Abstract
The preeminence of increased problem-solving ability as a goal of mathematics instruction has long been admitted; but like the weather, problem solving has been more talked about than predicted, controlled, or understood. The studies reviewed in this chapter were chosen from a large number published during the last five years that are relevant to the twin issues of how problem solving is learned and how it can be taught. The role of problems in developing students' mathematical activity was chosen by the International Commission on Mathematical Instruction as one of three topics for discussion at the 1966 International Congress of Mathematicians in Moscow. Reports to the Commission by the Conference Board of the Mathematical Sciences (1966) in the United States and by the Association of Teachers of Mathematics (1966) in England highlighted the importance of problems in mathematics instruction and indicated that educators need to know much more about using problems to stimulate independent and creative thinking.
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