Learning research in a laboratory classroom: a reflection on complementarity and commensurability among multiple analytical accounts

With the myriad theories generated through research over the years, a continuing challenge for researchers is to navigate the multitude of theories in order to communicate their research, integrate empirical results, and make progress as a field by building upon empirical research. The Social Unit of Learning project was purposefully designed so that researchers from multiple disciplines with different theoretical perspectives could work together to examine the complexity of the mathematics classroom. In this paper, we reflect on the multiple analytical accounts generated from the project, drawing from the notions of complementarity and commensurability. Two parallel analyses, applying the commognitive framework and the theory of representations respectively, are used as illustrative examples for discussion regarding complementarity and commensurability. The paper addresses two focal questions, as follows: in what ways do divergence or contradiction in incommensurable analytical accounts reflect methodological discrepancies or fundamental differences in the underpinning theories? Furthermore, in what ways do the accounts generated by the parallel analyses predicated on different theories lead to differences in instructional advocacy? The answers to these questions provide empirically-grounded insights into the consideration of incommensurability in educational research, and suggest ways in which researchers and practitioners might apply the notion of complementarity to reconcile or exploit incommensurable analytical accounts that have resulted in different instructional advocacies.