The Nature of External Representations in Problem Solving

Abstract

This article proposes a theoretical framework for external representation based problem solving. The Tic-Tac-Toe and its isomorphs are used to illustrate the procedures of the framework as a methodology and test the predictions of the framework as a functional model. Experimental results show that the behavior in the Tic-Tac-Toe is determined by the directly available information in external and internal representations in terms of perceptual and cognitive biases, regardless of whether the biases are consistent with, inconsistent with, or irrelevant to the task. It is shown that external representations are not merely inputs and stimuli to the internal mind and that they have much more important functions than mere memory aids. A representational determinism is suggested--the form of a representation determines what information can be perceived, what processes can be activated, and what structures can be discovered from the specific representation.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 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 an...

Teaching with concrete and abstract visual representations: Effects on students' problem solving, problem representations, and learning perceptions.

“…Studies have documented the central role that the problem representation step plays in redescribing problems in terms of concepts and principles learned (Chi, Feltovich, & Glaser, 1981), reducing the difficulty of the problem-solving process (Newell & Simon, 1972;Simon & Hayes, 1976), and promoting the solution of problems (Brenner et al, 1997;Collins & Ferguson, 1993;Mayer & Hegarty, 1996;Rittle-Johnson, Siegler, & Alibali, 2001;Zhang, 1997). Furthermore, expertise studies in a variety of domains have shown that visual representations are a fundamental tool to support the reasoning and problem solving of experts (Ericsson & Smith, 1991;Knorr-Cetina & Amann, 1990;Kozma, Chin, Russell, & Marx, 2000;Lynch, 1995; Lynch & Woolgar, 1990;Roth, Bowen, & McGinn, 1999).…”

“…And they were in notebooks and reference books, and in journal articles and advertisements on bookshelves and bench tops. (p. 209) In line with these findings, Schank (1994) identified the use of visual representations as one of the seven essential skills of professional biologists.The way in which visual representations are designed in instruction can play an important role in the lived experience of students and in their associated appropriation of effective graphing practices (Collins & Ferguson, 1993;Day, 1988;Kirshner, 1989;Zhang, 1997). Although diagrams have been shown to support reasoning and problem solving (Glasgow, Narayanan, & Chandrasekaran, 1995), the evidence that not all visual representations are equally helpful to all students suggests that their level of concreteness may have an effect on learning (Butcher, 2006).…”

Symbolic and Verbal Representation Process of Student in Solving Mathematics Problem Based Polya’s Stages

“…The result was consistent with the opinion of Lesh et al (1987) that the procedure in solving the problem, one of them can be done by explaining the problem solution by using verbal (written) or oral (speech). Besides Kaput (1987), Lesh (1987), Zhang (1997) Johnson (1998), and Milrad (2002 explain that language representation skills (verbal) are characterized by a passion in translating the nature and relationships in mathematical problems into verbal or verbal representations. The verbal representation used by students is very effective in problem solving.…”

Externalismo, iconicidade e cognição distribuída em C.S.Peirce.

“…Este experimento, e outros que aparecem no mesmo artigo, levaram os autores a concluir que representações mais externalizadas são mais eficientes em tarefas de solução de problemas (ver também Zhang, 1997;Chuah, Zhang & Johnson, 2000).…”