Student and teacher interventions: a framework for analysing mathematical discourse in the classroom

Abstract

Mathematical discourse in the classroom has been conceptualised in several ways, from relatively general patterns such as initiation–response–evaluation (Cazden in classroom discourse: the language of teaching and learning, Heinemann, London, 1988; Mehan in learning lessons: social organization in the classroom. Cambridge, MA: Harvard University Press, 1979) to concepts for more fine-grained description such as the ‘Advancing Children’s Mathematics’ framework (Fraivillig et al. in J Res Math Educ 30(2):148, 1999). This article suggests a framework to be used for detailed studies of mathematical discourse on a turn-by-turn basis. This framework was used to study how single turns affect each other to form patterns in one teacher’s practice. The method used belongs to conversation analysis: studying single turns and characterise these according to their role in the conversation. Two main repeating patterns were identified: one between student explanations and the teacher’s focusing actions, and the other between the teacher’s progressing actions and students’ teacher-led responses. The findings also included other connections that demonstrate how various student interventions (explanations, teacher-led responses, unexplained answers, partial answers, and initiatives) are followed by different types of teacher actions. One implication is that, by developing concepts capable of describing qualities of a discourse on a turn-by-turn basis, it then becomes possible to analyse when mathematical talk fosters delivery of facts and when it fosters mathematical argumentation, debate, and critique.