in order to make substantial progress in the next decade. In some cases, these directions represent an attempt to connect research on mathematical problem solving with other active and potentially related fields of research. In other cases, these directions simply represent questions or issues which are fundamental and for which the time seems ripe for investigation. These observations led me not only to write this paper but also to ask a number of scholars in the field of mathematics education to write papers that are related to the directions in which I am suggesting we move. Thus, this paper serves not only as my personal view of some currently important issues to be addressed in research on mathematical problem solving but also as an introduction to the other papers in this section of the book.
