A Transfer-in-Pieces Consideration of the Perception of Structure in the Transfer of Learning

Abstract

Many approaches to the transfer problem argue that transfer depends on the recognition of the same or similar abstract structure in 2 different situations. However, mainstream cognitive perspectives and contrasting Piagetian constructivist accounts differ in their conceptualizations of structure. These differences, not clearly articulated in the literature, have significant implications for accounts of transfer. Using interview data involving undergraduates learning elementary principles of probability and statistics, and Wagner's (2006) transfer-in-pieces perspective, I extend existing constructivist accounts of transfer in at least 2 ways. First, I show how the notion of a concept projection (diSessa & Wagner, 2005; Wagner, 2006) reveals fine-grained mechanisms of transfer that demonstrate how people structure situations and that elaborate on the Piagetian processes of assimilation and accommodation. Second, I examine how what experts consider a single mathematical concept or principle may come to be recognized through a variety of assimilatory cognitive resources whose usefulness is influenced by contextual factors. That is, an individual might structure 2 contextually dissimilar situations differently while perceiving the same mathematical principle at work in both. Similarly, 2 or more individuals may agree on the relevance of a particular mathematical concept in a situation, even though each structures the situation differently.