The project consisted of three related series of studies, designed to (a) determine some of the underlying competencies that contribute to experts' successful problem solving performance in college level mathematics, (b) to determine what productive behaviors students lack, or what counterproductive behaviors they have, that keep them from being effective problem solvers, and (c) to determine if a course in mathematical problem solving that explicitly teaches problem solving strategies could significantly improve students' problem solving performance. A variety of new methodologies and measurement techniques were developed for examining cognitive processes in broad domains such as "general mathematical problem solving." Experts were shown to perceive the "deep structure" of problems where novices were misled by the "surface structure." Experts have much better "executive" or metacognitive strategies than novices, which prevent them from squandering their problem solving resources in the way that students do. Moreover, it was shown that students'"belief systems" about mathematics and the way it is done often make it difficult for them to learn mathematics or to use it effectively. The problem solving course provided clear evidence that, with direct instruction, students' problem solving performance could be substantially improved. These results have obvious implications both for research and teaching in mathematical thinking.