Teaching as problem solving. Collaborative conversations as found talk-aloud protocols. (English)

Li, Yeping (ed.) et al., Proficiency and beliefs in learning and teaching mathematics. Learning from Alan Schoenfeld and Günter Törner. Rotterdam: Sense Publishers (ISBN 978-94-6209-298-3/hbk; 978-94-6209-297-6/pbk). Mathematics Teaching and Learning 1, 125-138 (2013).

From the introduction: Alan Schoenfeld uncovered critical aspects of problem solving, identifying the way that learners use resources, heuristics, control, and beliefs to guide their activities around non-standard mathematical problems. In his groundbreaking research, he used talk-aloud protocols during problem solving sessions with undergraduates and audio recorded them to analyse their thinking. His investigation of students’ talk and choices led him to develop his now well-known problem-solving framework [{\it A. H. Schoenfeld}, Mathematical problem solving. Orlando, FL: Academic Press (1985; ME 1986a.01069)]. In this chapter, I illustrate some key findings of my research on teachers’ collaborative talk, demonstrating the places where “found" problem solving episodes corroborate and extend Schoenfeld’s framework for mathematical problem solving. Like Schoenfeld, I find differences in how participants’ beliefs, resources, and strategies influence their progress. Because I begin my analyses at the level of problem formulation, my work highlights the socially negotiated nature of problem solving. By articulating to and extending Schoenfeld’s framework, this chapter contributes to a more general framework of human problem solving.