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Educational Studies in Mathematics

, Volume 82, Issue 1, pp 97–124 | Cite as

The emergence of objects from mathematical practices

  • Vicenç Font
  • Juan D. GodinoEmail author
  • Jesús Gallardo
Article

Abstract

The nature of mathematical objects, their various types, the way in which they are formed, and how they participate in mathematical activity are all questions of interest for philosophy and mathematics education. Teaching in schools is usually based, implicitly or explicitly, on a descriptive/realist view of mathematics, an approach which is not free from potential conflicts. After analysing why this view is so often taken and pointing out the problems raised by realism in mathematics this paper discusses a number of philosophical alternatives in relation to the nature of mathematical objects. Having briefly described the educational and philosophical problem regarding the origin and nature of these objects we then present the main characteristics of a pragmatic and anthropological semiotic approach to them, one which may serve as the outline of a philosophy of mathematics developed from the point of view of mathematics education. This approach is able to explain from a non-realist position how mathematical objects emerge from mathematical practices.

Keywords

Classroom discourse Conventional versus realist mathematics Epistemology Mathematical objects Onto-semiotics 

Notes

Acknowledgment

The research reported in this article was carried out as part of the following projects: EDU2009-08120 and EDU2010-14947 (MICINN, Spain).

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Vicenç Font
    • 1
  • Juan D. Godino
    • 2
    Email author
  • Jesús Gallardo
    • 3
  1. 1.Departament de Didàctica de les Ciències Experimentals i la Matemàtica, Facultat de Formació del ProfessoratUniversitat de BarcelonaBarcelonaSpain
  2. 2.Departamento de Didáctica de la Matemática, Facultad de EducaciónUniversidad de GranadaGranadaSpain
  3. 3.Departamento de Didáctica de las Matemáticas, Didáctica de las Ciencias Sociales y de las Ciencias Experimentales. Facultad de Ciencias de la EducaciónUniversidad de MálagaMálagaSpain

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