Literature on Mathematics and Language

This page is just for literature focused on teaching Maths and language. This might be literacy issues for native speakers learning Maths, or Maths in a foreign language for CLIL or Bilingual Education.

I started by listing things I'd read myself, but as before the invitation goes out to any of you who would like to contribute with links and comments about pieces you read and think should be shared. Send them in and I'll publish them here.

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14 Multilingualism in Mathematics Classrooms: Global Perspectives

Richard Barwell (2009) Multilingual Matters

(Book)

A clear, informative and erudite collection of articles from a number of diverse maths learning contexts placing the role of language in the maths classroom at the centre of the discussion.

Barwell identifies three 'tensions' in the multilingual maths classroom:

1) between maths and language

2) between formal and informal maths

3) between home languages and language of school and schooling

... and says that attention, thought and planning need to be given to all of these tensions.

Chapter 2 - Mapping the maths landscape was of particular interest to me as an amateur geek when it comes to language of the curriculum. I read with interest the data collection and analysis of the language of maths Monaghan reports. Would like to get my hands on this rich maths corpora.

Chapter 5 - Mathematical word problems and bilingual learners in England.

Getting students to write their own word problems helps them with understanding and dealing with word problems they meet in maths. Simple but true.

Chapter 6 - How language and graphs support conversation in a bilingual mathematics classroom.

Reminds me of the 'semi-script' from Geddes. Using diagrams (or diagrammatical representations of content) of any kind is a great for supporting and guiding learners in producing content language.

Chapter 9 - Bilingual Latino students, writing and mathematics

A case study in the US which describes creating a culture of communication in the maths classroom which brings below average (bilingual) achievers above average in a short space of time.

I know I'll carry this book around with me, to read again, and again. It will then sit on the shelf nearest my desk so I can easily access it when needed in the future.

11 USING TWO LANGUAGES WHEN LEARNING MATHEMATICS

JUDIT MOSCHKOVICH

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.

Bessie Davis Cooke and Dilek Buchholz (2005)

Early Childhood Education Journal, Vol. 32, No. 6, June 2005

Couldn't find a free version of this, but there is a link in ERIC.

This is a very readable account of observation of pre-school maths classes and description of techniques for interaction between the teacher and learners for developing learner oral skills in maths. Specifically, the conclusion is that the teacher acts as interface between the learner and the subject facilitating learner production in a number of ways:

- providing opportunities for informal self-expression

- acting as facilitator while learners are busy on task

- providing opportunities for students to connect new understandings to prior knowledge

- linking classroom management activities and routines with maths

- asking a variety of questions

- encouraging the use of appropriate terms

I enjoyed reading this, straightforward, immediately useable ideas and completely relevant to classroom practice.

5 Using Halliday’s functional grammar to examine early years worded mathematics texts

Keiran Abel & Beryl Exley

Queensland University of Technology

Australian Journal of Language and Literacy, Vol. 31, No. 3, 2008. pp. 227–241

There is an 'author version' of this article available as of March 24th, 2010, from:

The Department of Pre-School Education, Faculty of Education, Florina, University of Western Macedonia, cultural studies, semiotic structures and practices.

Comments

I'm working on a lot of Maths through English as a foreign language recently and so am collecting papers which discuss language and Maths. Will organize this page into headed sections as soon as I can get the time.

This is a significant article since it is written about mother tongue speakers of English learning Maths and the literacy issues which arise because of the aspects of language which appear in the Maths which aren't taught in the English curriculum.

The authors use very concrete examples with 6 Maths tasks which they analyze for language demands and then describe to what extent the language is covered in the English curriculum.

It's written in a very clear style and is straight to the point, which is 'Isn't it unfair to expect children to succeed in Maths if they haven't been taught the language they need to do the Maths?' This is my wording, not the authors'.

This article so impressed me that I got out and dusted off my copy of Functional English Grammar to follow up on the aspects of language which are described in the article. I think the 'system' used to describe and analyze language and then plot this against the language curriculum is very useful.

There isn't anything about how the language could be dealt with in the class, which would make a good follow up article though there is a broad reference to the need for 'scaffolding' in learning. This is what is particularly important for CLIL and bilingual education.

The bibliography is worth exploring further. Am now looking for Unsworth 1999.

Quotations:

'if students do not learn to differentiate between and work with the unique language attributes and structures of key learning area texts, then they will be disabled in their use of literacy across the curriculum in the future'. (from Unsworth 1997, page 231)

It is 'important that those who teach maths also explicitly prepare students with the essential skills necessary for carefully and appropriately dealing with the language demands of maths worded texts.' (page 237)

'Students require specific knowledge of () grammatical structures and their functions to successfully decode and make sense of this mathematical discourse.' (page 240)