During recent years many research studies have focused on the teaching of problem solving. However, due to the complexity of the problemsolving process, many questions concerning the most effective way of teaching problem solving remain unanswered.What alternatives exist with respect to the teaching of problem solving? Have any of these alternatives been shown to be more effective than others? Can the problem-solving performance of elementary school students be significantly affected by certain instructional approaches to problem solving?The techniques suggested here have been used in several fifth-grade classrooms with much success. As an alternative method to some of the standard approaches currently being used, the visualization approach has generated new enthusiasm for mathematics in a unique setting and has improved the problem-solving performance of fifth-grade students.Conventional Approaches Current efforts to teach problem solving have resolved around three general approaches: (1) organizing instruction by content area; (2) organizing instruction by strategy; and (3) organizing instruction by presenting many varied problems. Each of these approaches has demonstrated some degree of success in improving the problem-solving performance of elementary school students.Many educators have preferred to teach problem solving by organizing problems according to content area. Problems could be classified as geometric, algebraic, arithmetic, etc.; then further subdivisions could be established such as, work problems in algebra, area problems in geometry, division problems in arithmetic, etc. Each introductory instructional period would be devoted to only one type of problem. Skill in being able to recognize and to solve each type of problem would be promoted.Another alternative is to group problems according to the strategy which is most clearly elicited in their solution. Such strategies as problem simplification, pattern recognition, working backwards, making analogies, and constructing organized lists are examples of possible classifications. Each introductory instructional period would be devoted to only one strategy. Again, skill in using each strategy, as well as in recognizing efficient strategies for a given problem, would be emphasized.141

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The recently published Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, Commission on Standards for School Mathematics 1989, 21) clearly states that educators should devote less attention to “ complex paper-andpencil computations” and “rote memorization of rules.” The time currently spent in the elementary school mathematics curriculum on these topics should instead be devoted to other areas, such as geometry and problem solving. Students should “visualize and represent geometric figures with special attention to developing spatial sense” and learn to appreciate “geometry as a means of describing the physical world” (p. 112). But elementary school mathematics textbooks typically contain few activities that deal with the development of spatial sense.

The American female earns 59 cents to every dollar the American male earns. Approximately 66% of this variance is the result of type of employment, age, and amount of work experience.