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The language of mathematics attracted recently the attention of philosophers, historians of mathematics, and researchers in mathematics education (see Dutilh Novaes in Formal languages in logic. A philosophical and cognitive analysis. Cambridge University, Cambridge, UK, 2012, Hoyrup in The development of algebraic symbolism. College Publications, London, 2010, Kvasz in Communication in the mathematical classroom. Wydawnictwo Uniwersitetu Rzeszowskiego, Rzeszów, pp. 207–228, 2014, Lakoff and Nunez in Where mathematics comes from. Basic Books, New York, 2000, Macbeth in Realizing reason. A narrative of truth and knowing. Oxford University Press, Oxford, 2014, Serfati in La Révolution Symbolique. La Constitution De L"Ecriture Symbolique Mathematique. Editions Petra, Paris, 2005, or Sfard in Thinking as communicating. Human development, the growth of discourses, and mathematizing. Cambridge University Press, Cambridge, UK, 2008). There exist a considerable number of approaches, each of which studies one particular aspect of the language of mathematics that is relevant in the particular context. Nevertheless, what is lacking is a theoretical framework that would make it possible to integrate these different approaches to the study of the language of mathematics and use their potential for a deeper theoretical foundation of mathematics education. The aim of the present paper is to argue for the need and to outline the possible structure of an integrative theoretical framework for the study of the language of mathematics. The author is convinced that such an integrative initiative can arise from the philosophy of mathematics that is historically grounded and educationally motivated.

DOI: 10.1007/978-3-319-77760-3_14

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