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This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding. In addition to the existing techniques for analysing concept maps, two new techniques are developed for analysing qualitative data based on student-constructed concept maps: (1) temporal clumping of concepts and (2) the use of adjacency matrices of an undirected graph representation of the concept map. Findings suggest that students may find it more difficult to make connections between concepts like eigenvalues and eigenvectors and concepts from other parts of the conceptual field such as basis and dimension. In fact, eigenvalues and eigenvectors seemed to be the most disconnected concepts within all of the students' concept maps. In addition, the relationships between link types and certain clumps are suggested as well as directions for future study and curriculum design. [ABSTRACT FROM AUTHOR]

This paper discusses student difficulties in grasping concepts from Linear Algebra - in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student understanding of concepts within a problem-solving context. We discuss some barriers to student understanding and suggest ways of using geometrical interpretations and visualisations of eigenvectors and eigenvalues to address these barriers. These technological interventions can readily implement this geometric approach, permitting students to easily experiment with a visual interpretation of eigenvectors and eigenvalues. [ABSTRACT FROM AUTHOR]

This article discusses student difficulties in grasping concepts from linear algebra. Using an example from an interview with a student, we propose changes that might positively impact student understanding of concepts within a problem-solving context. In particular, we illustrate barriers to student understanding and suggest technological interventions to address these barriers. [ABSTRACT FROM PUBLISHER]