The effects of teaching heuristics within the context of a prescriptive metacognitive control system on the problem-solving performance of eighth-grade general mathematics students

Most of the research in mathematics problem solving has focused on the teaching of heuristics. Heuristics, a term coined by Polya (1945), refers to problem solving strategies that, if used properly, enhance one\u27s ability to solve problems. Unfortunately, several mathematics educators (Kilpatrick (1985, Lesh (1985), Lester (1980, 1985), Schoenfeld (1985), Silver (1985)) reported that the results of these studies have been disappointingly inconsistent. They agreed that one of the primary reasons for these inconsistencies is the failure of the studies to account for metacognition.^ The purpose of this study was to consider whether the problem solving ability of average eighth-grade students would be enhanced if these students were taught heuristics with an emphasis on what Schoenfeld (1985) referred to as metacognitive control. Control is the ability of students to monitor when and how certain heuristics would facilitate the solving of a problem.^ In this investigation, fifty-five eighth-grade students were assigned to three treatment groups: TR1 was taught specific problem solving heuristics and when and how to use them; TR2 was given various types of problems, but was not made aware of the specific heuristics that might facilitate their solution; CL was not given any problems and served as the control for the experiment. These students were taught in their regular classrooms for a period of sixteen weeks (one academic semester), and the problem solving was made part of the regular general mathematics curriculum, with the investigator serving as the students\u27 regular teacher.^ All students were administered a pretest and posttest consisting of matched pairs of problems. Subsequent analysis, using an analysis of covariance for repeated measures, revealed that although students in TR2 significantly outperformed those in CL (p $\u3c$ 0.5), they in turn were outperformed by those in TR1 (p $\u3c$.01). Boys generally outperformed girls at all levels, although the girls in TR1 outperformed all gender subgroups except the boys in TR1 and TR2.