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Educational Studies in Mathematics

, Volume 77, Issue 2–3, pp 189–206 | Cite as

Semiotic and theoretic control in argumentation and proof activities

  • Ferdinando Arzarello
  • Cristina Sabena
Article

Abstract

We present a model to analyze the students’ activities of argumentation and proof in the graphical context of Elementary Calculus. The theoretical background is provided by the integration of Toulmin’s structural description of arguments, Peirce’s notions of sign, diagrammatic reasoning and abduction, and Habermas’ model for rational behavior. Based on empirical qualitative analysis we identify three different kinds of semiotic actions featuring the organization of the argumentations, and related to different epistemological status of the arguments. In such semiotic actions, the students’ argumentation and proof activities are managed and guided according to two intertwined modalities of control, which we call semiotic and theoretic control. The former refers to decisions concerning the selection and implementation of semiotic resources; the latter refers to decisions concerning the selection and implementation of a more or less explicit theory or parts of it. The structure of the model allows us to pinpoint a dialectical dynamics between the two.

Keywords

Argumentation Proof Semiotic control Theoretic control Abduction 

Notes

Acknowledgment

This study is jointly funded by the MIUR and the Università di Torino (PRIN 2007B2M4EK).

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.University of TorinoTorinoItaly

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