Abstract
Mathematics is a multimodal/multisemiotic discourse (O’Halloran 2005) where three
semiotic systems, at least, are used: verbal language, algebraic notations, and visual
forms. A general overview of the status of visual representations (diagrams, graphs,
shapes, etc.) in mathematical texts indicates that the role of these representations is
‘‘ignored’’ by the mathematical community which considers them to be limited in
representing knowledge (O’Halloran 2005) and of an ‘‘informal and personal
nature’’ (Misfeldt 2007). At best, mathematicians conceive these representations have
messages that students need to discover (Shuard and Rothery 1984). In this study
visual representations as resources available for meaning-making are considered.
Halliday (1985) develops a Systemic Functional Linguistics (SFL) framework
and argues that any text fulfils three meanings: ideational (represent the world),
interpersonal (create social relations), and textual (coherence). Morgan (2006)
develops a linguistic approach by adopting SFL for analysing written mathematical
texts. Furthermore, SFL has been extended to include non-verbal modes. Kress and
van Leeuwen (2006), for example, develop a grammar to ‘‘read’’ images.
Following these efforts this study intends to investigate what meanings visual
representations offer in mathematical texts. The plan is to develop a descriptive
framework to analyse students’ communication (1314 years old) during solving
geometrical problems and what meanings students construct when they use
diagrams/shapes. This framework is informed basically by Morgan’s linguistic
approach (2006), Kress and van Leeuwen multimodality approach (2006),
O’Halloran (2005) framework and the commognition approach (Sfard 2008). A
first draft of this approach has been developed that still needs more thinking and
developing.
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