From Experiences in a Dynamic Environment to Written Narratives on Functions

  • Samuele Antonini
  • Anna Baccaglini-Frank
  • Giulia LisarelliEmail author


This study focusses on high school students’ written discourse about their experiences in a dynamic interactive digital environment in which functions were represented in one dimension, as dynagraphs, that are digital artifacts in which the independent variable can be acted upon and its movement causes the variation of the dependent variable. After the introduction of the notion of Dynamic Interactive Mediators within the theory of Commognition, we analyze and classify students’ written productions describing their experience with the dynagraphs. We present this classification as a tool of analysis that allows us to gain insight into how their writing reflects the temporal and dynamic dimensions of their experience with the dynagraphs. This tool is used to analyze 11 excerpts; finally, epistemological, cognitive and didactic implications of this tool are discussed.


Covariation Commognition Dynagraph Dynamic interactive mediator Function Narrative 



We thank Nathalie Sinclair for her support in developing the activities described in this paper, and for all the fruitful conversations she has engaged in with us, together with David Pimm. This study has been partially supported by Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA) of the Italian Istituto Nazionale di Alta Matematica “Francesco Severi”.

Compliance with Ethical Standards

Conflict of Interest

On behalf of all authors, the corresponding author states that there is no conflicts of interest.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics “F. Casorati”University of PaviaPaviaItaly
  2. 2.Department of MathematicsUniversity of PisaPisaItaly

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