Images of Theory in the Practices of Theorizing in Mathematics Education Research

In this chapter, we describe, illustrate, and discuss three images that we see as significant and pervasive in theory and theorizing in the field of mathematics education research (MER). We inspect their epistemological, ontological, and axiological entailments, as well as some of their unexpected or undesired consequences. Indeed, we see these images as shining light on broader spatial imaginaries, that is, on the way that social-spatial relations are understood at a collective level and performed through socio-spatial practices. Spatial imaginaries describe how things are, as well as how they ought to be, and therefore entail ontic and epistemic commitments. They operate at multiple levels in MER, including the way in which theories are structured, how theories relate to each other, the role that MERs see theory playing in their research activities, the relationship of theory to other aspects of MER practice, and the axiological dimension of theory (its aesthetic and ethical values). By working explicitly with the images through which spatial imaginaries are expressed, we not only make these assumptions more visible but can also offer alternative ones. Such spatial imaginaries may enable people to become less fixed in their ontological and epistemological assumptions and more serious about negotiating new assumptions. We suggest that the axiological dimension of theorizing, which is rarely explicitly addressed in MER practices, can also play an important role in this negotiation, by helping to articulate both the historical contours of MER theories—what problems they have addressed and under what circumstances—and the aesthetic and ethical stakes involved. This chapter should be read more as a commentary than as a response to the questions or an argument about how MERs could or should be thinking theory. That said, if we engage in this commentary, it is not just to point to particular norms and practices but also to raise the question, for the field, of whether—and, if so, how—theorizing can help MERs address some of the major differences that have arisen in the field.