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From Experiences in a Dynamic Environment to Written Narratives on Functions

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Abstract

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.

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Notes

  1. We use “DynaGraph” to refer to the original constructions described in the literature and used by Goldenberg, Lewis and O’Keefe, and “dynagraph” for the constructions used in this study.

  2. In Sfard’s words (2008): “Thus, just as zoology, chemistry, and history can be defined as discourses about animals, chemical substances, and past communities, respectively, so can mathematics be described as a discourse about mathematical objects, such as numbers, functions, sets, and geometrical shapes. The simplicity of this claim is misleading, though, because the notion of mathematical object, unlike that of an animal or chemical substance, is notoriously elusive” (p. 129).

  3. There is a “1” written on the far right of the screen.

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Acknowledgements

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”.

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Authors and Affiliations

  1. Department of Mathematics “F. Casorati”, University of Pavia, Pavia, Italy

    Samuele Antonini

  2. Department of Mathematics, University of Pisa, Pisa, Italy

    Anna Baccaglini-Frank & Giulia Lisarelli

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  1. Samuele Antonini
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  2. Anna Baccaglini-Frank
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  3. Giulia Lisarelli
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Correspondence to Giulia Lisarelli.

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Appendix

Appendix

Below we provide screenshots of the 7 dynagraphs that we referred to in this study:

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Antonini, S., Baccaglini-Frank, A. & Lisarelli, G. From Experiences in a Dynamic Environment to Written Narratives on Functions. Digit Exp Math Educ 6, 1–29 (2020). https://doi.org/10.1007/s40751-019-00054-3

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