Machine Learning
Realization of a geometry-theorem proving machine
Computers & thought
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Diagrams often play an important role in human problem solving. A diagram can make a task more difficult, however, when it obscures important problem features, or requires repeated effort to interpret what it represents. Moreover, the nature and origin of diagrams can be as important as their exploitation during problem solving. This paper chronicles the complex interleaving of visual cognition with high-level reasoning in three subjects. Their diagrams and subsequent verbal protocols offer insight into human cognition. The diversity and richness of their response, and their ability to address the task via diagrams, provide an incisive look at the role diagrams play in the development of expertise. This paper recounts how their diagrams led, and misled, them; how their diagrams both explained and drove explanation; and how a spatial approach reported here can lead to deeper understanding of other simple games.