Abstract
In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching–learning. To analyze them, we introduce a suitable model, the semiotic bundle. It allows focusing on the relationships of gestures with the other semiotic resources within a multimodal approach. It also enables framing the mediating action of the teacher in the classroom: in this respect, we introduce the notion of semiotic game where gestures are one of the major ingredients.
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Notes
For a definition of gesture, see McNeill 1992, p. 11, and the comments in Edwards, this volume.
“The semiotic systems must effectively allow to accomplish the three cognitive activities, which concern every representation. First they must constitute a trace or a set of perceivable traces that are identifiable as a representation of something in a precise system. Second, it must be possible to transform such representations only because of the rules of the system, so that fresh representations can be obtained that can constitute a contribution to knowledge with respect to the initial representations. Last, it must be possible to convert the representations produced within a system into another system, so that the latter representations permit to make explicit further meanings with respect to what is represented by them. Not all semiotic systems allow such three basic cognitive activities, for example the morse or the route code. But the natural language, the symbolic languages, graphs, geometric figures, etc. do that. We shall then speak of registers of semiotic representation” (translation by the authors).
For example, according to the definition of Duval (see the quotation above), there are three forms of semiotic activities: (a) production (“formation” in French) of representations within a semiotic register; (b) transformation of semiotic representations within the same register; (c) conversion of a semiotic representation from a register to another.
Because of the introduction of the semiotic bundle, which enlarges the definition of semiotic register, the notion of semiotic activity given in the previous note is broadened too, provided that the three clauses listed by Duval make sense also for semiotic bundles. This is the case, as it is proved in Arzarello (2006). Hence, from now on, when we speak of semiotic activities we refer to productions, transformations and conversions of representations in semiotic bundles.
The elimination of actual infinitesimals from Analysis made by Weierstrass has not definitely settled this delicate point: see Robinson’s non-standard Analysis or the most recent so called microanalysis (Bell 1998). Also from a cognitive point of view things are not settled at all: see Tall and Tirosh (2001).
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Arzarello, F., Paola, D., Robutti, O. et al. Gestures as semiotic resources in the mathematics classroom. Educ Stud Math 70, 97–109 (2009). https://doi.org/10.1007/s10649-008-9163-z
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DOI: https://doi.org/10.1007/s10649-008-9163-z