PROCESSES INVOLVED IN MATHEMATICAL PROBLEM SOLVING

grade subjects learned to solve nonroutine geometry problems and (b) changes in those processes as the problem-solving ability of the subjects developed. The second, more important section indicates a direction for future research in problem solving and sets forth suggested hypotheses for investigations, both clinical and experimental, resulting from reflection on the regularities observed in the problem-solving behaviors of the first section. The Study Mathematics educators agree that the development of the ability to solve complex, nonroutine problems is one important goal of mathematics instruction. An individual is faced with a problem when he encounters a question he cannot answer or a situation he is unable to resolve using the knowledge immediately available to him. He must then think of a way to use the information at his disposal to arrive at the goal, the solution of the problem. A problem differs from an exercise in that the problem solver does not have an algorithm that, when applied, will certainly lead to a solution. To complete an exercise, one must first determine the applicable algorithm,