Conceptualising and researching mathematics classrooms as sites of communication

Candia Morgan


In this chapter, I explore the notion of a slight shift of focus from studying communication or use of language in mathematics classrooms to conceptualising mathematics classroom practices themselves as forms of communication. This seems a very minor or pedantic difference, yet I contend that it offers some interesting directions for research that have potential to provide new insights. Fundamentally, rather than seeing language and other forms of communication as things that happen in the classroom, I want to think about classroom practices as essentially taking place discursively. Rather than seeing “Language in mathematics classrooms” as one research topic alongside others such as “Assessment in mathematics classrooms” or “Technolog)' in mathematics classrooms”, the theories and methodologies that we use and develop for studying communication in mathematics classrooms move to become tools for thinking about and studying a much wider range of topics.

The significance of language and other semiotic systems in doing mathematics is very widely recognised, whether seen as the way we access mathematical concepts (Duval,2006) or as the way they are constituted (Sfard,2008). Not only are the objects or concepts of mathematics encountered discursively but mathematics is overwhelmingly practised through the use of language and other semiotic systems. In Dowling’s terms, the practice of mathematics is discursively saturated, in that the principles of mathematical activity are made available discursively and the practice can thus be carried out relatively independent of any particular material context (Dowling, 1998). Linguistic, semiotic and discursive approaches to studying mathematics classrooms are thus indicated - as well as study of the language, other semiotic systems and discourse used in the teaching and learning of mathematics.

However, school mathematics practices involve more than just doing mathematics. Mathematical content is selected, ordered and transformed according to curricular and pedagogical principles (what mathematics is considered desirable to be learnt by children, how does it need to be presented in order for children to learn, what do children need to do in order to demonstrate that they have learnt). Such principles are manifested in policy documents, curriculum documents, assessment instruments, teacher education encounters, textbooks and so on. The process of construction of school mathematics is thus carried out through successive acts of communication, each of which reflects the interests of the participants.

These interests arise from the fact that classrooms are situated within societal and institutional contexts that shape the social relationships among the participants. These social relationships are also, to a large extent, realised through language and other means of communication. Institutional expectations about the roles to be played by teachers and by students shape and are shaped in classroom communication, governing who may speak, what kinds of things they may say, how they may speak and to whom. Understanding teaching in mathematics classrooms demands that we study these non-mathematical components and the relationships that these may have with the mathematics that students may learn (Morgan, 2014).

I will generally refer to ‘communication’ rather than ‘language’ because it is important to remember that mathematics teaching may make use of a wide range of communicational modes, including specialised mathematical notations, various forms of visual images, gesture and other bodily forms of communication, information and communication technologies, as well as spoken and written language.The implications of considering multiple modes of communication rather than focusing solely on verbal language are discussed more fully in Morgan, Planas and Schiitte (Chapter 1). In the next section of this chapter, I discuss some theoretical considerations and the theoretical resources that I draw on in order to research mathematics education from this perspective. I then consider how some fundamental questions about mathematics education might be reformulated and elaborated. Finally, I outline and illustrate some analytic approaches.

Theoretical resources

In thinking about communication and mathematics classrooms the first theoretical issue that needs to be addressed is how to conceptualise the relationship between ‘what is said’ and ‘what is spoken of’ - between the word and the world. Consistent with my wish to conceptualise teaching as communicating, I choose not to separate the word from the world. I do not deny that there is a material world and that this constrains our experiences, but our experience of materiality is also shaped by the ways in which we speak about the world. As Foucault put it, discourses are not just sets of words and other signs that represent the world in particular ways but are practices that “systematically form the objects of which they speak” (Foucault, 1972, p. 49)

While this notion of discourse is an important theoretical frame, I wish to focus attention on the detail of communication within discursive practices - the lexi- cogrammar, logical relationships and textual structure of language-in-use and the equivalent level of analysis of other communicational modes. My contention is that looking at the detail can provide insight into the concepts, values and possible posi- tionings, actions and relationships that constitute the discursive practice. As Halliday and Matthiessen (1999) argue, the language provides the semantic resources through which we experience the world. To illustrate this point, consider the ways in which mathematics educators may speak and think about classrooms in which the participants speak more than one ‘national’ language.

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