Updating, Modernizing, and Testing Polya’s Theory of [Mathematical] Problem Solving in Terms of Current Cognitive, Affective, and Information Processing Theories of Learning, Emotions, and Complex Performances.
James Carifio

Polya’s classic work How to Solve It: a New Aspect of Mathematical Method still ranks high on various lists of most read and most referenced books. Polya claims that true problem solving is accompanied by the cognitive activities of mobilization, organization, isolation and combination, and by the meta-cognitive evaluations of relevancy, proximity, and quality. These meta-cognitive evaluations occur as a result of monitoring cognitive activities on an on-going basis. According to Polya, these particular meta-cognitive activities are a necessary part of true [mathematical] problem solving and they generate positive, negative and oscillating emotions during problem solving which help or hinder obtaining a solution to the problem. The studies we have done, which are summarized in this article, have provided good initial and formative support of Polya’s model and particularly so in terms of the disruptive influence of emotions (both positive and negative) and the oscillation of emotions during mathematical problem solving and particularly for difficult mathematical problems, which we call “Polya Problems.” As part of our inquiry, we updated and modernized Polya’s theory in terms of research that has occurred and understanding that have been developed in psychology in the last twenty years. Both Polya’s theory and our updates and modernizations of it are presented in detail.

Full Text: PDF     DOI: 10.15640/jehd.v4n3a12