Depicting the role of problem solving in mathematics education throughout the twentieth century : finding basic themes through an historical perspective

Problem solving is a central activity of mathematics and has been throughout its history. Recognizing the problem of problem solving, however, seems to be less explicit in the historical record. In studying three principal contributors to the study of problem solving-Rene Descartes, John Dewey, and George Polya-I have found that problems arise in two broad categories. Mathematics itself generates more mathematical problems, and problems embedded in a wider context can generate mathematics. Recognizing a mathematical problem in a rich context-problem finding-has received much less attention. John Dewey recognized the importance of problem finding and emphasized its role in problem solving. Descartes and Polya spent less time on problem finding, Polya the least of all.