Wolf, Goat, and Cabbage: An Analysis of Students’ Roles and Cognitive and Metacognitive Behaviors in Small Group Collaborative Problem-Solving

The research reported on in this paper examines students’ cognitive and metacognitive behaviors as they are manifested in non-routine problem-solving in small groups in a mathematics classroom. Students’ cognitive and metacognitive moves are analyzed as well as the connection between the interaction of both cognitive and metacognitive processes and the effectiveness of the problem-solving process. Some links between modes of discourse, modes of thought in social interactions in small groups, group communicative patterns, and the interplay among students’ roles within the groups are investigated, in order to identify factors which influence the process of collaborative problem-solving, and which contribute to optimal and successful cooperative work in group settings. The results of the study indicate that a setting with a balance between the incidence of cognitive and metacognitive behaviors of the participants and relatively equal participation of all the members of the group, without pronounced patterns of domination and with a high degree of tolerance of other’s opinions, are factors which contribute to successful work in group settings.