Reverse‐scaffolding algebra: empirical evaluation of design architecture

The didactical metaphor of scaffolding has become so ubiquitous in the rhetoric of education researchers and practitioners, that its meaning has become diffuse, its theoretical rationale unquestioned, and its pedagogical operationalization vague (Pea 2004). We submit that scaffolding is a victim of its own popularity: its adoption by multifarious and even competing theories of learning has rendered untenable any consistent definition of what exactly scaffolding means. And yet precisely due to its consequent murkiness, the idea of scaffolding might serve as a prism onto a range of educational theories: If all educational scholars would each define what they mean when they say “scaffolding”, we may get a rainbow of clearly juxtaposed theories of learning. Still, we suspect, not all theorists have ready definitions for scaffolding. We certainly did not. Yet by way of implementing our own ill-defined notion of scaffolding in the form of well-defined learning activities, we could begin to ascend from intuitive to articulated notions of “scaffolding”. This exercise led us to realize that our own conceptualization of scaffolding differs from the standard conceptualization in ways that might be pedagogically significant. We came to call our own conceptualization “reverse scaffolding”. The idea of reverse scaffolding was conceived as a response to what we view as an enduring dilemma in mathematics education. On the one hand, it is harmful to Abstract Scaffolding is the asymmetrical social coenactment 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 mixedmethods analyses of a quasi-experimental implementation with 40 students.