The Mathematical Working Space model: An open and adaptable theoretical framework?
Résumé
For more than a decade, a theoretical approach focusing on mathematical work in schooling has been developed by an international community of researchers. Grounded on geometry education research, the Mathematical Working Space (MWS) model emerged from this collaborative work and has been developed during symposia, the fifth of which being held in Florina in July 2016. may be helpful for discovering this model and its current state. This poster aims at illustrating and discussing one of the specificities of the model, which means that it was conceived to interact with other approaches. As Artigue (2016, p. 938) underlies: But the MWS construction is an object of a very different nature, at least in its current state. Its logic seems more that of an assembly that would incorporate, possibly with adaptation, a diversity of constructs and perspectives developed in the field, without privileging any of them. This gives the MWS structure a plasticity that big theories (...) do not have, and certainly contributes to its accessibility and attractivity. Conversely, this plasticity and attractiveness pose the challenging question of the real nature of its relationships with other theoretical approaches, which may be grounded on very different epistemological and methodological principles. In this poster our purpose is to address this question through some examples. For that reason, some key-points of the model will be presented and, in particular, how the study of mathematical work in schooling is framed. Then, some examples will be given to illustrate possible interactions with other theoretical and exogenous frameworks. All the examples come from special issues on MWS model and MWS symposia. The list of examples is not complete and other frameworks have been used, although they do not appear in the poster (Didactical Situation Theory, Anthropological Didactical Theory, Semiotic registers, etc.). Naturally, all the examples cannot be considered in detail but the fact that the model is supported on a diagram assists to illustrate interactions. The poster is organized around diagrams showing the findings of the different papers and questioning the openness and adaptability of the MWS model. Combining the model with Drouhard's epistemography. Drouhard's epistemography use has changed the view on tool and instrument in the MWS model (Kuzniak, Nechache & Drouhard, 2016). Depending on their nature and on the way they are being exploited to solve the problem, tools may be situated in any of the three poles of the epistemological plane. In the cognitive plane, one speaks of an instrument whenever a subject interacts with a tool in order to tackle a task effectively. Thus, a tool is associated with a corresponding instrument in the cognitive plane.
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