Student connections of linear algebra concepts: An analysis of concept maps

Douglas A. Lapp, Melvin A. Nyman, John S. Berry

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalInternational Journal of Mathematical Education in Science and Technology
Volume41
Issue number1
DOIs
StatePublished - Jan 2010
Externally publishedYes

Keywords

  • Concept maps
  • Conceptual fields
  • Linear algebra
  • Mathematical understanding
  • Representations

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