Educational Studies in Mathematics

, Volume 82, Issue 3, pp 397–415 | Cite as

Plato, Pascal, and the dynamics of personal knowledge

  • Michael Friedrich Otte
  • Tânia M. M. Campos
  • Alexandre S. Abido


Abstract educational practices are to be based on proven scientific knowledge, not least because the function science has to perform in human culture consists of unifying practical skills and general beliefs, the episteme and the techne (Amsterdamski, 1975, pp. 43–44). Now, modern societies first of all presuppose regular and standardized ways of organizing both our concepts and our institutions. The explanatory schemata resulting from this standardization tend to destroy individualism and enchantment. But mathematics education is in fact the only place in which to treat the human subject’s relationship with mathematics. And that is what mathematics education is all about: make the human subject grow intellectually and as a person by means of mathematics. At first sight, mathematics, in its formal guise, seems the opposite of philosophy, because philosophy constructs concepts (meanings), whereas mathematics deals with extensions of concepts (sets). We shall, however, turn this problem into an instrument, using the complementarity of intensions and extensions of theoretical terms as our main device for discussing the relationship between philosophy and mathematics education. The complementarity of the “how” and the “what” of our representations outlines, in fact, the terrain on which epistemology and education are to meet.


Philosophy in mathematics education Complementarity Plato Pascal Peirce 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Michael Friedrich Otte
    • 1
  • Tânia M. M. Campos
    • 2
  • Alexandre S. Abido
    • 3
  1. 1.University of BielefeldBielefeldGermany
  2. 2.Universidade BandeirantesSão PauloBrazil
  3. 3.Universidade Federal de Mato GrossoCuiabaBrazil

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