Skepticism and Constructivism

In this chapter, I consider the role of skepticism in the genetic epistemology tradition of mathematics education research. First, I lay out what I see as some of the fundamental and useful lessons I have learned from this tradition about how to conduct and communicate research that models students’ mathematical reasoning. These include the principle of subjective rationality (that researchers should assume that study participants do what they do because it made sense to them) and the need to attribute knowledge to a knower (that we must attend to distinctions between what we know as researchers, what we think one of our research subjects knows, and what those students actually know). Second, I consider how these principles are related to the radical constructivist commitment to remaining agnostic about the question of correspondence, which is the question of whether our knowledge corresponds to ontological reality. This agnosticism has been the hallmark of radical constructivism, which is an influential tradition of work within genetic epistemology. I argue that the principles I endorsed in the first section can be employed as methods of good science, rather than as consequences of agnosticism about ontological reality. Based on this, I make two recommendations. First, radical constructivists should be clear in communicating the precise nature of their skepticism. Second, they need not insist on this agnosticism for other scholars to engage in this tradition of research.