Seeing Deep Structure From the Interactions of Surface Features

Abstract

Transfer is typically thought of as requiring individuals to “see” what is the same in the deep structure between a new target problem and a previously encountered source problem, even though the surface features may be dissimilar. We propose that experts can “see” the deep structure by considering the first-order interactions of the explicit surface features and the second-order relationships between the first-order cues. Based on this speculative hypothesis, we propose a domain-specific bottom-up instructional approach that teaches students explicitly to focus on deriving the first-order interactions cues and noticing the second-order relationships among the first-order interaction cues. To do so, researchers and instructional designers need to first extract from experienced solvers or experts how they derive such first-order cues. Transfer is assumed to be based on the similarities in the second-order relationships, which are familiar everyday relationships such as equal to, greater than, and so forth.

ACKNOWLEDGMENTS

We are grateful for the support provided by the Institute of Education Science to the first author (Grant Number R305A110090 and R305A110811) and the National Science Foundation (REESE Grant Number 0910221) to the second author, for the preparation of this article. We appreciate and benefited tremendously from the reviews and comments provided by Sam Day and two anonymous reviewers.