Abstract
This chapter concentrates on the often formulated question about the ontological status of the concepts of mathematics. As an alternative to philosophical approaches this paper uses arguments from linguistics and semiotics. Through comparing mathematics in school and mathematics at the university we are confronting the question of how to translate between the two of them. The result of such deliberations is that at least the assumption of a Platonistic view on mathematical concepts is not fruitful.
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Notes
- 1.
The relationship of mathematics and mathematics education was not always stress-free and is still the subject of a series of lectures and symposia. Just to mention two examples, several texts in “Mathematics and mathematics education: Searching for common ground” (Fried and Dreyfus 2014) and papers in “Transformation—A fundamental idea of mathematics education” (Rezat et al. 2014) concentrate on this relationship. Both collections, interestingly, emerged as commemorative books for Theodore Eisenberg and Rudolf Sträßer respectively, two well-known however already retired researchers in mathematics education.
- 2.
The question of the equality of 0.9999…. And 1 is a problem often discussed in school. This example allows one to address a number of properties of the limit of a sequence.
- 3.
Hannah Arendt edited in 1968 in “Illuminations” a number of Benjamin’s papers on art, literature and translation.
- 4.
Significant deliberations on this issue can also be found in the chapter by Sáenz-Ludlow and Zellweger (2015).
- 5.
However, there is an asymmetry from the technical view in favor of university mathematics here.
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Kadunz, G. (2018). A Matter of Translation. In: Presmeg, N., Radford, L., Roth, WM., Kadunz, G. (eds) Signs of Signification. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70287-2_7
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