Title

Using heuristics to teach problem-solving in Algebra I: A metacognitively controlled approach

Date of Completion

January 1991

Keywords

Education, Mathematics

Degree

Ph.D.

Abstract

For more than a decade there has been a strong emphasis on the need to incorporate problem solving into the curriculum of our schools. NCTM (1989) has placed Problem Solving first in the list of standards at every grade level.^ The purpose of this study was to show that the use of heuristics originally espoused by Polya (1945) can effectively enhance the problem-solving skills of regular ability Algebra I students.^ In this investigation 128 students in six intact classrooms were randomly assigned to control and experimental groups. The investigator taught the experimental group of 58 students (three classes). Two colleagues taught the control group of 70 students (three classes). All students were taught the regular Algebra I curriculum.^ In addition, the experimental group was taught specific heuristic strategies in a metacognitively controlled situation. Metacognitive control is here defined to mean making a conscious, executive choice of problem solving strategies. Students were given reinforcement through worksheets addressing specific heuristics: working backwards, drawing diagrams, Venn diagrams, guess & check, making an organized list, logical reasoning, and complex translation. Two worksheets were completed each week during the 11 week treatment. A pretest and posttest of matched pairs of problems were given to all participants, and the data were examined using ANCOVA.^ Results showed that on complex translation problems there was no significant gain in the treatment group's ability to recognize the strategy or execute the solution. There was, however, a significant difference on process problems, in both recognizing the strategy and executing the solution. There was no indication of difference due to gender. Having taken a previous problem-solving course did have a significant effect on problem-solving performance. Therefore, teaching specific heuristics of problem solving with an emphasis on metacognition should become an integral part of the curriculum if, indeed, we intend to heed the recommendations of NCTM's Standards. ^