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The ostensive dimension through the lenses of two didactic approaches

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Abstract

The paper presents how two different theories—the APC-space and the ATD—can frame in a complementary way the semiotic (or ostensive) dimension of mathematical activity in the way they approach teaching and learning phenomena. The two perspectives coincide in the same subject: the importance given to ostensive objects (gestures, discourses, written symbols, etc.) not only as signs but also as essential tools of mathematical practices. On the one hand, APC-space starts from a general semiotic analysis in terms of “semiotic bundles” that is to be integrated into a more specific epistemological analysis of mathematical activity. On the other hand, ATD proposes a general model of mathematical knowledge and practice in terms of “praxeologies” that has to include a more specific analysis of the role of ostensive objects in the development of mathematical activities in the classroom. The articulation of both theoretical perspectives is proposed as a contribution to the development of suitable frames for Networking Theories in mathematics education.

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Notes

  1. The definition of Semiotic Set is a generalisation of the definition of Semiotic System, as it is given in Ernest (2006, pp. 69–70).

  2. Another example, made of gazes, speech, gestures and inscriptions has been studied by F. Ferrara in her PhD Dissertation (Ferrara, 2006).

  3. The “euclideanism”, as a general epistemological model of mathematics, pretends to reduce mathematical activity to the process of deducing theorems from a finite set of propositions (the axioms) concerning the so called primitive terms, which are only indirectly defined. The truth of the axioms flows from the axioms to the theorems through deductive canals of truth transmission (the proofs) (Lakatos, 1978).

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Acknowledgments

Research program supported by MIUR and by the Università di Torino and the Università di Modena e Reggio Emilia (PRIN Contract n. 2005019721).

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Torino, Italy

    Ferdinando Arzarello & Cristina Sabena

  2. FUNDEMI Facultat d’Economia IQS, Universitat Ramon Llull, Barcelona, Spain

    Marianna Bosch

  3. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

    Josep Gascón

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  1. Ferdinando Arzarello
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  2. Marianna Bosch
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  3. Josep Gascón
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  4. Cristina Sabena
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Correspondence to Cristina Sabena.

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Arzarello, F., Bosch, M., Gascón, J. et al. The ostensive dimension through the lenses of two didactic approaches. ZDM Mathematics Education 40, 179–188 (2008). https://doi.org/10.1007/s11858-008-0084-1

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