A method for using adjacency matrices to analyze the connections students make within and between concepts: The case of linear algebra

Natalie E. Selinski, Chris Rasmussen, Megan Wawro, Michelle Zandieh

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation of and connections between concepts. Three cases provide examples that illustrate the usefulness of this approach for comparing differences in the structure of the connections, as exhibited in what we refer to as dense, sparse, and hub adjacency matrices. We also make use of mathematical constructs from digraph theory, such as walks and being strongly connected, to indicate possible chains of connections and flexibility in making connections within and between concepts. We posit that this method is useful for characterizing student connections in other content areas and grade levels.

Original languageEnglish (US)
Pages (from-to)550-583
Number of pages34
JournalJournal for Research in Mathematics Education
Volume45
Issue number5
StatePublished - Nov 1 2014

Keywords

  • Adjacency matrices
  • Connections
  • Linear algebra
  • Research method

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education

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