Processes Involved in Mathematical Problem Solving

The investigation was a longitudinal exploratory study of processes involved in solving mathematics problems as problem-solving ability developed under heuristic instruction in geometry. A clinical methodology was employed. The consistent use of heuristics and the regular patterns of analysis and synthesis were noted in the solutions of problems with process-product scores above the subject's own median. In most cases the tendency to use heuristics increased as problem-solving ability developed. A direction for problem-solving research is suggested and hypotheses for future studies, both clinical and experimental, are discussed.