An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence

Megan Wawro, Chris Rasmussen, Michelle Zandieh, George Franklin Sweeney, Christine Larson

Research output: Contribution to journalArticle

28 Scopus citations


In this paper we present an innovative instructional sequence for an introductory linear algebra course that supports students' reinvention of the concepts of span, linear dependence, and linear independence. Referred to as the Magic Carpet Ride sequence, the problems begin with an imaginary scenario that allows students to build rich imagery and formal definitions. The approach begins by focusing on vectors, their algebraic and geometric representations in ℝ2 and ℝ3, and their properties as sets. Samples of student work are provided to illustrate the variety of student solutions and how these solutions lead to the creation of formal definitions.

Original languageEnglish (US)
Pages (from-to)577-599
Number of pages23
Issue number8
Publication statusPublished - Dec 2012



  • Linear algebra
  • linear independence
  • research in undergraduate mathematics education
  • span
  • student thinking

ASJC Scopus subject areas

  • Mathematics(all)
  • Education

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