Treffer: Keeping Theorizing in Touch with Practice: Practical Rationality as a Middle Range Theory of Mathematics Teaching

This chapter characterizes the practical rationality of mathematics teaching as a middle range theory, a theory that is developed through the practice of research. We argue that a middle range theory of teaching permits theorizing that keeps in touch with practice, the exploration of complementarities and mutual sharpening of competing constructs, and the pursuit of an agenda of scientific research on mathematics teaching. We illustrate how empirical research on practical rationality has enabled not only the progressive characterization of phenomena hypothesized by the basic concepts of the theory (e.g., what are the norms of instructional situations) or the uncovering of relationships among those concepts (e.g., complementarities and tensions among contractual and situational norms) but also the drawing of relationships with other constructs (e.g., teachers’ beliefs and knowledge). We use this example to argue that progress in theorizing teaching can benefit from a middle-range theory, to illustrate in what way subject-specificity and subject-genericity can complement each other in theorizing, and to speculate on what the field needs from different theorizations to advance toward better understanding of the practice of teaching.