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The onto-semiotic approach to research in mathematics education

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Abstract

In this paper we synthesize the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. We also assume complementary elements from different theoretical models used in mathematics education to develop a unified approach to didactic phenomena that takes into account their epistemological, cognitive, socio cultural and instructional dimensions.

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Notes

  1. The publications of Godino et al. can be downloaded from Internet: http://www.ugr.es/local/jgodino.

  2. Here, meaning is interpreted in terms of systems of practices related to the object.

  3. Initially we use the expression “mathematical object” as synonymous of “mathematical concept”. Later we extend the use indicating any entity or thing to which we refer, or talk about it, be it real or imaginary and that intervenes in some way in mathematical activity.

  4. “... mathematical discourse and its objects are mutually constitutive” (Sfard, 2000, p. 47.)

  5. “Personal objects” include cognitive constructs such as conceptions, internal representations, conceptual images, etc.

  6. Named by Eco (1979) as semiotic function.

  7. A semiotic conflict is any disparity or difference of interpretation between the meanings ascribed to an expression by two subjects (persons or institutions).

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Acknowledgment

This research work has been carried out in the frame of the project, MCYT- FEDER: SEJ2004-00789.

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Authors and Affiliations

  1. Departamento de Didáctica de la Matemática, Universidad de Granada, 18071, Granada, Spain

    Juan D. Godino & Carmen Batanero

  2. Departament de Didàctica de les Ciències Experimentals i la Matemàtica, Universitat de Barcelona, 08035, Barcelona, Spain

    Vicenç Font

Authors
  1. Juan D. Godino
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  2. Carmen Batanero
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  3. Vicenç Font
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Correspondence to Juan D. Godino.

Additional information

In memoriam of Hans-Georg Steiner who encouraged our interest in the Theory of Mathematics Education and helped us recognize its complexity, and the need for adopting a holistic, interdisciplinary and systemic approach in our research.

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Godino, J.D., Batanero, C. & Font, V. The onto-semiotic approach to research in mathematics education. ZDM Mathematics Education 39, 127–135 (2007). https://doi.org/10.1007/s11858-006-0004-1

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