Psychologists, teachers and researchers have a common interest in understanding how students solve mathematics problems. We want, and need, to understand how solutions to problems are developed so that interactions with both successful and unsuccessful problem-solvers can become more effective. In order to build a more sophisticated understanding of problem-solving we must consider a number of major factors — the instructional setting, the nature of the problem-solver, the resources available, the structure of the mathematical content and the student's understanding of that, and the processes used in the solution. Also needed is a technique for identifying those processes in samples of students' mathematics performance. What we learn from using the technique influences the design of future instruction.