Development of a Cognitive-Metacognitive Framework for Protocol Analysis of Mathematical Problem Solving in Small Groups

A framework is presented that explicitly delineates the roles of metacognition and cognition within small-group heuristic problem solving in mathematics. This framework is used to describe the videotaped behaviors of 27 seventh-grade students of varying ability working in small groups to solve a mathematical problem. The results suggest the importance of metacognitive processes in mathematical problem solving in a small-group setting. A continuous interplay of cognitive and metacognitive behaviors appears to be necessary for successful problem solving and maximum student involvement. Within the groups, students returned several times to such problem-solving episodes as reading, understanding, exploring, analyzing, planning, implementing, and verifying. Stimulated-recall interviews held after completion of the task underscored an additional dimension of importance. Attitudes, particularly those of high-ability students, seemed to affect the interactions and the problem-solving behaviors of fellow group members. The framework shows promise of being a powerful tool for the future study of mathematical problem solving in a small-group setting.