| Summary: | Engaging the student's prior knowledge is considered by educational researchers to be an important part of constructing a strong foundation for new learning. Diagrams are one technique used in the classroom. Jill Larkin and Herbert Simon described the computational advantages of diagrams over text when used to communicate information in their 1987 article entitled 'Why a Diagram is (Sometimes) Worth Ten Thousand Words.' This case study describes a novel abstract diagramming technique facilitated in four separate university classroom settings. Using paper and crayons, the students created three diagrams that represented the externalization of their unconscious perceptions of their own prior knowledge. The study illustrates how differences in prior knowledge can be visualized using diagrams with greater speed in less time than the traditional use of text-based descriptions. The use of the abstract diagramming technique led to an unexpected finding. The student diagrams were shown to contain a hidden conceptual topology, one that is described by Egenhofer in his 1991 article entitled 'Reasoning About Binary Topological Relations.' This topology is recommended as a framework for structuring and facilitating student collaboration and sharing of prior knowledge and new learning. The present study recommends the diagramming technique as the basis for the establishment of a standard diagram research framework that can be used across multiple research disciplines and subject domains. This dissertation describes a domain-general abstract diagram technique that can be adapted for domain-specific subjects and made operational using basic materials (paper and crayons). The study also describes the instructors' responses to questions about the diagram technique used in their classes. The case study offers recommendations for future diagram research. === Ph. D.
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