Problem Solving in Mathematics (PSM) is a program of problem-solving lessons for grades 4-9. The content objectives of these lessons are similar to those of most textbooks. However, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the development of such skills. These strategies include direct instruction, guided discovery, laboratory work, small-group discussions, nondirective instruction, and individual work. This guide shows how PSM lessons should be used and how PSM activities can be integrated into the regular mathematics curriculum to provide students with a more stimulating problem-solving experience. Areas addressed include: the nature of problem-solving in mathematics; the philosophy of the PSM program; how PSM is different from other problem-solving materials; implementing PSM in schools; what research says about problem-solving; and evaluation of student work. Fifteen problems (with answers) for teachers to complete are included. These problems are designed to increase the teacher's confidence level and ability in problem-solving methods. Also included are suggestions for creating a classroom climate for problem-solving, a list of teacher behaviors indicative of problem-solving (in the form of a self-evaluation checklist), and an observational chart (with instructions) for evaluating problem-solving behaviors in the classroom. (JN)