Educational Studies in Mathematics (2005) 64: 121–144
DOI: 10.1007/s10649-005-9005-1 C Springer 2005
There is a link to this article via the University of Arizona

- Suggests sociolinguistic studies more relevant than psycholinguistics for informing us about bilingual maths communication.
Describes perspectives of psycholinguistics (individual) and sociolinguistics (social)

- Stresses important trend of investigating bilingual competence without comparison to monolingual competence and explains the misunderstanding which is existent of bilingualism that if bilinguals are not equally fluent in both languages then they are not true, real or balanced bilinguals. Rejects the term ‘semilingual’.

- Explains code switching and language switching. Here language switching is used ‘to refer to the use of two languages during solitary and / or mental arithmetic computation.’ Page 5 and code switching is used to mean using two languages during conversations.

- This is where the article becomes interesting for me since the author is suggesting that language switching has a specific role in mathematics and she goes on to cite studies which look into the preferred language of bilinguals for computation, whether or not it’s the language of instruction.
There is a suggestion of a link between reaction time and preferred language which isn’t surprising but there is a message for classroom practice which is ‘allow bilingual students to choose the language they use for arithmetic computation in the classroom’. Page 7
The author does point out another important message from this study. It’s potentially a point which in my view would make a major focus given the numbers of children round the world now receiving their education (maths or other) through the medium of another language. That is to what extent may teachers be ascribing low achievement to lack of maths knowledge, when in actual fact it is down to language, or working through the ‘non-preferred’ language?

- Bilinguals do carry advantages according to the author, such as ‘selective attention’ which means that bilinguals are able to focus on relevant parts and ignore information which is not needed for solving a problem.

- There is debate in the piece around code switching in order to stress that it represents a formal characteristic of bilingual speech and shouldn’t be assessed as lack of knowledge. On the contrary code switching can be a reflection of any one of many complex aspects of interaction between two bilingual speakers in the same way that monolinguals ‘select’ language for the same reasons depending on why they are talking to, where, when etc.

The message to the maths teacher then is to examine specific contexts carefully where learners may be using two language simultaneously and not jump to oversimplified conclusions about student level.