Development of local theories in design-based research in mathematics education

Abstract Design-based research (DBR) develops interventions and associated local theories about ways of supporting students’ learning of particular mathematical topics through iterative cycles of empirical investigation and retrospective analysis. Although DBR has been conducted in mathematics education for various topics and at different educational levels, the theorising processes that take place in DBR studies have received little attention. In the current conceptual paper, we address this issue by exploring how elements of a local theory in a DBR study are generated, revised, and organised over multiple research cycles. We first draw on relevant literature to develop a framework for representing the structure of a local theory in DBR, and we then apply this framework to examine and illustrate the incremental theorising process in one of our completed DBR studies. Our discussion shows how prior scholarship plays a range of roles in the development of a local theory in DBR and how these roles intersect with empirical investigation over the DBR cycles. We conclude by discussing how our framework can serve not only as a methodological tool for analysing theory development in DBR but also as a useful tool for supporting such development.