Comprehension Monitoring and Polya\u27s Heuristics as Tools for Problem Solving by Developmental Mathematics Students

Mathematical problem solving has been the focus of mathematics education research for several decades. George Polya, in his now classic text, How to Solve It (1945), set forth the concepts and strategies of heuristics which has formed the basis for teaching and learning how to solve mathematical problems. The early 1980s saw an emergence of metacognitive research and educational psychology as providing insights to the mathematical problem-solving process, but still there is not a definitive understanding o f this process. There is no coherent framework that explains all of the aspects of mathematical thinking and problem solving. Students still do not know how to use all of the information available to them, and perhaps more importantly, they do not know what it is that they do not understand. This study compared the mathematical performance and use of metacognitive problem-solving techniques of students in three different sections of developmental algebra. It focused on the use o f comprehension monitoring techniques, alone and in conjunction with Polya’s heuristics, to investigate whether developmental mathematics students who were taught these techniques performed better in mathematical problem solving than those students who were not taught these techniques, and to determine if being taught these techniques increased their conscious use of metacognitive strategies. The study concludes that while there was no apparent difference in the conscious use of metacognitive techniques by any o f the groups, that students who receive increased emphasis in the use of comprehension monitoring strategies, regardless of the inclusion o f Polya’s heuristics, perform better in mathematical problem solving than students who do not receive this type of instruction