Emergent Properties and Structural Constraints: Advantages of Diagrammatic Representations for Reasoning and Learning

Ken Koedinger

This paper explores some general issues in diagrammatic reasoning using the domain of geometry as the primary example. Geometry has consistently played an important role as a model domain for studying diagrammatic reasoning and it’s relation to human and machine problem solving. In one of the early Artificial Intelligence papers, Gelernter (1963) showed how problem diagram could help prune backward search in geometry theorem proving. More recently, in an article by Larkin and Simon (1987), which has been a real driving force of much of the current interest in diagrammatic reasoning, the authors turn to geometry as one source of evidence for their claims about the advantages of using diagrams in reasoning. Others have explored the role of visual images in geometric reasoning (Furnas, 1990; Kim, 1989) and learning (Suwa and Motoda, 1991). Without setting out to do so, we have found ourselves contributing to this literature as well. In trying to account for the abstract planning behavior of geometry experts, we discovered that a diagram-based representation provided a much better explanation of this behavior than the standard, sententially-based approaches to abstract planning (Koedinger and Anderson, 1990). We built a computer simulation called DC (the Diagram Configuration model) to demonstrate this. We start the paper by summarizing the work of Larkin and Simon (1987) in characterizing the advantages for diagrammatic representations. Then drawing upon our own experience and the history of research in geometry problem solving, we elaborate on these issues and, in particular, discuss in more detail some advantages that were not fully addressed in Larkin and Simon. While there has been much said about the role of diagrams in problem solving, we also discuss their role in learning and in shaping the representations that result from this learning.

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