The focus of this book is on a rationale and a set of strategies for problem generation in mathematics. Six chapters attempt to involve readers in the process of posing problems and in understanding why that process is important. Chapter 1 discusses two problem posing perspectives, while chapter 2 looks at the first phase of problem posing. The "what-if-not" problem posing strategy is presented in chapter 3, and depicted in action in chapter 4. Some natural links between problem posing and problem solving are discussed in chapter 5. Finally, conclusions are briefly presented. Each chapter contains illustrative problems as well as suggested questions or directions. In the appendix, a college course on problem posing is described, also with illustrative examples. Finally, a bibliography is provided. (MNS)