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Introducing students to geometric theorems: how the teacher can exploit the semiotic potential of a DGS

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Abstract

Since their appearance new technologies have raised many expectations about their potential for innovating teaching and learning practices; in particular any didactical software, such as a Dynamic Geometry System (DGS) or a Computer Algebra System (CAS), has been considered an innovative element suited to enhance mathematical learning and support teachers’ classroom practice. This paper shows how the teacher can exploit the potential of a DGS to overcome crucial difficulties in moving from an intuitive to a deductive approach to geometry. A specific intervention will be presented and discussed through examples drawn from a long-term teaching experiment carried out in the 9th and 10th grades of a scientific high school. Focusing on an episode through the lens of a semiotic analysis we will see how the teacher’s intervention develops, exploiting the semiotic potential offered by the DGS Cabri-Géomètre. The semiotic lens highlights specific patterns in the teacher’s action that make students’ personal meanings evolve towards the mathematical meanings that are the objective of the intervention.

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Notes

  1. When using the term “sign” we refer to the indissoluble relationship between signified and signifier. In the stream of other researchers (Radford 2003; Arzarello 2006) we developed the idea that meaning originates in the intricate interplay of signs (Bartolini Bussi and Mariotti 2008; for a thoughtful discussion see also Sfard 2000, p. 42ff).

  2. The expression “Cabri figure” is meant to express both the image produced on the screen and its dynamic behaviour preserving the properties defined in its construction.

  3. Actually, if we consider the whole set of tools available in a DGS, including for instance “measure of an angle”, “rotation of an angle” and the like, the set of possible constructions does not coincide with that attainable only with ruler and compasses. For a full discussion see Stylianides and Stylianides (2005).

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  1. University of Siena, Siena, Italy

    Maria Alessandra Mariotti

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  1. Maria Alessandra Mariotti
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Correspondence to Maria Alessandra Mariotti.

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Mariotti, M.A. Introducing students to geometric theorems: how the teacher can exploit the semiotic potential of a DGS. ZDM Mathematics Education 45, 441–452 (2013). https://doi.org/10.1007/s11858-013-0495-5

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