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Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA

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Abstract

This paper presents a networking of two theories, the APOS Theory and the ontosemiotic approach (OSA), to compare and contrast how they conceptualize the notion of a mathematical object. As context of reflection, we designed an APOS genetic decomposition for the derivative and analyzed it from the point of view of OSA. Results of this study show some commonalities and some links between these theories and signal the complementary nature of their constructs.

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Acknowledgments

This research has been carried out as part of projects EDU2012-32644 and EDU2012-31464, and by Asociación Mexicana de Cultura A. C, and ITAM.

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Authors and Affiliations

  1. Departament de Didàctica de les CCEE i la Matemàtica, Facultat de Formació del Professorat, Universitat de Barcelona, Passeig de la Vall d’Hebrón, 171, Barcelona, 08035, Catalonia, Spain

    Vicenç Font Moll

  2. Departamento de Matemáticas, Instituto Tecnológico Autónomo de México, Río Hondo #1, Tizapán, San Angel, México DF, 01000, México

    María Trigueros

  3. Departament de Didàctica de la Matemàtica i de les Ciències Experimentals, Facultat d’Educació, Universitat Autònoma de Barcelona, Room 136, Building G5, Cerdanyola del Vallès, Barcelona, 08193, Catalonia, Spain

    Edelmira Badillo

  4. Departamento Académico de Ciencias, Pontificia Universidad Católica del Perú Av. Universitaria, San Miguel, 1801, Lima-32, Perú

    Norma Rubio

Authors
  1. Vicenç Font Moll
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  2. María Trigueros
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  3. Edelmira Badillo
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  4. Norma Rubio
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Correspondence to Vicenç Font Moll.

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Font Moll, V., Trigueros, M., Badillo, E. et al. Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educ Stud Math 91, 107–122 (2016). https://doi.org/10.1007/s10649-015-9639-6

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  • DOI: https://doi.org/10.1007/s10649-015-9639-6

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