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This study examines the construct of problem representation and the processes used by learners to construct or modify problem representations in problem-solving situations. Students (n=14) from freshman calculus courses at the University of California at San Diego participated in videotaped interviews in which they were asked to think aloud as they encountered dilemmas in solving certain tasks. The videotape protocols for each participant were analyzed and results were reported in the form of case studies. The case studies were considered as a group for the purpose of generalizing results. Three sections summarize the findings of the study. First, the levels of solution activity that the students were inferred to achieve during the interview are summarized. Second, the results of a pair of case studies are presented to illustrate individual differences in solvers' ability to construct representations. Third, the results are discussed in more general terms, including a comparison to other research findings about representation. Results indicate that: (1) traditional views of representation need to be reconsidered, (2) the process of representation appears more dynamic than previously thought, and (3) the solvers' use of increasingly abstract levels of solution activity suggests the need to address qualitative aspects of mathematical performance. Contains 23 references. (MDH)

Descriptors: Case Studies, Cognitive Processes, Cognitive Structures, Cognitive Style, College Freshmen, Constructivism (Learning), Higher Education, Interviews, Mathematics Education, Problem Sets, Problem Solving, Schemata (Cognition), Word Problems (Mathematics)

Autor: Cifarelli, Victor


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