Math teaching as jazz improvisation: Exploring the 'highly principled but not determinate' instructional moves of an expert instructor

When engaging students in genuine mathematical problem solving, how can instructors maintain a productive learning environment? In this paper, I examine a series of improvised instructional moves of Alan Schoenfeld, a renowned teacher of mathematical problem solving, and investigate his dilemmas, considerations, and in-the-moment decisions. I use the TRUmath framework to unpack the conflicts that underlie Schoenfeld's dilemmas, and to propose a tacit teaching heuristic that help explains his hard-to-justify moves. I conclude that Schoenfeld's in-the-moment decision making is tacitly oriented towards maintaining certain kinds of balances between his pedagogical principles. On the basis of this analysis, I recommend exploring further the use of TRUmath as a framework for analyzing in-the-moment decision making in the context of conflicting pedagogical principles.