Studies show that students with the language of instruction as their first language often perform better in mathematics than students with a different first language (Kasper et al., 2020; OECD, 2016). Compared to other countries, Germany shows the highest difference between these two groups’ mathematics achievement (Meyer, Prediger, César, & Norén, 2021). However, everyday language skills in the language of instruction do not suffice for academic success (Cummins, 2001).

Language has different functions in mathematics classrooms. On the one hand, classroom interaction as well as learning assessment take place through language (Durkin & Shire, 1991). On the other hand, language is a vehicle for developing mathematical knowledge (Prediger, 2017). Therefore, language can become an obstacle for students regarding understanding and solving tasks, as well as developing procedural and conceptual knowledge. The mentioned obstacles are relevant for students’ mathematics achievement, which makes it necessary to investigate linguistic difficulties during mathematical learning processes (Prediger, Wilhelm, Büchter, Gürsoy, & Benholz, 2015).

Pöhler and Prediger (2015) distinguish lexical means, which are important for establishing a conceptual understanding: Technical terms and phrases can be located on the wordlevel, while “meaning-related vocabulary” (Pöhler & Prediger, 2015, p. 1701) contains all lexical means necessary to explain the meaning of technical terms and therefore also includes grammatical elements. Thus, the meaning-related vocabulary goes beyond the word level and can be considered on the sentencelevel.

On the discourse level, students must be able to follow and participate in discursive practices. Explaining and arguing are the most common and the most important discursive genres for the construction of conceptual understanding of mathematics (Erath, 2021). Despite these high requirements on different language levels, language support in mathematics classrooms predominantly addresses the word level. This indicates that linguistic competences on the sentence and discourse level in the language of instruction are implicitly expected. At the same time, linguistic skills on all levels are distributed unequally among students, so these expectations often disadvantage students from low socioeconomic backgrounds and those with other first languages (Prediger, 2017). However, it is important to mention that the cited studies refer to secondary mathematics education and so far, the question of whether these findings also apply to elementary mathematics education remains unanswered.

In addition, learners' first languages play an important role in promoting their conceptual understanding (Ellerton & Clarkson, 1996). Even though it is particularly difficult in classrooms comprised of speakers of several different languages, as it is the case in Germany, Meyer et al. (2021) suggest various measures to foster first languages in mathematics teaching. Other studies criticize the lack of acceptance of multilingualism in the classroom (Baur & Küchler-Hendricks, 2021). Overall, an insufficient support in the language of instruction and a lacking integration of other languages could create a difference between speakers of the language of instruction and speakers of other languages. This difference would reproduce the social power relationship between speakers of the majority language and speakers of minority languages (Cummins, 2001).

The presented project therefore investigates the main research question:

How do teachers interact with linguistically diverse learners in elementary school mathematics and how is difference produced in the process?

This research question can be broken down into smaller research questions as follows:

1. How do teachers in elementary school mathematics use technical terms and how do students adapt it?
2. At which levels do language obstacles occur in elementary school mathematics classrooms and what practices of dealing with these barriers are evident?
3. How are learners’ first languages included in elementary school mathematics instruction?
4. How are language hierarchies visible in elementary school mathematics classrooms?

This study employs participant observation as a method of ethnography, which is often used to analyze social power relations. Ethnography allows for repeated observations of similar situations, making implicit things more apparent, which often plays an important role in creating differences and commonality (Fritzsche & Tervooren, 2012). Data is collected in three different schools and in one classroom at each school. First, a private school was selected, where students mostly come from socioeconomically privileged families and where two different languages of instruction, namely German and English, are used. Since it is an international school, students come from a variety of countries and show varying language abilities in both English, and German. In contrast, the second school is located in a socioeconomically disadvantaged neighborhood, where the percentage of population with immigrant background is high and there are many different first languages. The student profile of the third school is socioeconomically average in comparison to the other two schools and it is attended by fewer students with a first language other than the language of instruction. Participant observation will be conducted in two phases in each of the three schools. In total approximately eight weeks of observation of mathematics instruction will take place at each school: The first phase lasts approximately five weeks, and the second phase approximately three weeks. Between the two phases, an initial evaluation will be conducted in order to take the results into account in the second phase of observation. The observational protocols will be analyzed with open coding and further analysis steps of Grounded Theory. The objective of this analysis is to develop a category system that can be used to answer the research questions. Furthermore, it is planned to use data from the INTERFACH video study, for which 60-minute mathematics lessons from 25 different teachers are videotaped. The video study also includes a class from at least one of the schools, where I conducted preliminary classroom observations. This final step is to examine whether the results can be replicated in other classes and schools, using the developed category system.

Since the study is still in the phase of data collection, the following descriptions are preliminary results of a first analysis. In the lessons observed so far, situations repeatedly arose in which linguistic obstacles caused mathematical difficulties for certain students. How the teachers dealt with these barriers varied: Teachers often made explanations in the language of instruction, which were supported by gestures, illustrations, and representations. In some cases, other students were asked, or devices were used to translate tasks into other languages. It remains to be determined, which of these responses can be described as practices of dealing with linguistic obstacles. Furthermore, teachers repeatedly discussed technical language usage on the word level. However, no statement can be made, yet, about language support on the sentence or on the discourse level. First language usage and its integration into mathematics lessons differed between the classrooms. In the private school, the students themselves used other languages in extracurricular conversations. However, in the school attended by learners with intermediate socioeconomic status, a first language was actively included by the teacher in mathematical conversations. This language is shared by several students who started learning the language of instruction only very recently. In both schools, however, it can be assumed that many other first languages are not used at all. In the third school, only very few observations have taken place so far. Therefore, no conclusions can be made about the practices yet. The first phase of observation will be completed in all schools by the end of March and the first evaluation of the collected data is planned for April. Depending on the clarity of its results, I plan to focus on one or two of the research questions presented above, in the presentation at the Emerging Researchers’ Conference.

Baur, C., & Küchler-Hendricks, A. (2021). "Außer Deutsch darf keine Sprache in diesem Unterricht gesprochen werden" - Sprache und Heterogenität im deutschen Schulsystem. Kölner Online Journal Für Lehrer*innenbildung, 3(1), 70–82. Cummins, J. (2001). Language, power and pedagogy: Bilingual children in the crossfire (Reprinted.). Bilingual Education & Bilingualism: Vol. 23. Clevedon, Buffalo: Multilingual Matters LTD. https://doi.org/10.21832/9781853596773 Durkin, K., & Shire, B. (1991). Language in mathematical education: Research and practice. Open University Press. Ellerton, N. F., & Clarkson, P. C. (1996). Language Factors in Mathematics Teaching and Learning. In International Handbook of Mathematics Education (pp. 987–1033). Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1465-0_27 Erath, K. (2021). Enhancing students' language in collective processes of knowldege construction in group work: the case of enlarging figures. ZDM - Mathematics Education, 53, 317–335. Fritzsche, B., & Tervooren, A. (2012). Doing difference while doing ethnography? Zur Methodologie ethnographischer Untersuchungen von Differenzkategorien. In B. Friebertshäuser, H. Kelle, H. Boller, S. Bollig, C. Huf, A. Langer, . . . S. Richter (Eds.), Feld und Theorie: Herausforderungen erziehungswissenschaftlicher Ethnographie (pp. 25–40). Berlin/Toronto: Budrich Verlag. Kasper, D., Köller, O., Selter, C., Wendt, H., Schwippert, K., McElvany, N., & Steffensky, M. (2020). TIMSS 2019. Mathematische und naturwissenschaftliche Kompetenzen von Grundschulkindern in Deutschland im internationalen Vergleich. Waxmann Verlag. Retrieved from https://directory.doabooks.org/handle/20.500.12854/60948 https://doi.org/60948 Meyer, M., Prediger, S., César, M., & Norén, E. (2021). Making use of multiple (non-shared) first languages: state of and need for research and development in the European language context. In R. Barwell, P. Clarkson, A. Halai, M. Kazima, J. Moschkovich, N. Planas, . . . M. V. Ubillús (Eds.), Mathematics Education and Language Diversity: The 21st ICMI Study (pp. 47–66). Springer. OECD (2016). Pisa 2015 Results (Volume I): Excellence and Equity in Education. PISA. Paris: OECD Publishing. https://doi.org/10.1787/9789264266490-en Pöhler, B., & Prediger, S. (2015). Intertwining Lexical and Conceptual Learning Trajectories - A Design Research Study on Dual Macro-Scaffolding towards Percentages. EURASIA Journal of Mathematics, Science and Technology Education, 11(6), 1697–1722. https://doi.org/10.12973/eurasia.2015.1497a Prediger, S. (2017). "Kapital multipliziert durch Faktor halt, kann ich nicht besser erklären" - Sprachschatzarbeit für einen verstehensorientierten Mathematikunterricht. In B. Lütke, I. Petersen, & T. Tajmel (Eds.), DaZ-Forschung. Deutsch als Zweitsprache, Mehrsprachigkeit und Migration: Vol. 8. Fachintegrierte Sprachbildung: Forschung, Theoriebildung und Konzepte für die Unterrichtspraxis (pp. 229–252). Berlin/Boston: De Gruyter. Prediger, S., Wilhelm, N., Büchter, A., Gürsoy, E., & Benholz, C. (2015). Sprachkompetenz und Mathematikleistung - Empirische Untersuchung sprachlich bedingter Hürden in den Zentralen Prüfungen 10. Journal Für Mathematik-Didaktik, 36(1), 77–104.