A Matter of Translation

The question about the nature of "mathematical objects" is discussed both in the philosophy of mathematics and within mathematics education. Several of these texts use semiotic approaches and look for answers by combining semiotics with sociocultural theories (Radford, 2013). Other authors (e.g. Duval, 2006) attempt to describe the meaning and significance of mathematical objects with the recourse to theories from structuralism. My paper takes a different approach. It focuses on the relationship of mathematical languages, the language of school mathematics and of University Mathematics.

There is thus a good correspondence between the types of language employed in school mathematics and research mathematics …(cf. Ernest, 2008, p. 44).

This correspondence can be described by different means. Ernest refers amongst others to proposals of Halliday (1985) and Rotman (2000). Another way to investigate this relationship, asks whether one of these languages is the „correct" mathematical language and how a translation between these languages can be done successfully. The theories on the issue of translation I use in this text concentrate on Walter Benjamin and Ludwig Wittgenstein. Both authors suggest that a successful translation does not need the assumption of an objectively existing mathematical instance.