Communication in mathematics classrooms includes teacher-pupil dialogue, the role of diagrams, pupil-pupil dialogue that is often missed in the classroom and the interaction between pupils and technology. Some forms of communication adopted in classrooms militate against some students being able to display mathematical skills in favour of other students. While some students have strong preferences for oral or written communication, others find written or diagrammatic communication more effective. Not all of these forms of communication are valued in the same way by teachers even though teachers may claim that they are. Pupils appear to cope differentially with apparent inconsistencies and hidden messages, when a teacher says one thing and means another.
In Chapter 7, Robyn Zevenbergen argues that pedagogical practices can be socially biased and may contribute to a learner's success or failure to participate in classroom dialogue. She looks particularly at the social context of mathematics and how this is implicated in social disadvantage. Her interest is in the 'linguistic habitus' of primary children, the ways they interact and talk in classrooms, and how this affects the way they are recognised or marginalised as learners.
She found the patterns of interactions in middle-class families are most similar to the discourse of primary classrooms. This means that pupils whose linguistic habitus matches that of the formal school setting will have greater access to knowledge through the pedagogic practices. For example, the statement 'Will you get out your mathematics books' can be interpreted as a question or an instruction. If pupils interpret an intended instruction as a question then they are immediately disadvantaged.
Zevenbergen describes the type of talk that goes on in classrooms as 'triadic' dialogue where the teacher remains in control and the interactions are highly ritualised. In this form of dialogue the teacher maintains control over the structure and content of the lesson and over the behaviour of the pupils. She argues that the 'triadic' dialogue precludes a community of practice where the pupils have control over their learning. This suggestion has an impact on the notion of a three-part lesson currently being recommended by government agencies in England - the first part often being entirely in the form of a triadic dialogue. This begs the question whether it is possible for teachers to create a community of practice when starting lessons with a triadic dialogue.
The use of diagrams can show pupils' ability to communicate in a variety of forms and use of a diagram can be helpful in solving problems. In Chapter 8, Candia