A validation of a special theory of cognition by building multiple models of students' modeling behaviors: Three telescoping case studies
Abstract
The purpose of the present study was to develop models of problems and models of students' modeling behaviors as they engage in problem solving activities using a Special Theory of Cognition as a theoretical framework. It was possible to develop models that illustrate how concepts can be formed and transformed to create a solution using the distinctions provided either explicitly or implicitly in the problem statements. Since the distinctions could be coordinated in alternate ways it was also possible to indicate how alternate solutions could be developed. The systems that coordinated and transformed the concepts to create an explanation that acted as a solution to the problem were the conceptual systems. The conceptual systems both interpreted the information provided in the problem and acted as means of creating an explanation that became a source for reinterpretation. In the processes of interpreting and explaining, two models were built: a contextual model based on experience and a problem model based on type of solution required. The model-model interactions acted as a means of guiding the development of each model as they became modified by each cycle of activity. The problem model developed during the analysis of the problem provided a means of detailing the conceptual systems of students as inferred from the artifacts of their problem solving activities. There was a consistency between what the problem analysis indicated the students might do, what they actually do and what students thought they did.
Degree
Ph.D.
Advisors
Lesh, Purdue University.
Subject Area
Mathematics education
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