Representation transformations in transition from empirical to structural generalization

Abstract

Pattern generalization can be either empirical or structural. A considerable body of research on pattern generalization has shown that learners of different ages tend to generalize based on numerical evidence or visual perception alone rather than an underlying structure of a pattern. Although there is evidence that learners can start with empirical investigation and then shift their attention to the structural aspects of a problem, mechanism of such a transition remains underexplored. Relying on Duval’s theory of registers of semiotic representations, this study used data from task-based interviews to examine the extent to which transformations of semiotic representations can support transition from empirical to structural generalization in figural pattern generalization tasks. This study identified structurally useful treatment and mathematically significant conversion as two types of representation transformations that supported transition from empirical to structural generalization. In contrast to structurally useful treatment, mathematically significant conversions often lead to generalizations that explains why the generalizations are the right ones. Moreover, this study identified two ways in which representation conversions supported transition from empirical to structural generalization: (1) by supporting addition of a structural insight to an empirical generalization; (2) by supporting reasoning based on an observed property. These results contribute to our understanding of the role of representation transformations in transition from empirical to structural generalization.