A hypothetical learning trajectory for conceptualizing matrices as linear transformations

Christine Andrews-Larson, Megan Wawro, Michelle Zandieh

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


In this paper, we present a hypothetical learning trajectory (HLT) aimed at supporting students in developing flexible ways of reasoning about matrices as linear transformations in the context of introductory linear algebra. In our HLT, we highlight the integral role of the instructor in this development. Our HLT is based on the ‘Italicizing N’ task sequence, in which students work to generate, compose, and invert matrices that correspond to geometric transformations specified within the problem context. In particular, we describe the ways in which the students develop local transformation views of matrix multiplication (focused on individual mappings of input vectors to output vectors) and extend these local views to more global views in which matrices are conceptualized in terms of how they transform a space in a coordinated way.

Original languageEnglish (US)
Pages (from-to)809-829
Number of pages21
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number6
StatePublished - Aug 18 2017


  • Linear algebra
  • hypothetical learning trajectory
  • linear transformation

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education
  • Applied Mathematics


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