External representations are involved in many cognitive tasks, such as multiplication with paper and pencil, grocery shopping with a written list, geometrical problem solving, graph understanding, diagrammatic reasoning, chess playing, and so on. Few would deny that external representations play certain roles in these tasks. However, in comparison with internal representations, relatively little research has been directed towards the nature of external representations in cognition. This might be due to the belief that very little knowledge about the internal mind can be gained by studying external representations, or due to the view that external representations are nothing but inputs and stimuli to the internal mind, or simply due to the lack of a suitable methodology for studying external representations.This article explores the functions of external representations, using problem solving as the task domain and test bed. It takes the position that much can be learned about the internal mind by studying external representations because much of the structure of the internal Direct all correspondence to: Jiajie Zhang, Department of Psychology, The Ohio State University, 1827 Neil Avenue, Columbus, OH 43210, e-mail: zhang.520osu.edu.
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180ZHANG mind is a reflection of the structure of the external environment (e.g., Anderson, 1993;Shepard, 1984; Simon, 1981). It argues that external representations are not simply inputs and stimuli to the internal mind; rather, they are so intrinsic to many cognitive tasks that they guide, constrain, and even determine cognitive behavior. By focusing on what information in external representations can be perceived and how the information in external representations affects problem solving behavior, this article develops a theoretical framework for external representation based (henceforth, ER-based) problem solving. This framework is not only a functional model that can make specific empirical predictions, but also a methodology that can be used to systematically analyze ER-based problem solving tasks.This article is divided into five parts. The first part introduces the theoretical background, including a definition of external representations, a discussion on the relationship between internal and external representations, and a brief review of the important roles of external representations in cognition. The second part proposes the theoretical framework for ER-based problem solving. The third part uses the framework as a methodology to analyze the structure of the Tic-Tat-Toe and as a functional model to make specific predictions about the behavior in the Tic-Tat-Toe. The fourth part reports three experiments designed to test the predictions of the framework and examine the general properties of external representations. The last part summarizes the experimental results, evaluates the theoretical framework, and suggests a representational determinism.
THEORETICAL BACKGROUND
A Definition of External RepresentationsIn the present study, external representations are defined as ...