The tension for teaching and learni

The tension for teaching and learning arises from a need for students to develop recognisable ways of communicating mathematics set against a desire on the part of teachers that their students should meaningfully discuss mathematics. This tension is often seen as a trade-off, in which teachers allow a degree of informal expression to ensure that students understand the mathematics, while seeking to gradually en- hance students’ use of more formal or standard forms of expression (Adler 2001; Khisty 1995). Indeed both Setati and Adler (2000) and Clarkson (2009) develop explicit models to deal with this tension. In each case, the approach consists of recognising and building from students’ informal expression of mathematics in any language, towards more formal expression of mathematics in any language, with perhaps the ultimate goal that students are proficient users of formal mathematical English. These models encapsulate the underlying tension between the centripetal forces of standard mathematical language and the centrifugal forces of language diversity, where diversity includes both natural and social languages.