The Genesis of Mathematical Language

Project leader

Dr. Marcus Schütte

Institution

Goethe University Frankfurt am Main

Duration

24 months, 01.07.2011 – 31.01.2013

Funding volume

12,200 € Focus Line Goethe University Frankfurt

Research question and state of research

Against the backdrop of the ongoing societal discussion about the educational opportunities of children with a migration background in the German school system, the planned project examines the relationship between language and learning in subject teaching. In this context, mathematics gains great importance, as alongside German it has the strongest selective function for the transition to secondary schools. According to the results of international comparative studies such as PISA 2003 and IGLU, there is a connection between the quality of "everyday language at home" and the linguistic and mathematical competencies of adolescents. Adolescents whose everyday language at home does not match the language of instruction achieve lower competency scores in all domains of the PISA tests. As a result, not only pupils with a migration background appear to be disadvantaged, but also those from less educationally oriented homes with a usually low socio-economic status (cf. on this also Bernstein 1996). Through a quasi-longitudinal comparison of the PISA study 2003 and IGLU (Bos et al. 2003), the following can be stated: a decisive approach to improving not only the educational opportunities of pupils with a migration background and those with a lower socio-economic status in German schools, but of all learners, appears to be improving their access to language and to the rules of interaction in the classroom (s. a. Heinze and Rudolph 2008). The planned research project thus aims at analysing the development of language use in mathematics teaching. It pursues the following questions:

1. Which subject-related linguistic competencies do children develop before and during their primary school years?

2. How does a subject-related linguistic competence develop in children before and during their primary school years?

Through the research findings of linguistics, a great deal is known about children's first-language acquisition (e.g. Tracy 2007, Rothweiler 1990), and a development can be traced here

from research on language acquisition in children with specific language development disorders (e.g. Rothweiler 2001 or Schulz 2007) to the increased investigation of second-language acquisition in children (see e.g. Schulz/Tracy/Wenzel 2008). In this context, in the field of educational science migration research, the approach of "academic language" by Gogolin (2006, p. 82) exists. According to Gogolin, in the German school system the normative demand is placed on all pupils to master, productively and receptively, the language varieties cultivated in lessons in order to be educationally successful.

In mathematics-education research, only isolated approaches can be found that deal with linguistic learning and teaching in mathematics lessons. In the German-speaking world, Maier (2004) has, above all, undertaken investigations in this area. A central focus of Maier's work is the meaningful use of technical language in mathematics teaching. Bauersfeld (1995), on the other hand, describes interaction in mathematics teaching as a language game in the manner of Wittgenstein. Understanding mathematical concepts or procedures is, accordingly, not only a matter of learning vocabulary or algorithms, but rather the gradual integration of new mathematical concepts into a complex network of concepts, action routines, conventions of speaking, etc. Consequently, learning mathematics, according to Bauersfeld, can only be appropriately analysed and understood if aspects of the interactional practice of mathematics teaching are taken into account. Pimm (1987) draws on Halliday's (1975) concept of register and understands mathematics as a social activity that is closely linked with verbal communication. He describes the teacher as a "native speaker" of mathematics. Pimm sees the task of pupils as acquiring a mathematical register linguistically and thus being able to act verbally in and with this register like a "native speaker" of mathematics. Zevenbergen (2001), on the other hand, in her studies on the possibility of mathematics learning by "working-class children" and "middle-class children" (ibid., pp. 40 f.), states "that the mathematics curriculum is acting as a social filter" (ibid. p. 40), since socially disadvantaged pupils master different forms of language than those required in the mathematics or school context. These very different approaches do not yield a unified picture of how a mathematical language develops, and some of them, such as Maier's or Bauersfeld's approaches, appear to be only weakly empirically grounded.

If one considers both lines of research, approaches from linguistics rarely focus on the specific features of the subject. This may not be surprising, since investigations into first- and second-language acquisition often focus on the respective periods of childhood development before school entry. Yet, alongside language acquisition – understood as the rather implicit learning in the everyday world outside school – language learning also takes place within school and gains particular importance for first-language learners from less educationally oriented homes and for second-language learners who receive few stimuli in the second language at home. In these linguistic learning processes in subject teaching at school, however, it is essential to view subject-related and linguistic learning as a reciprocal process. Mathematics-education research, by contrast, appears largely to leave unilluminated the circumstances in which children live and learn, as well as the resulting access to language. In mathematics education, efforts to improve teaching linguistically focus mainly on developing task formats or creating learning situations in which technical language can be practised. These efforts mainly go back to the above-mentioned approaches by Maier (2004), focus prominently on vocabulary learning of technical terms, and entirely disregard, for example, investigations of academic language or of second-language acquisition. In connection with the question of how primary mathematics teaching introduces all pupils to formal aspects of an academic school language, the applicant is particularly concerned with the question of how learners acquire abilities to use language purposefully in classroom interaction in order to learn mathematics through active participation. Pupils must therefore not only learn to master the language of teaching, but must also be able to bring this into the social interaction of teaching in an appropriate way. They thus need interactive or communicative competencies (cf. Pimm 1987). In this respect, a research gap can be identified that, before the development of task formats or learning situations, explores how the development of mathematical language proceeds, in order then, in subsequent steps, to design solutions in a targeted way to support this development.