Leveraging failure in design research

Even in the resource-rich, more ideal conditions of many design-based classroom interventions, unexpected events can lead to disappointing results in student learning. However, if later iterations in a design research study are more successful, the previous failures can provide opportunities for comparisons to reveal subtle differences in instruction that supported or constrained learning. This article presents design research in which a failure in an early iteration was addressed in a later iteration through an impromptu and unplanned response that better supported student learning. The responsive and interventionist nature of design research played a pivotal role in the emergence of the more successful outcome in the later iteration. The suitability of design research for investigating sociomathematical norms and for conducting conceptual analyses facilitated the deepening of our understanding of both the early failure and the later success. Specifically, our retrospective comparative analysis of these two non-consecutive iterations revealed that one sociomathematical norm better supported student learning of a particular mathematical concept then another norm, led to new insights into the conceptual complexity of division in rate situations, and revealed how the interrelatedness of sociomathematical norms and particular mathematical content can provide an important support for learning. We discuss how our cross-iteration analytic method extends existing approaches to leveraging failure in design research.