Complexity and collaborative problem solving

Through research conducted in a classroom, this dissertation explores problem solving in choice-affluent environments where students have abundant access to resources beyond their own and their group's knowledge and experience. Contrary to the conventional notion of problem solving as an isolated activity reliant on individual resources, such as knowledge, experience, or sudden insights, this dissertation highlights the collaborative nature of problem solving. Being similar to problem solving in society and among mathematicians, problem solving amongst students in mathematics classrooms should involve accessing external resources like the work of their peers, technology, the internet, and social connections. Using classroom video, I conducted an analysis of students engaged in problem-solving activities. Combining Schoenfeld's theory on resources with Koichu's shifts and choices model for problem solving in choice-affluent environments and Mason's work on shifts of attention, I investigated how groups collaborate in their own group and between other groups to make progress in solving a problem. The findings suggest that collaborative problem solving is not a deterministic process – the stages in the process do not follow a sequence. The processes that students follow when solving problems are non-linear and unpredictable due in part to the complex nature of the learning environment. Additionally, the research showcases a relatively new methodological tool, gaze-dialogue transcripts, to document the dialogue, gestures and gazes during collaborative problem solving from a video source.