Vol.:(0123456789) 1 3 ZDM (2018) 50:1013–1027 https://doi.org/10.1007/s11858-018-0952-2 ORIGINAL ARTICLE Using a transdisciplinary framework to examine mathematics classroom talk taking place in and through a second language Sally‑Ann Robertson 1  · Mellony Graven 1 Accepted: 31 May 2018 / Published online: 8 June 2018 © FIZ Karlsruhe 2018 Abstract This paper proposes a transdisciplinary framework to allow for a multifocal exploration of classroom talk practices. It draws on data from a broader study of talk in South African Grade 4 mathematics classrooms where the language of teaching and learning (English) was the home language for neither the teachers nor their students. Lesson transcript data from one teacher’s lessons on fractions are used to demonstrate how working with three strands of conceptual insight from the disciplines of psychology, sociology and linguistics conduces to a potentially richer understanding of a teacher’s use of classroom talk in mediating her students’ mathematical understanding. By drawing on elements of Vygotsky’s sociocultural psychology, we make visible in the lesson data the ways in which this teacher used the ‘everyday’ in trying to navigate her students’ towards more ‘scientifc’ conceptualizations of unit fractions. By then taking up aspects of Bernstein’s sociological work, we articulate, and make visible, how societal circumstances impinge on students’ access to exploratory mathematical discourse needed for epistemological access to abstract and generalized mathematical concepts. Finally, through Halliday’s work on the power of particular linguistic registers for meaning-making, we highlight challenges in learning mathematics in and through a second language and reveal the constraints placed on students’ opportunity to maximally exploit the distinct forms of meaning contained within the mathematics register. Keywords Transdisciplinarity · Mathematics classroom talk · Spontaneous and scientifc concepts · Recognition and realization rules · Mathematics register 1 Introduction We argue in this paper for the use of a transdisciplinary framework to scrutinize aspects of mathematics classroom talk. Our purpose is to illustrate how, by examining such talk through a multifocal conceptual lens, transdisciplinar- ity allowed us to build up a more holistic image than might otherwise have been possible. Although this is a conceptu- ally- rather than empirically-driven paper, we import data from a broader study of mathematics classroom talk into our discussion as empirical exemplifcation of the ideas we have taken from the disciplines of psychology, sociology, and lin- guistics, represented—respectively—by Vygotsky, Bernstein and Halliday. It is the work of these three luminaries that constitutes our sources of conceptual and theoretical insight. Given the common threads running through Vygotsky’s, Bernstein’s and Halliday’s work, namely emphasis on the centrality of language in mediating learning and on the infuence of sociocultural, sociopolitical, and sociohistori- cal factors on learning outcomes, their work coheres well. We see their work as having particular cogency for analyses of post-colonial educational circumstances, where a majority of learners are learning in a colonial language not spoken at home. The following question guides our discussion: ‘In what ways might a transdisciplinary approach potentially enrich insights into challenges facing a primary school math- ematics teacher in getting her students to engage in class- room talk on fractions in and through a language (English) in which they are not yet fuent?’. Before sharing aspects of our ‘dialogue across disci- plines’ (after Martin 2011) in exploring how one Grade 4 mathematics teacher used classroom talk to mediate (or not) her students’ understanding of fractions, we engage in a generic consideration of transdisciplinarity. * Sally-Ann Robertson s.a.robertson@ru.ac.za 1 Rhodes University, Grahamstown, South Africa