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Digital technologies to teach and learn mathematics: Context and re-contextualization

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Abstract

The central assumption of this paper is that, especially in the field of digital technologies to teach and learn mathematics, the influence of the context in which research is carried out has not been given enough attention, so that research results are not really useful outside this context. We base our discussion on the work of a group of European teams carrying out research with a special methodology of “cross-studies” and carrying out “cross-analyses” of particular studies. A context for a research study is described as a dynamic construction by researchers, connecting relevant contextual characteristics in the settings (empirical and academic) where research activity takes place and helping to gain insight from the outcomes of the study. Analyzing the design of two “Didactical Digital Artefacts,” and the associated cross-studies involving teams of three countries, we identify more or less conscious influences of characteristics in the researchers' contexts upon research outcomes. Cross-studies and cross-analysis help to go further by making researchers more aware of their context and of its characteristics. It also helps researchers to “re-contextualize,” that is to say to identify new contextual characteristics in the settings they are acting in, to gain insight from research outcomes that emerged in other contexts.

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Notes

  1. The metaphor “to gain insight into something from research findings” is very popular in research, emphasizing the fact that research results or outcomes are not useful in themselves if they do not “shed light” on some overarching question, issue or phenomenon. Like “meaning” in cognition, “insight” needs a context for disambiguation and for coherence with a larger whole.

  2. Monaghan (2009 p.23): “the term ‘technique’ in my country’s everyday mathematics-education-speech refers to value-free manipulation”.

  3. Italics are used in the rest of the paper to indicate that the notions are to be understood as they are introduced in this section.

  4. DIDIREM is now integrated into the Laboratoire de Didactique André Revuz, University Paris-Diderot, UNISI was a team in Università degli Studi di Siena, ETL was a team in the Educational Technology Lab, NKUA Athens.

  5. For instance, a shift of a graph occurring while animating a parameter in the formula of a function was quickly interpreted by the teacher as the effect of a geometrical transformation, and in Maracci et al. (2013, p. 474)’s analysis “there is the risk that the meaning attached to (this mathematical concept will be) confined to the actual use of Casyopée.”

  6. Institut National de la Recherche Pédagogique, named now Institut Français d’Education: http://ife.ens-lyon.fr/ife/institut/presentation

  7. http://casyopee.eu

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Authors and Affiliations

  1. Laboratoire de Didadactique André Revuz, University Paris 7 DIDEROT, Paris, France

    Jean-Baptiste Lagrange

  2. University of Reims, Reims, France

    Jean-Baptiste Lagrange

  3. Educational Technology Lab, N.K. University of Athens, Athens, Greece

    Chronis Kynigos

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  1. Jean-Baptiste Lagrange
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  2. Chronis Kynigos
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Correspondence to Jean-Baptiste Lagrange.

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Lagrange, JB., Kynigos, C. Digital technologies to teach and learn mathematics: Context and re-contextualization. Educ Stud Math 85, 381–403 (2014). https://doi.org/10.1007/s10649-013-9525-z

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