The study investigates linguistic and mathematical features of oral and written explanations in addressee-based variations of language use. The experimental approach aims at the intra-individual linguistic flexibility in the academic mathematics register of future primary-school teachers. Register is here defined as those aspects of intra-individual variation of language that are influenced by situational and functional settings(Biber & Conrad 2009), and a broad understanding of situation and function is adopted. One theoretical tradition used in mathematics education research, where register phenomena have received much attention, is systemic functional linguistics(e.g. Halliday 1973, Halliday & Hasan 1989, Morgan 2006).

Situationally appropriate language choices instantiate the linguistic flexibility of speakers, a pivotal aspect of the human communicative capacity. Its development begins with the earliest phases of language acquisition and continues during adolescence and adulthood. The development of mathematics register fosters not only technical lexis, syntactic diversification but also metalinguistic awareness needed for the comprehension and production of abstract concepts (Gellert & Hümmer 2008, Prediger 2013). During the school years, the acquisition of conceptually written communicative forms of argumentation improves the general compliance of the students with the requirements of specific academic discourse (Straehler-Pohl et al. 2014). Acquisition processes of academic register, particularly in the context of teacher education, support the association of language forms with functional settings. Research on the late phases of register development is thus intrinsically concerned with the acquisition of functionally motivated linguistic variation and with the factors conditioning the availability and appropriate use of formal registers in specific scientific or vocational discourses (Lütke et al. 2017).

The aim of the study is to understand in which way performable signs (oral and written language, mathematical symbols, illustrations) are recognized and regrouped as belonging to distinct, differentially valorized semiotic registers by a group of future teachers of mathematics for primary school. The research questions are:

RQ 1: Which variation of performable signs is used by future primary-school teachers for explanations of school-mathematical facts?

RQ 2: How do the registers used by the future primary-school teachers vary according to different addressees?

Although the research is realized in one national context (Germany), the research questions on register variation as well as the expected results are highly relevant beyond national borders and across languages. Register variation is an important topic in the context of recent migration in Europe. 

Systemic functional linguistics allows to model register methodologically as a particular setting of systemic probabilities. The experimental design of the study models the effects of situational features (Halliday & Hasan 1989, Biber & Douglas 2009) as predictors of register variation in the field of mathematics: mode of communication (oral and written). The mathematical topic is mathematical argumentation (Duval 1991, Harel & Sowder 2007, Reid & Knipping 2010) and the future teachers explain a mathematical fact to three different types of audience: a lecturer of an elementary mathematics course for future teachers; a fellow teacher-education student; a 10 to 12-year-old student. As intra-speaker variation is targeted, the study includes variables related to the tenor of discourse such as the 'social relation of interlocutors' which models the social status of the speaker as equal, higher, lower than the status of the addressee - a fellow-teacher student, a school student, or a lecturer. Adopting an experimental approach, an elicitation task is applied to trigger explanations of mathematical facts such as: >> Please explain why the sum of two odd numbers is always even but their product is always uneven. << Input-related performance is assessed by collecting oral and written explanations produced by fourth-year students (N = 40) in the primary-school teacher education programme. The written explanations provide one part of the data corpus. The oral explanations, together with their accompanying drawings and writings, are videotaped and transformed into transcripts that are sensitive to the multimodal character of the oral explanations. Explorative analyses aim at discerning linguistic and other semiotic features for the register of mathematics (O'Halloran 2003) and at locating them with respect to the 'oral-written' or 'formal-informal' dimensions suggested in the literature. Primarily, the focus is on linguistic features attributed to academic discourses (Biber & Douglas 2009, Gellert 2011) such as termini and formulas, passives and nominalisation, connectives and grammatical metaphors, by taking the effects of the academic input and the situational factors into account. Prospectively, the experimental series are to be developed into a longitudinal investigation monitoring further phases and factors in the acquisition of the scientific registers in the beginning and at the end of the teacher-education studies.

The results allow inferences about the mathematical register at the group level (inter-subject variation) and also about the intra-subject variation in the specified contexts. The investigation on the future teachers' mathematics registers will help to differentiate the contributions of professional education and individual traits to developing the teacher students' abilities for audience design, a highly relevant professional skill of primary-school teachers.

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