Structured affordances in the use of open-ended tasks to facilitate collaborative problem solving

Contemporary curriculum demands the development of both problem solving skills and negotiative skills required for collaborative group work. Tasks are required that create the best possible conditions for students to develop both of these skill sets. Open-ended tasks have been shown to provide these conditions, but they also require the teacher to relinquish some level of control over student activity, since the open-endedness of the tasks provides students with the opportunity to realize their intentions rather than just the teacher's. It is necessary to investigate the nature of the affordances created by the use of open-ended tasks in order to anticipate how they might best be used for both instruction and learning. What is needed is a structured way to identify the affordances offered by open-ended tasks. This paper reports a study conducted in a laboratory classroom equipped to record classroom social interactions in great detail using advanced video technology. The reported analysis addresses the following question: What are the foci of the students' social interactions during collaborative problem solving while attempting open-ended mathematical tasks? Analysis was carried out in relation to each type of data generated: written response, transcripts and videos. Our research has identified structures to represent these affordances so that teachers can both anticipate them and draw on them in monitoring and facilitating student collaborative problem solving. The structured identification of affordances in relation to (a) written product and (b) negotiative focus provides teachers with two frameworks by which to scaffold student collaborative work while attempting open-ended tasks.