The Semantic Hyperspace: Accumulating Mathematical Knowledge across Semiotic Resources and Modalities

The nature of mathematical language and the linguistic challenges of learning mathematics have been explored since the 1970s. Schleppegrell (2007) provides a comprehensive synthesis of the research completed by applied linguistics and mathematics educators which aims to identify the linguistic structures in mathematics and how these differ from everyday language. In particular, Michael Halliday (1978) developed the notion of the mathematical register to explain how language is used to construct mathematical knowledge in ways that differ from other academic subjects. Halliday (1978: 195-196) explains that mathematics is not just a question of new words, but it is also new ’styles of meaning and modes of argument ... and of combining existing elements into new combinations’. From here, systemic linguists investigated the grammatical forms of the scientific register (e.g. Halliday, 2006; Halliday & Martin, 1993; Martin & Veel, 1998; Veel, 1999) using Halliday’s (2004) systemic functional grammar. More recently, researchers working in the systemic functional tradition have expanded the focus on language to view mathematics as a multisemiotic discourse constructed through language, image (e.g. diagrams and graphs) and mathematical symbolism (e.g. Lemke, 2003; O'Halloran, 1999, 2005, 2009). Current trends indicate the systemic approach, located within the wider domain of multimodal analysis and multimodality (e.g. Bednarek & Martin, 2010; Jewitt, 2009), holds much promise for future research in mathematics education (Clarke, 2001; Schleppegrell, 2007).