The nature of external representations in problem solving

Abstract

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. 179 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 ...

Internal representations, external representations and ergonomics: towards a theoretical integration

“…Although related specifically to 'graphical' representations, their conclusions seem generalizable to any tasks involving an external component. Scaife and Rogers (1996) We note here that Scaife and Rogers' (1996) views closely parallel the proposals summarized above by Larkin (1989), O'Malley and Draper (1992), Zhang (1997), Bryant and Tversky (1999) and Cox (1999), who all presents a fundamentally similar picture that emphasizes the benefits of external representations in cognition. Moreover, when considering external representations (including related notions of 'distributed models' and 'distributed cognition') the researchers above frequently remind us that the interaction between internal cognition and the external components of a task must be considered in combination, since external representations certainly will impact on the conclude, therefore, that task-based interactions fundamentally involve multiple mental representations manipulated in WM, that are informed by knowledge and constrained by the external environment.…”

“…It will be seen in subsequent sections that the framework proposed by Endsley (2000) contains many of the components depicted in the 'relations of mappings' in mental models as described by Moray (1999), as well as key aspects of Zhang's (1997) theoretical proposals for discussing the role of external representations in problem solving. A framework such as SA seems very powerful, and its application is potentially wide ranging.…”

“…For example, 'affordances' are the information in the environment that can guide behaviour and provide action opportunities directly through perceptual processes (Gibson, 1979). Zhang (1997) describes how the actions supported by affordances do not depend solely upon their physical properties, but also upon the properties of the perceiver. Whilst affordances can make a task easier, they can equally make it more difficult.…”

“…With a diagram people appear to form a visual representation of the depicted information and then imagine moving elements around this image to solve the task (Johnson-Laird 1996). Zhang (1997) considers external representations in problem solving in great detail, and proposes that much about the internal mind can be learned through studying external representations, since the mind reflects the structure of the external world.…”

“…Like Johnson-Laird (1996), Zhang (1997 is especially keen to emphasize the striking benefit of diagrams for task performance, and notes how information can be processed by perceptual systems alone, such that internal representations may not even be required for performance if external representations are available. This view clearly contrasts with the common assumption inherent in traditional research in Artificial Intelligence and Cognitive Science, which views external information as being internalized before internal processing is then externalized (e.g.…”