The Development of Register Theory

A significant body of research examining language issues in the learning and teaching of mathematics has recognised that language use in school differs in some important ways from language use outside of school. Moreover, subjects such as mathematics are characterised by specific registers (see Halliday, 1978; Halliday & Hasan, 1985). However, the term “register” as it is used in linguistics is contested, and commentators use it in various ways, including those who have focused on indigenous languages (Barton et al., 1998). A number of terms have been used to refer to the construct that characterises the specialised language of mathematics, including “register”, “style” and “discourse”. These terms are

often used interchangeably but can represent quite different concepts in the literature. Therefore, it is important to identify which definition is being used in this thesis, particularly in regard to the idea of the register in applied and sociolinguistic research. The following sections examine the origins and definitions of the term “register” and its use in mathematics education.

Discussion on the features and definitions of the mathematics register can be traced back to studies using register theory and the much broader field of SFL, sometimes known as Hallidayan linguistics after Halliday, the major proponent of the theory (Schleppegrell, 2004). While categorising the newly created pāngarau register is not a major component of this thesis, it is through the work in SFL that definitions of the mathematics register were initially formulated, and issues to do with learning the register have subsequently been discussed (for example, see Dale & Cuevas, 1992).

The foundations of the sociolinguistic work of both SFL and Halliday (1978) have proceeded from a functionalist perspective of language, in contrast to formalist views such as Chomsky’s (1957) development of transformational-generative grammar. The classical linguistic “formalists”, exemplified by Chomsky, asserted that language is an innate universal feature of human beings, and that the different languages are mere manifestations of this feature (Crystal, 1995). Chomsky was concerned only with the formal properties of languages such as English, which he believed was indicative of the nature of what he called universal grammar (Chomsky, 1966). Chomsky’s theory of universal grammar suggested that, although groups of people speak different languages, all human languages are essentially governed by common rules or principles that are universal, and linguistic form can be characterised independently of meaning and function (Chomsky, 1966).

Under Halliday’s (1978) view of language, even if it were a universal feature, language cannot be separated from context (and thus culture). Hence, the universal grammar as promulgated by Chomsky would not have relevance without real-life contexts and experiences. Unlike Halliday,

Hymes (1972), one of the most influential writers in sociolinguistics, publicly took issue with Chomsky for the failure of his transformational- generative grammar to account for linguistic variation. Chomskyan linguistics focused on the aspects of language that are uniform across speakers, ignoring language variation by stipulating idealised speakers/hearers in completely homogeneous communities as its research object (e.g., Chomsky, 1957). In contrast, Hymes (1972) was concerned with actual linguistic diversity as found in speech, and suggested that studies of language should be grounded in ethnographic study rather than introspective theorising. The work of Halliday (1978) also inspired work in critical linguistics (Fowler et al., 1979) that questioned traditional linguistic theory that ignored the sociocultural contexts. This critical work in turn influenced LPP.

The focus of SFL is thus on how people use language and how language is structured for use. Because language situations differ, the primary construct in SFL theory for explaining linguistic variation is the register. According to de Beaugrande (1993), the forerunner of the concept of register was the term “restricted language” discussed in foundational linguistic works (p. 7). Firth (as cited in Leon, 2007, p. 1) also talked of “restricted language”, which “can be said to have its own grammar and dictionary. Firth (as cited in Leon, 2007, p. 9) considered science, technology, politics and sports as domains of restricted language. The early work of Bernstein (1971), where he discussed the concepts of restricted and elaborated codes, also subsequently influenced Halliday’s work (Lowe, 2008). Halliday (1964) suggested that the term register was first used in a linguistic context by Thomas Bertram Reid in 1956 and was brought into currency in the 1960s by a group of linguists who wanted to distinguish between variations in language according to the user, and variations according to use. However, Halliday, a disciple of Firth, is perhaps too modest here because many researchers have subsequently suggested that it was the seminal work of Halliday (1975a, 1978) himself, albeit clearly influenced by the work of Firth, Bernstein and Whorf, that eventually gave currency to the term register in academic research (Lewandowski, 2010).

The central premise of SFL is that language is functional and varies according to the situation in which it is used, and these varieties of language can be referred to as registers (Halliday, 1978; Halliday & Hasan, 1985, 1989). A central notion is ‘stratification’, such that language is analysed in terms of four strata: Context, Semantics, Lexico-Grammar and Phonology-Graphology (Halliday, 1978). Context was interpreted by Halliday (1978) as the linguistic features typically associated with a configuration of situational features: the “field”, the “mode” and the “tenor” (see Appendix A). These three values—field (the context), mode (the social roles and relationships) and tenor (how it is communicated)—are thus the determining factors for the linguistic features of the register as proposed by Halliday (1978) and expanded on by Halliday and Hasan (1989).

Meaning (semantics) in SFL is analysed in terms of three metafunctions. The metafunctions of language are to: understand the environment (ideational meaning); how people act in the situation (social meaning); and how the text is structured as a message (textual meaning) (Mathiessen & Bateman, 1991). These three metafunctions relate to the field, the mode and tenor described above. The lexico-grammar concerns the syntactic organisation of words based on the function of the language and the word options the speaker (or writer) chooses (Halliday, 1996). For example, a speaker could choose to express a mathematical instruction in either active or passive form.

Halliday’s later definitions tend to place a primary emphasis on semantic patterns and context. According to Halliday (1996), the term register refers to specific lexical and grammatical choices made by speakers depending on the situational context, the informants in the conversation, and the function of the language in the discourse. The common feature in these definitions of register is the view that both “situational and linguistic variables need to be part of register characterisation” (Leckie-Tarry, 1995, p. 7).

Halliday (1985) also saw the context of situation embedded specifically within the wider context of culture, both of which are incorporated in the

text by the users. This idea also supports the notion that mathematics is a social and cultural construct, an idea underpinning much of the recently established research domain of ethnomathematics (Barton, 2008), and related discussion on the role of culture in mathematics education (Bishop, 1991).