A learning trajectory for the fundamental theorem of calculus using digital tools

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Abstract

This study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture about the mathematical relationships embedded in it. The study was guided by the theory of knowledge objectification. We included two rounds of analysis: one, to detect ‘learning focuses’ involved in learning the FTC and to identify the relationship between them; the other, to identify the ways in which students used the tool to become aware of each focus. Data analysis identified nine focuses in the process of learning the FTC. We described these focuses, the relationships between them, and the ways in which students interacted with the tool to characterize the learning trajectory of the FTC.

Original languageEnglish
Pages (from-to)542-562
Number of pages21
JournalInternational Journal of Mathematical Education in Science and Technology
Volume51
Issue number4
DOIs
StatePublished - 18 May 2020

Keywords

  • Awareness
  • digital tools
  • fundamental theorem of calculus
  • learning trajectory

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