This monograph was developed with the intention of addressing the concerns of high school mathematics teachers in Alberta (Canada) who want to base their programs on problem solving but have questions about effective and efficient ways to do so. Considered are the most basic philosophical questions, and a framework is provided to use in solving problems. Contained is a section which includes ideas for teachers to use in their own classrooms as they encourage their students to become better problem solvers. In addition, sample problems are presented, along with their prerequisites, complete solutions, and some suggestions for extensions. A problem bank organized by strands is presented from which teachers can obtain some additional problems for use in their classroom. A two-part bibliography of six pages contains suggestions on where to obtain information on the pedagogy of problem solving, as well as where to obtain more problems. (TW)