Students' conception of introductory linear algebra notions: The role of metaphors, analogies, and symbolization
Abstract
The focus of this research is on students' conception of basic linear algebra notions, specifically, the notions of linear dependence and linear independence of sets of vectors. Drawing upon Sfard's (1991, 1997) perspective on concept formation, this research investigates the role of metaphors, analogies, and symbolic representations in the shift from operational to structural conception. The study focuses on how students' spontaneous analogies, semantic interpretations of metaphors and reasoning with symbols influence conceptualization and problem solving. In addition, the study considers the history of linear dependence and linear independence as a source of insights for understanding and possibly explaining students' difficulties in learning these concepts.
Degree
Ph.D.
Advisors
Wood, Purdue University.
Subject Area
Curricula|Teaching|Mathematics education
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