Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

Andrea Dorila Cárcamo Bahamonde, Josep Maria Fortuny Aymemí, Joan Vicenç Gómez i Urgellés

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)


© 2016 Informa UK Limited, trading as Taylor & Francis Group. In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.
Original languageEnglish
Pages (from-to)338-352
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number3
Publication statusPublished - 3 Apr 2017


  • actual learning trajectory
  • design-based research
  • emergent models heuristic
  • Hypothetical learning trajectory
  • mathematical modelling
  • span
  • spanning set


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