Metatheory

Abstract

This chapter explores the possibility of an ontological turn in mathematics education research (MER). The chapter draws upon dialectical critical realism and the all-quadrants, all-levels, all-lines, all-states, and all-types (or AQAL) model of integral theory to investigate the explicit need for the inclusion of multiple metatheories currently used within MER. The chapter begins with an introduction to one of the most important and persistent challenges facing MER and its pedagogy: the explicit call for a metatheory. Section 1 identifies new possibilities regarding the role of metatheory in practice by unpacking the metatheoretical coordinates of critical realism and integral theory. After providing a brief history of the origins of critical realism and integral theory, I review the ontological, epistemological, and methodological metatheorems of basic critical realism, and I put them to work to offer a dialectical omissive critique of integral theory. Section 2 reviews some of the traditional applications of the AQAL model without critical realism to mathematics education and pedagogy. It also brings the AQAL quadrants to bear on a dialectical phenomenology for explaining the necessity to use multiple metatheories in MER that describe its development diachronically as a research field. The chapter concludes with a discussion of the benefits and drawbacks of metatheory.