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The act of explaining can help students to develop new understandings of mathematical ideas, construct rules for solving problems, become aware of misunderstandings or a lack of understanding and develop their mathematical communication. Their explanations can also offer opportunities for a teacher to understand more fully what the students are thinking. Yet, previous research has focused mainly on tasks, questions and other teacher actions that prompt student explanations and on generalising what counts as an explanation. Using a conversation analytic approach, transcripts of mathematics lessons from different schools and different teachers were analysed, looking specifically at the interactions where students gave explanations. This paper describes two interactional contexts where students gave explanations without being explicitly asked for one by the teacher. The structures and content of the interactions in which these student explanations occur reveal further ways in which teachers can encourage students to offer explanations beyond asking how or why questions. We suggest that awareness of the underlying structures of interactions is likely to leave the teacher better equipped to exploit such situations as they arise in their classrooms.

Students explaining their mathematics is vital to the teaching and learning of mathematics, yet we know little about how to enable and support students to explain in whole class discussions beyond teachers asking particular questions. In this chapter we use a conversation analytic approach to explore the interactional structures that make student explanations relevant. Through a detailed examination of interactions where a student explanation occurs, three distinct structures are identified where a student explanation is perceived to be relevant Our focus in the analysis is the social actions students themselves do in their explanations to display their interpretation of the interaction as requiring an explanation and constraining the type of explanation. However, these structures also offer ways that teachers can use the structure of interaction to encourage students to offer explanations in their responses.

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