Using typological perspectives in mathematics register development

There are many communities who speak languages that have not previously been used for formal schooling and which are often undocumented who would like to be able to use their languages in school for teaching their children. For both communities and linguists, the obvious place to start has often been with literacy in the community language. Another school subject that is widely regarded as a core school subjects is mathematics. The language of mathematics or mathematics register includes both specific mathematical lexicon and the grammatical structures that are used in mathematical expression and practice (Halliday, 2004). Developing a school mathematics register in languages that have not previously been used in this way has some particular linguistic challenges. In some circumstances, typological approaches and perspectives can have useful application to these challenges.

For example, prepositions in English have many grammatical functions both in general language and in mathematics. Many English prepositions have a core spatial meaning which is directly relevant to mathematics, but these meanings can be metaphorically extended into other domains such as number, for example talking about numbers occurring before or after each other in a sequence. Talking about learning mathematics in English, Jorgensen (2010) states that “coming to learn mathematics is heavily associated with the use of prepositions” (p. 29). Jorgensen compares the number of prepositions in English and Pitjantjatjara, seeing the absence of numerous prepositions in Pitjantjatjara as an impediment to teaching or learning mathematics in that language. However, Pitjantjatjara has an extensive case system (Bowe, 1990), which performs many of the same functions in assigning roles to nouns, as is performed by the prepositions of English. There are languages such as Finnish and Estonian, with extensive case systems, which are successfully used in mathematics education, as demonstrated by results in the Programme for International Student Assessment (PISA) tests (http://www.oecd.org/pisa/data/). To develop a mathematics register in Pitjantjatjara, it might be useful to look at a typologically similar language, such as Finnish or Estonian, for a model on how particular mathematical processes might be expressed, rather than comparing with a language such as English which is typologically different in this area. Other areas of language that are mathematically significant, and to which a typological perspective may be useful in mathematics register development, include modality (used in conjecturing and hypothesizing), comparatives, and spatial frame of reference.

Typology as a discipline is largely concerned with describing languages in a framework neutral manner (Nichols, 2007) and with developing concepts that are analytically compatible in all languages (Evans & Dench, 2006). The proposed applied approach described here is framed by a theoretical conception of mathematics, which can vary both from within different cultures and languages and from the perspective of the research (Barton, 2009). A key guiding element is function: by considering the mathematical and other functions are performed by a language feature in one language, it becomes possible to ask in what other ways are these functions performed in other languages.