![]() ![]() This paper presents and discusses findings from an empirical evaluation study designed to investigate whether reverse scaffolding might effectively serve as a pedagogical design framework for discovery-based learning. Thus whereas in direct scaffolding cultural mediation fades out, in reverse scaffolding it fades in (see Fig. These artifacts would thus implement for the students’ what they already know to do, not what they do not know to do. By way of enabling the student to arrive at the principles themselves, the cultural tools that implement these principles could become transparent to the child rather than opaque. On the other hand, once students have reinvented critical principles of cultural-historical techniques, educators may intervene by introducing artifacts that implement those principles more efficiently, thus relieving the student to pursue more advanced problems. ![]() Imposed methods are liable to remain opaque to a child who has not had opportunities to explore the problem space, recognize the limitations of familiar methods, and determine relevant embedded properties, patterns, intermediary states, and goal functions that would satisfy solution criteria. On the one hand, it is harmful to show a child how to solve a problem (Kamii and Dominick 1998). The idea of reverse scaffolding was conceived as a response to what we view as an enduring dilemma in mathematics education. We came to call our own conceptualization “reverse 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. 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”. Still, we suspect, not all theorists have ready definitions for scaffolding. 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. 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. 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 argue for the method’s potential via reporting on findings from mixed-methods analyses of a quasi-experimental implementation with 40 students. We demonstrate our approach by discussing a novel technological learning activity, Giant Steps for Algebra, wherein students construct models of realistic narratives. 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 point to tensions between traditional conceptualizations of scaffolding and discovery-based pedagogical methodology for mathematics education. ![]() But where process is content, such as mathematics, scaffolding is liable to undermine tenets of reform-oriented pedagogy. Granted, in many cultural practices novices need not understand underlying process. What the novice may not learn, however, is how the expert’s co-enactments support the activity. 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. ![]()
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