Describes an attempt to promote both mathematical and nonmathematical problem solving. Suggests that the goals for the average mathematics course need revision, in practice, or additional courses introduced, which will develop thinking ability as a primary objective. (EB)

Two learning strategies are discussed: (1) fluent and creative idea-production involving concepts and problems, and (2) metacognition, or students' awareness of and direction of their thinking. The sample included college students, as well as teachers who used these strategies in elementary and secondary mathematics classrooms. Techniques for…

Although teachers may sequence instructions carefully, they are unable to respond to the complex unique experience of each individual learner. Divergent production should be an instructional choice that enables individuals to learn through their own recall and idea construction. Learning is problem solving; when individuals do not know how to deal…