Reverse-scaffolding algebra: empirical evaluation of design architecture

Scaffolding is the asymmetrical social co-enactment of natural or cultural practice, wherein a more able agent implements or performs for a novice elements of a challenging activity. What the novice may not learn, however, is how the expert’s co-enactments support the activity. Granted, in many cultural practices novices need not understand underlying process. But where process is content, such as mathematics, scaffolding is liable to undermine tenets of reform-oriented pedagogy. We point to tensions between traditional conceptualizations of scaffolding and discovery-based pedagogical methodology for mathematics education. Focusing on co-enactment as a critical feature of scaffolding activities, we introduce “reverse scaffolding”, wherein experts enact for novices only what they know to do rather than what they do not know to do. We demonstrate our approach by discussing a novel technological learning activity, Giant Steps for Algebra, wherein students construct models of realistic narratives. We argue for the method’s potential via reporting on findings from mixed-methods analyses of a quasi-experimental implementation with 40 students