Kay O'Halloran

Department of English Language and Literature, National University of Singapore

Literacy, Grammar and Mathematics

The analysis of written mathematical discourse using systemic-functional frameworks for language, mathematical symbolism and mathematical visual images (O’Halloran, in press) illustrate the different systems and grammatical strategies through which each resource encodes meaning. The systemic functional framework for language is provided by Halliday (1994) and Martin (1992; 2003). The systemic framework for mathematical symbolism is based on Halliday’s (1994) grammar and Martin’s (1992; 2003) discourse systems for language which have extended to incorporate new systems found in mathematical symbolism. The framework for visual images is based on O’Toole’s (1994) systemic functional framework for paintings. The investigation of ‘intra-semiosis’ within language, the mathematical symbolism and the visual images is accompanied by an examination of the semantic expansions which occur through ‘inter-semiosis’ across the three resources. The systemic functional framework for intersemiosis is an attempt to extend existing systemic theory in multimodality (for example, Baldry (in press) Kress et. al. (2001), Kress and van Leeuwen (2001), Royce (1998); Thibault (2000); O’Halloran (2004), Ventola et. al. (forthcoming)) and scientific language (Halliday and Martin (1993), Martin and Veel (1998). The proposed systemic frameworks are used to analyse intersemiotic moves in a mathematics text to demonstrate how metaphorical expressions in the form of semiotic metaphors arise. Mathematics succeeds through accessing the meaning potential of language, mathematical symbolism and visual display, and utilizing the semantic expansions which occur inter-semiotically. The implications for literacy (for example, Christie & Misson (1998)) are discussed in terms of the grammars, strategies for encoding meaning, and metaphorical shifts which take place in mathematical discourse. The nature of mathematical and scientific language is contextualized in relation to the functions of mathematical symbolism and visual display, and the grammatical means through which those functions are fulfilled. In this discussion, the metaphorical nature of mathematical pedagogical discourse is addressed.