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New migrants, new challenges? – Activating multilingual resources for understanding mathematics: institutional and interactional factors

New migrants, new challenges? – Activating multilingual resources for understanding mathematics:... 1IntroductionThe integration of migrants into European societies is among the most profound societal challenges of today although migration is not a challenge that only occurred recently. For at least 60 years now, and even though this fact has often been denied, western European countries can be viewed as countries of immigration, their societies as societies of immigration with varying shapes. Germany, too, faced various phases of migration. These include the invited immigration of so-called “guest workers”In Germany migrant workers were called “Gastarbeiter”, which translates verbatim into “guest workers”. This denomination implies the expectation the workers will only stay temporarily without settling and bringing their families and will be going back to their origin country after the work was done. from Italy, Spain, Greece, former Yugoslavia and Turkey from 1955 until 1973; the refugees from the Yugoslavian civil war in the 1990 s and refugees from various conflicts in the Middle Eastern and African countries followed in recent years.This list is by no means complete and has no intent to marginalize the refugees and other migrants from Asia, Eastern Europe, or elsewhere. Despite this German history of immigration, integration has not always or mainly been subject of societal and political discussions, especially not with respect to the integration of migrant students in the educational system. This has significantly changed in the last decade (cf. Hoßmann and Karsch 2011).In Germany, successful integration into an educational system is predominantly discussed as being based on learning German – alongside with extensive and expensive programs for integrating German-Russian ‘Spätaussiedler’ at the turn of the century. However, it should never be underestimated that migrants bring an extensive linguistic knowledge with them – which is not necessarily limited to a single language. For example, a Syrian refugee from northern Syria might actually be raised with Arabic, Kurdish and French plus potential school languages such as English. Moreover, “Arabic” has to be differentiated into its numerous regional varieties and dialects (in our exemplarily case here into Syrian Arabic and Modern Standard Arabic), as these differ greatly from each other (cf. Versteegh 1997: 189–208). Given the linguistic capabilities and affordances of migrants, limiting the discourse on linguistic integration to the acquisition of the target language would mean to marginalize the communicative and epistemic resources of migrants and thus to reduce their chance of participation in school.Efforts to foster bilingual education or education in the heritage languages started in Germany in the mid-1980’s (cf. BAGIV 1985) and have been revived recently (Benholz et al. 2010). Instead, we join the position that providing possibilities for using all available linguistic resources, in language learning as well as subject learning, leads to a more successful and accelerated integration into an educational systemWe would further argue that opening monolingual structured educational systems for other languages besides the target language could also have ripple effects on other domains of society (cf. Rehbein 2013).. To put it simply: ‘use multilingualism as resource’ is an educational principle that is key to integration as it incorporates individual language-related capabilities into the societal educational system, as the research on Translanguaging also suggests (e. g. García 2009).But even though most migrants are either already multilinguals or have to become multilinguals at least to some degree, not all multilinguals can be treated the same way when participating in a multilingual learning environment. Different backgrounds call for different means to fully unfold the respective potential. This can be seen when looking at specific groups of multilingual students. In this paper, we will focus on new migrants from Arabic speaking countries, as an example of one of the largest groups of migrants that has recently sought to take part in the educational system. This group will be compared here with the most present one in the German educational system, namely the third generation of migrant workers from Turkey, who are classified as native resident multilingual students by virtue of the fact that they are born in Germany and raised with both German and Turkish to various degrees, though faced with the domain of classroom discourse being shaped by German only (in the following abbreviated as: Multilingual Germans).We will narrow down the group of interest by focusing on the group of adolescents of twelve to fourteen years, an age group that rarely is put into focus of educational research (SVR research report 2018). Even more so, adolescent migrants are mostly overlooked, even though they face very distinct and complex linguistic challenges when arriving in the target country of their migrationWe are aware of the very heterogenous and often difficult experiences during the process of migration that constitute complex challenges of their own. However, here we will mostly focus on the linguistic aspects of these challenges.. Most importantly, adolescent migrants have often already been schooled in a language other than the language(s) of the target country and thus have language-specific subject knowledge at their disposal.So far the benefits of multilingual education in maths, even when introduced at a late stage of the student’s school careers, have been shown for Multilingual Germans (i. e. Prediger and Redder 2020; Schüler-Meyer et al. 2019; Redder et al. 2018; Wagner et al. 2018). With these students, incorporating their entire linguistic and cognitive repertoire does not serve as an integration tool but rather as a means to foster subject-related understanding and thus to improve their performance in school. Of course, compared to newly arrived adolescent migrants, these students face different challenges in the mathematics classroom (Prediger et al. 2018). Hence, the question is, how the insights from a multilingual education of Multilingual Germans can be transferred to the case of adolescent refugees, and, referring to the title of this paper, in which way this group of new migrants provides the teachers with new and unique challenges.In this paper, we will introduce the concept of ‘multilingual profiles’ both as a broad theoretical input and a more refined outcome of discourse analyses. The concept comprises the ‘linguistic repertoires’ (Gumperz 1972) and additionally integrates a set of further aspects of linguistic knowledge from an action theoretical point of view (see below). A multilingual profile thus serves as a methodological instrument that makes the differences between groups of multilingual students more tangible and enables didactics as well as linguistic analyses to fully take them into account (as shown for the didactical analysis in Prediger et al. 2019b). The aim of ‘multilingual profiles’ is to focus the students’ individual language proficiency in terms of not only linguistic means that manifest as linguistic signs but the full range of qualifications for linguistic action including language-specific mental processes (cf. Rehbein 1977; Ehlich 2013). All these linguistic qualifications serve as the students’ prerequisites for any participative action in classroom discourse. This can subsequently provide teachers with more specific information on how to approach multilingual teaching and learning. This will be achieved by focusing on linguistic knowledge as a subjective dimension of the concept of the ‘constellation’ (Rehbein 1977; Bührig 2005) which is central for linguistic action in general and for multilingual action in particular. Constellations are shaped by specific needs that call for the individual’s linguistic action to fulfill them and pursue respective purposes (cf. Bührig 2005: 148). Hence linguistic action is treated to systematically mediate conditions of the non-linguistic reality for both interactants, speaker and hearer, with their (productive and receptive) linguistic knowledge acquired by socialization processes and their common discursive management up to a certain result determined by their purposes.In consequence, linguistic repertoire and sociolinguistic domain are linked together on a meso-level of analysis.In the following, we will offer some insights into the conceptual ideas behind our notion of multilingual profiles and the categories we included therein, as based within the framework of Functional PragmaticsAlso known as “functional-pragmatic discourse analysis” (cf. Bührig 2005: 144).. After a subsequent elaboration of functional-pragmatic methodology and the data we are working with, we will conduct three analyses in which we will show the benefit of incorporating multilingual profiles in a linguistic analysis of authentic data from mathematicsMathematics is chosen as a subject that often is seen as the subject that requires the lowest language proficiency, because it mostly is said to rely on mathematical symbols – an assumption that could not be further apart from the reality (cf. Prediger et al. 2018). classroom interaction with multilingual students. We will conclude the chapter with a discussion of our findings in these analyses with a distinct prospect on the implications for teaching and learning with multilingual students.2Conceptual background and approachHouse and Rehbein (2004) identify the concept of ‘multilingual communication’ to be the nucleus for treating individual as well as societal multilingualism. In a theoretical reflection of empirical findings, Franceschini (2011) makes the case for ‘discursive multilingualism’ to be taken into account for innovative research. And most recently, Li Wei (2017) calls for an ‘action theory’ to cope with multilingualism. In accordance to these positions, we will approach our data from a functional-pragmatic perspective, using its well-developed action-theoretical and psycholinguistic shape as opposed to, for instance, systemic functional linguistics (i. e. Halliday 1978) which seems to be the closest alternative approach.cf. Redder (2008), as well as Gruber (2012), for a critical comparison of Functional Pragmatics and Systemic Functional Linguistics that highlights the differences between the approaches. Gruber points out that Functional Pragmatics is more focused on the action character of communication while SFL is more focused on the semiotization of it. In doing so, we pursue our research on fostering subject-matter understanding by means of multilingual classroom discourse, which already led to the reconstruction of supportive and non-supportive linguistic strategies on part of teachers and on part of students (Redder et al. 2018).2.1Multilingual profiles in theoryTo specify the respective linguistic knowledge of students as being actors in classroom discourse and hence to specify linguistic knowledge as a distinguishable and outstanding dimension of the interactive constellation, we introduce the concept of ‘multilingual profiles’. As has been pointed out above, simply speaking of multilingual students and thus assuming a homogeneity of a vastly heterogeneous group of students would be naive and could lead to problems in the educational process. The mere consciousness and naming of more than the official language in classroom discourse can initiate the process of overcoming a monolingual habitus. For going beyond this step, teachers should identify their students’ multilingual resources in the first place. For this purpose, García et al. (2017) have developed the “Bilingual Student Identification and Profile” (García et al. 2017: 31) to support teachers to “systematically collect information about who their students are, the languages they speak, their cultural practices, their experiences, and the world that they know” (García et al. 2017: 31). The institutional aim of their idea is to go beyond the three categorizations of children in the U. S. that differentiate “English Language Learners, former English Language Learners and fully English proficient” (García et al. 2017: 31) and instead put the students’ individual linguistic resources into focus and to use these resources for teaching and learning. Thus, a checklist for teachers as well as a form for bilingual student profiles was developed, comprising five aspects: Bilingual use at home, bilingual friends, bilingual exposure in the life of student, education in the LOTE (= Language other than English) and literacy in LOTE (García et al. 2017: 170). The results of the checklist are then to be included in the more concrete bilingual student profiles that consist of six aspects: LOTE spoken or heard consistently at home, countries where the student has lived since birth, countries where the student has gone to school since birth, nativity and residence, education in English, education in LOTE (cf. García et al. 2017: 171).Despite this approach being helpful to create an awareness of the individual linguistic resources of the students and thus to get an idea which of these resources might be helpful in everyday teaching and learning, we suggest that the approach would benefit from further development. These suggestions come as a spring-off from detailed discourse analyses in several constellations of free choice for multilingualism in classroom discourse. As we found out, it is not self-evident to foster subject understanding by any kind of opening the floor for multilingual action or any teacher’s strategy to cope with such interaction formats (cf. Redder et al. 2018). Multilingual discourse has to be evolved far beyond any turn-taking mechanism or surface structure of utterances. However, it still remains to be analyzed how multilingual knowledge processing works on a micro-level and how it can be fostered before this can be applied for educational purposes.Thus, a linguistic analysis (especially an interaction-centered analysis) requires as much meta-data about the students as possible, i. e. their individual multilingualism, their language proficiency and their situational language use in education. Here, we intend to develop the concept of multilingual profiles further beyond the meta-data and make it usable for linguistic analyses.Multilingual profiles are understood as the focalization of those factors of an individuals’ linguistic capability which affect his or her participation in educational discourses. Individual knowledge and capabilities, the mechanisms of perception, evaluation and belief as well as motivation constitute, as Rehbein (1977) spelled out in his theory of action, are the main factors of the mental or “subjective” dimension of a constellation as being distinct from the objective ones (namely: field of action, interactive space, field of control and system of purposes, see Rehbein 2007: 441). Hence an action-centered discourse analysis should take them into account.The idea guiding this approach is not to conduct an individualistic sociological research of every students’ biography, but to identify factors for characterizing groups of students by means of interfaces and similarities in their biography which appear to have impact on the implementation of multilingual teaching and learning formats. This also implies the possibility to modify and extend the multilingual profiles recursively with and after discourse analyses. The aim of multilingual profiles is not so much to provide a basis for multilingual subject-matter teaching but to identify the general possibility for multilingual teaching through an identification of the students’ linguistic resources; hence multilingual profiles go a step further than the concept of García et al. 2017 and differentiate between the language of instruction and subject-related language(s). Thus, our concept goes beyond a mere identification of languages spoken but take, in the long run, language-bound mental processes of knowledge formation as well as the illocutionary dimension of knowledge processing into account. With respect to those mental processes, multilingual profiles exceed explicit or implicit relations to the semiotic-based concept of multilingual repertoires (i. e. Creese and Blackledge 2010). Through this, the concept of multilingual profiles sets to enable a more differentiated view towards the falsely assumed homogeneity of multilingual students. This is necessary to enable for example the differentiation of Multilingual Germans who are raised as multilinguals but are not treated as multilinguals in the educational system and of newly migrated students who turn into emergent multilinguals in Germany as they have been formerly schooled in other languages than German.2.2Shaping multilingual profilesFollowing these general remarks on the concept of multilingual profiles, we now turn to a more concrete reflection of it. The different profiles derive from previous research on Multilingual Germans (cf. Redder al. 2018; Wagner et al. 2018; Prediger et al. 2019a) and the attempt to transfer the respective results to the case of new adolescent migrants in Germany, as will be elaborated in more detail in the methods section of this chapter.The notion behind multilingual profiles is hermeneutic in nature. The core aspects of the profiles were identified through empirically based, functional-pragmatic discourse analyses and serve as a foundation for tailor-made multilingual teaching models as well as further research that might lead to more precise differentiations not considered as of now.Multilingual profiles can be understood as a methodological tool to approach the heterogenous group of multilingual students and shed light on their respective needs in classrooms. Thus, multilingual profiles explicitly seek not to marginalize individual or group-specific differences but to emphasize and operationalize them in a way that allows for taking them into account when developing multilingual teaching models.At the core of multilingual profiles are the languages as a linguistic knowledge of individual actants on how to interact verbally as a common member of a language society.Our action-theoretical categorization of the given capacity is appropriate to overcome any additional type of pragmatics when coping with the simple distinction of language system (langue) and language use (parole). Here we focus on a certain group of verbal actants and the characteristics of its or their linguistic action in the various constellations of everyday life. Different constellations require different usages of languages. Primarily, this concerns linguistic action forms rather than lexical-semantic or grammatic structures. This follows pragmatic and sociolinguistic positions and findings that a conceptualization of language as an ensemble of lexicon and grammar that is regulated by conventions does not fit to linguistic reality.For the purpose of this paper, the reconstruction and operationalization of the multilingual profiles of Arabic speaking adolescent migrants and Multilingual Germans helps to identify them as two distinguishable groups of linguistic actants that require different teaching methods; especially we focus on the following (intertwining and correlating) aspects: (1) the type of acquisition of the German language, (2) the students’ constellation-specific language proficiencyLanguage proficiency, in the sense of this paper, is mainly determined by an individual’s capacity for linguistic action (see Bührig 2005: 147, on the relation of Functional Pragmatics and the speech act theory of Austin 1962). Rehbein and Karakoç 2004, specify the complexity of this notion of language proficiency for multilinguals. and (3) the way subject-specific knowledge is acquired.The type of acquisition of German (as a second language)It is a well-known difference if a language is acquired as a second language or as a foreign language, or if two languages are acquired simultaneously or successively (e. g., Meisel 2019). For many Multilingual Germans, it is often not decidable which language is L1 and which L2. In contrast, new adolescent migrants have to go through an accelerated acquisition of German as a second language. In school, already the mere observation of a students’ type of acquisition of German could lead teachers to activate their knowledge about second language acquisition processes, if available, and opt for certain discourse strategies – not only in language classrooms but also in subject-matter classrooms. In particular, the type of acquisition has an effect on the differences between the new migrants’ and Multilingual Germans’ constellation-specific language proficiency.Constellation-specific language proficiencyAs mentioned above, different constellations require different forms of linguistic acting. In multilingual societies with predominant monolingual school systems such as Germany, this often means that only one language within the multilinguals’ repertoire is activated and academically developed to a certain level – in this case German.This of course does not count for every single multilingual student in Germany, but for the major part it does. There are schools that teach family languages, but only very few. For example, in Hamburg, only 8 out of 411 schools offer Turkish language classes (see https://bildungsserver.hamburg.de/tuerkisch/unterricht/schulen/; retrieved 1/25/21) Thus, Multilingual Germans usually use the German language in schools whereas their family language remains undeveloped on the academic or pre-academic level (cf. Redder et al. in press; Gilham and Fürstenau 2020). Sometimes, writing and reading in the family language is not acquired at all. The wide and recently growing range of family languages in Germany do have their domain mostly in the family and in non-institutional constellations (cf. Rehbein and Grießhaber 1996: 76 f. for the German situation).Compared to Multilingual Germans, new adolescent migrants have of course developed their family language to a high degree, but participating in a German-only classroom discourse is a big challenge, as German is still in the process of acquisition. Subject-matter learning is restricted by these limitations.Linguistic quality of subject-specific knowledgeAs the Multilingual Germans’ family languages are usually not systematically used for learning in school, especially not in subject-matter classrooms (beyond any CLIL-enterprise), subject-specific knowledge is usually bound in the language of schooling, namely German, only. But the family language usually allows a rather tangible or, as based on everyday-knowledge, practically concrete approach to subject-related issues by means of everyday language.Here again, with new adolescent migrants these relations present themselves to be very different. Due to previous schooling in their home country, their knowledge acquired so far is bound in the family language for the most part, whereas the level of proficiency in German enables to a rather pragmatic, concrete approach to subject matter.A reflection of these issues regarding a certain group of multilingual students bears a risk of leading to a grossly simplified and undifferentiated treatment for the individual. However, the identified factors can provide the basis for an assessment of the abilities to perform and linguistically act in school as well as the development of fitting teaching models.Another major issue that impacts the multilingual profiles is the students’ experiences with different educational cultures. Students with individual experience of migration might have been schooled in more than one country in course of seeking refuge, for instance in Iraq, Turkey, Greece or Italy before reaching Germany. But there is few research on the differences of educational cultures; especially no comparative research of the German and the (Syrian-)Arabic educational culture exists. We know from comparative, German-Italian analyses on academic discourse at universities (Thielman, Redder and Heller 2015) that teaching and learning in Germany does significantly involve a lot of verbal interaction amongst students, of talking about the epistemic status of knowledge at hand, as well as of the ability to explain and to exchange arguments. Hence educational cultures imply certain expectations with respect to linguistic action formats for knowledge processing in classroom discourse.When looking at the group of new migrants, two possible additional aspects have to be addressed that differ from the needs from Multilingual Germans:–First-hand experience of migration. Individual migration experience can induce psychological stress or even traumatization which strongly determine the individuals’ ability for linguistic action in classroom discourse as it influences the individual action space and hence the selection of possible and adequate actions.–Continuous education from at least age six. Whereas in Germany, every child is obliged to attend a school from the age of six for at least ten years, other countries have limited compulsory education or lack its monitoring. Additionally, the journey of refugees even lacks school attendance or a structured curriculum, notwithstanding the quality of schooling. In terms of language proficiency, this aspect helps to outline the pragmatic capacities of the students including their accordance to institutional determinations. Also their educational level might deviate significantly from same-age classmates in the target country.These two aspects of multilingual profiles will not be object of our analysis in this paper, but still have to be mentioned as teachers have to be aware that possibly traumatized students as well as students that never attended school could participate in their classrooms. To deal with this is not object of linguistics, but it highlights the need to identify possible challenges of new groups of students across disciplinary boarders.To sum up our discussion so far, the multilingual profiles for Multilingual Germans and new adolescent migrants can be displayed in a matrix (cf. Fig. 1).Fig. 1Aspects of the multilingual profiles of two different groups of students (basic model, recursively extendable by further analyses)The matrix illustrates a first-step exposition as starting-point for deeper investigation by indicators that can be recursively refined by identifying more specific linguistic qualifications in the course of research. It shows that multilingual students indeed have different challenges prerequisites into the classroom. Moreover, the groups of German-Turkish Multilingual Germans and Arabic-German new migrants differ massively from each other in most aspects and can even be regarded as diametrically opposed with respect to their multilingual profiles.3MethodsThe data we rely on with our concept of multilingual profiles is taken from an interdisciplinary research project (MuM Multi I and II) in which mathematics education researchers (Susanne Prediger) and linguists collaborate (Angelika Redder and, in the first phase, also Jochen Rehbein). In the first phase of the project (2014–2017) we developed and investigated a bilingual intervention. Its aim was to support multilingual students with low achievements in mathematics by allowing and enabling them to use their family language in the mathematics classroom. For this purpose, 41 Multilingual Germans in 7th grade were taught on the subject of fractions in a total of 11 groups with 2–5 students each over the course of 5 sessions. The sessions took place during school hours in the cooperating schools. The multilingual teachers were provided by our project and were schooled with regard to dealing with multilingualism. For this purpose, we adapted language-responsive teaching material on the subject of fractions (Prediger and Wessel 2013) to Turkish and provided it in German and Turkish.For the investigation, we used a mixed-methods design that incorporated a randomized control trial to compare a monolingual and a bilingual intervention (as independent variable), tested students’ conceptual understanding of fractions as the dependent variable, and language proficiency in German and Turkish, SES and fluid intelligence as control variables (see Schüler-Meyer et al. 2019). In the randomized control trial, we could show that our material and the intervention can be beneficial for Multilingual Germans (see Schüler-Meyer et al. 2019). The qualitative analysis of the video-recorded and transcribed teaching learning processes reveals interesting insights into typical mathematical learning pathways (Prediger et al. 2019a) and teachers’ as well as student’ strategies (Redder et al. 2018).Building on these insights, the second phase of the project (2017–2020) was dedicated to transferring our experience with German-Turkish Multilingual Germans with multilingual teachers to a different group of multilinguals, the so-called “new migrants” who came to Germany after September 2015 from Arabic-speaking countries. For this phaseThe overlaying goal of the project is to identify strategies to realize multilingual teaching and learning in regular mathematics classrooms with linguistically heterogeneous students., we translated and adapted the teaching material to Arabic and for the needs of the new migrants.As there was already quantitative data on the effectiveness of our intervention, we opted for a small-scale qualitative study with 8 groups of students from Syria with a total of 25 students in the age of 12–16. In this phase, different formats of multilingual teaching were developed: Bilingual teachers with an educational background in Germany as well as co-teaching formats with two teachers, one only speaking German and the other Arabic, hence acting in a supportive role as an expert in the family language of the students or as a second teacher.All sessions were videotaped with at least two cameras, additional audio equipment was used to ensure an adequate sound quality. Prior to recording, all students took a 90-minute mathematics test, a language test and additional questionnaires on their individual history of migration and situation-specific language usage.All students were participating at their free will and in accordance with the parentsWe provided the information about the project and the data collection in German and Arabic., the teachers, the schools as well as the ministriesIn the process of authorization of the projects, we adhered to all ethical standards and the anonymization of the students’ private data. and agreed to the data collection including video recording as a basis for transcriptions, the analyses of anonymized transcription as well as using the anonymized transcriptions for publications and in the process of archiving.The video-data was transcribed using the HIAT-conventions (Ehlich 1993). The special characteristic of HIAT is that transcribed data is presented in score areas, inspired by musical scores. This allows both to capture and display the simultaneity of spoken language as well as of nonverbal actions. In addition to a speaker’s verbal utterances, the nonverbal communication and actions are noted in their processual relation to the verbal utterances in own tiers. HIAT uses standard orthography. The only special characters are “•“ for pauses of 0.25 seconds, ”...” for indicating verbal terminations and ”/” for indicating repairs. The Arabic utterances were transcribed using the DMG-transliteration (Brockelmann et al. 1935) with specific modifications to enable the transliteration of spoken Syrian-Arabic (as elaborated in Krause 2018).In the following we will provide three analyses of our data:–In analysis 1 we will provide a quantitative overview of a bilingual German-Turkish session (lasting 90 minutes, recorded in the first phase of the project). Like his students, the 30-year-old Teacher 1 is a German-Turkish-speaking Multilingual German of 3rd generation. He speaks Turkish on a very elaborated level, currently takes his Master studies in German, Mathematics and Social Studies and has an additional education in multilingualism. For this quantitative overview (fully explored in Schüler-Meyer et al. 2019), the transcribed utterances were annotated according to surface-related criteria of language used, in this case “German”, “Turkish” or “Mixed” (if both languages were used in one utterance by code-switching etc.) as well as “not identified” if no definite annotation was possible. The snapshot provides the overview on frequencies of language use. It is then related to the qualitative analysis of the language constellations following the multilingual profiles in Figure 1.–In analysis 2, we provide a hermeneutic, functional-pragmatic discourse analysis of a bilingual German-Turkish mathematics session with German-Turkish-speaking Multilingual Germans. The 28-year-old Teacher 2 is also a German-Turkish bilingual and holds a teaching certificate with master degree for German and Mathematics. He was involved in the development of the bilingual teaching sessions.–In analysis 3 we provide another hermeneutic, functional-pragmatic discourse analysis, for comparison of an Arabic-German bilingual session with new migrants, three students who immigrated from Syria two and a half years ago and have learned German for about one year and ten months. The same Teacher 2 was involved and additionally Teacher 3, a 20-year-old Multilingual German who is born and raised in Germany with German and Lebanese Arabic (as Lebanon is part of Levantine, her dialect is very similar to the students’ Syrian dialect, cf. Fischer and Jastrow 1980). She is in her Bachelor studies for becoming a teacher in Mathematics, German and English. The teachers who held the sessions were trained in multilingual teaching and learning according to the findings of the preceding research project (cf. Redder et al. 2018).4Analyses4.1Analysis 1: A quantitative overview and its explanation by the multilingual profilesMultilingual learning situations can be analyzed on a surface level by just considering frequencies of languages used. The diagram in Figure 2 provides an example from one German-Turkish bilingual session of 90 minutes. Altogether the discourse consists of 2104 utterances.The whole corpus consists of a total of 67032 utterances with a total duration of 33 hours and 45 minutes. Out of these Teacher 1 uttered 1347, Student 1 384 and Student 2 373. The utterances per person were annotated according to the language they occurred in. The graphs show striking differences between the teacher’s and the students’ language use. Whereas the teacher uses both languages at approximately the same frequency (51.2 % German and 44.1 % Turkish), both students speak German in a much higher frequency than Turkish (84.6 % to 8.6 % and 76.4 % to 15.8 %).Fig. 2Frequency of Language Use in a German-Turkish bilingual sessionFor a quantitative analysis of a bigger dataset, see Schüler-Meyer et al. (2019).A hasty analysis could conclude that introducing multilingual teaching has no positive effect in the sense that the entire linguistic repertoire of the students is being activated more or less automatically, simply because they don’t speak much Turkish. But this conclusion neglects the specificity of the Multilingual Germans’ multilingual profile and how it is shaped by their linguistic experience: The students experience school as mainly monolingual, as most classrooms only allow German. This experience is included in the students’ presupposition and thus shapes their expectations towards tuition in general, especially when it takes place inside a school building during school hours. Every deviation from these expectations must be experienced by the students as an oddity. Thus, the students’ presuppositions, which are an effect of their multilingual profile, serve as an argument for the explanation of the distribution of languages. The presuppositions and the related expectations cause the mental activation of German to a much higher degree than Turkish, so that German still serves as the basal language. The students speak Turkish to a lesser degree not because they are not able to but because they find themselves in a constellation where their Turkish linguistic repertoire usually is not being asked for.In this way we could illustrate how the analysis of multilingual profiles can contribute to explaining quantitative surface data of frequency of language use. The two following analyses will reveal how the different language constellations coagulated into multilingual profiles which unfold in the classroom and thus affect both, the modelling of multilingual teaching and the linguistic analysis of these constellations. For this we will compare the Multilingual Germans with those of newly migrated studentsIt also has to be taken into consideration that the linguistic structures of the respective languages also play a significant role in concept formation and the course of multilingual teaching and learning and thus in the processing of mathematical knowledge. A few studies have already been conducted on this question (cf. Redder 2019 for German and Prediger et al. 2019 a for German and Turkish) however research on these aspects cannot be seen as completed..4.2Analysis 2: German-Turkish speaking Multilingual GermansThe profiles of five Multilingual Germans in the following excerpt correspond to the general consideration on Multilingual Germans: Their experiences with mainly monolingual schools in Germany have an immediate effect on their multilingual profile. Regarding their linguistic capabilities, German is usually developed to an educational level, but Turkish is not. The use of their family language is limited to everyday – often non-institutional – interactions, such as talking with friends and family after school. Therefore, their subject-related knowledge as well as the related linguistic knowledge is available in German but not in their family language. Nevertheless, the family language can serve as a means for gaining insights or for reasoning. But it does so in a rather concrete fashion.Multilingual teaching for Multilingual Germans takes advantage of the special character of the family language proficiency to develop subject-specific knowledge and understanding – accessible with the entire linguistic potential – based upon a tangible or graphic understanding of subject contents. The following excerpt documents such a case in an early stage of a German-Turkish mathematics session on fractions. The students are just getting adapted to using Turkish as a means to solve mathematical tasks and to reason about related problems and meanings. The transcript starts when students discuss whether a fictional students’ answer of 5/3 is an adequate mathematization for a graphical representation of 3/5. In Turkish, 3/5 are expressed as “five therein three”, here they discuss the inverse fraction “three therein five”.source: corpus MuM-Multi © Angelika RedderThe problem at hand here addresses a central difference between German and Turkish patterns for the wording of fractions: While in German, similar to English, the numerator is mentioned first followed by the denominator, in Turkish it is exactly the other way around (three fifths – drei Fünftel – beşte üç“Beşte üç” (Beş-te üç, Five-LOK three) translates verbatim to “Five therein three”.). The wording pattern, which uses a so-called locative suffix (-te in “beşte”) in addition to the word order, expresses a completely different conceptualization of fractions from the German one (Wagner et al. 2019 a; Prediger et al. 2018). The locative causes an integrated conception of the elements of a fraction, where the numerator is contained in the denominator, while the German formulation sets the elements apart from each other. The Turkish wording belongs to a rather technical register and is only receptively familiar to the students. In addition, the different patterns sometimes lead to difficulties in naming fractions. The pupils swap numerators and denominators in German and Turkish.The teacher works on exactly this problem. He does so by letting the students evaluate a fictional statement: “If in a fraction bar 5 of 3 boxes are colored green, this is the fraction 3/5.” After reading the statement in Turkish the students disagree whether or not it is correct. So, the teacher steps in, works up the solution first and then ties it back to the Turkish verbalization of fractions. He does so by drawing on the students’ everyday knowledge and language.The first step the teacher takes is to secure and explain the correct evaluation of the problematic statement. He therefore repeats the answer given beforehand – “Üçte beş olmuyo demiştiniz, demi?” (Three therein five does not work you said, right?; score area 63) – and gives an explanation that particularly emphasizes the aspect of the conceptualization of fractures expressed by the locative morpheme, i. e. the idea that one element is contained within the other: “Üçün içine beş girmiyo [...].” (Five doesn’t fit into three [...].; score area 63 f.). The emphasis is generated by the nominal phrase (Üçün içine – into three) and the verb (girmek – to enter, to come in). Both the nominal and the verbal phrase carry the notion of ‘something being placed or moved into something else’. The verbal phrase does so via the semantics of ‘girmek’ (to enter), which in this case is negated via the suffix -mi- (gir-mi-yo(r) – enter-NEG-PRS – It does not enterThe 3rd person suffix does not exist in Turkish.); the nominal phrase via the semantics of the root of “içine”„Üçün içine” (Üç-ün iç-in-e – Three-GEN inside-POSS-DAT) translates verbatim to “into the inside of (the) three”. (iç – the inside/ interior of something) combined with the dative suffix (-e), which also expresses an orientation towards a goal. In this way, one of the central notions of the Turkish conceptualization of fractions is carried out by means of everyday language.In the following step, the teacher chooses a similar approach. With the utterance “Yani o yüzden beşte üç oluyo, ama üçte beş, üçten beş...” (Well, therefore five therein three does work, but three therein five, of three five...; score area 64 f.) he gives the fraction that would be correct in connection with the statement (beşte üç – five therein three) and contrasts it to the wrong fraction (ama üçte beş – but three therein five). Afterwards he again reformulates the notion carried out by the wording pattern of fractions by using the ablative case (üçten beş – of three five). The ablative, usually labeling something as a point of departure in a tangible or abstract sense, here is used to express the notion that a certain number of pieces are being extracted from an accumulation of equal pieces. This use of the ablative case is very common in everyday situations where something has to be shared or divided amongst a group of individuals, or where an individual has to choose from an array of possibilities. With the following utterance, he gives an example of just one of these types of situations, again using the ablative case (üç tane arabadan – of three cars) to verbalize the relation between part and whole: “Mesela desem • • sana üç tane arabadan beş tane verecem.” (If I say for example, • • of three cars I give you five.; score area 66 f.). In line with the grammatical structure, the example is chosen from a more or less everyday situation.Regarding the conceptualization of numbers, here, the so-called ablative case carries out a rather concrete idea. Whereas the locative case causes a conceptualization of the numerator and denominator being integrated to a certain degree, the ablative case leads to a delimiting relation between part and whole.In this excerpt, the teacher transfers subject-specific knowledge (here conceptualizations of fractions) into everyday language and everyday experience. By doing so, he shifts the focus of understanding from an academic to a more accessible level and creates a “pivot” (Redder et al. 2018: 50 f.) in the students’ understanding and thus develops the conceptualizations and the respective linguistic means relying on the student’s family language. To help the student conceptually develop and understand the subject matter, the knowledge about problem solving in everyday live is actively put to use, by verbalizing it in the language the students’ usually or often use in these everyday situations. By this approach, the mental concept of the respective mathematical objects is tied to a concrete action, as already pointed out as beneficial for students by Gal‘perin (1989).4.3Analysis 3: German-Arabic Co-TeachingThe next excerpt is taken from a German-Arabic teaching session with two teachers in a co-teaching format: Teacher 2 acts as the main German-speaking teacher. He is experienced in terms of bilingual teaching, but in Turkish-German teaching. Teacher 3 acts as a co-teacher and is fluent in both, German and Arabic, both written and spoken. In the session, three students from Syria are present, but in the following excerpt only Student 6 and Student 7 are speaking.The excerpt of the transcript is taken from the very first session in which one might suspect the students to have troubles adapting to the unfamiliar situation of multilingual teaching with two teachers while at the same time having to adapt to an approach to mathematics that incorporates handling of graphical representations and everyday language resources as a means for conceptual understanding. But contrary to the expectations, the students handled the situation quite well and accepted the Arabic-speaking assistant teacher very fast and referred to her for obstacles in understanding.The students have to solve the following task: ‘One boy, Yassir, wants to share one bar of chocolate with his friends fairly. For this purpose, he creates a spreadsheet that includes fractions and also fraction bars to visualize the fractions, in which he marks the part of the chocolate he would get if he was to share the chocolate among 1, 2, 3 or 4 other children.’ The task is supposed to be solved in two ways: The fraction bars have to be marked correctly and the mathematical expression for the fraction must be given. The students begin by writing down the fractions and then turn to the marking of the bars – the latter being an approach to mathematics they just learned about. As expected, some problems with marking the bars occur: Instead of marking the part of the bar that visualizes the part Yassir would get, the students mark the part that the other children would get. From Teacher 2’s point of view, this is an unexpected and unusual approach but it still shows conceptual understanding, even if not in line with the phrasing of the task. After this was identified and understood – this process takes up quite a lot of time and leads to some confusion amongst the students and the teachers – Teacher 2 tries to dissolve the confusion and wants to make sure that the students solve the task accordingly afterwards. This is where the following transcript starts.source: corpus MuM-Multi II © RedderTeacher 2 admits that the students’ solution is also correct (score area 245 f.) and then wants to make sure the students solve the next task accordingly. However, Student 6 still wonders whether her mathematical solution is correct. Instead of asking the German-speaking Teacher 2, she asks Teacher 3 in Arabic (score area 249). One might interpret this question as an indicator that Student 6 could not follow the slightly confusing utterance of Teacher 2, perhaps even because of the lack of language proficiency. But looking more closely, it is really more of a reinsurance – for affirming of her own solution – that she needs for carrying on with the task and, as can be seen in score area 250 f., also for transferring parts of this knowledge to Student 7 and thus possibly clearing some of his problems in the process. Teacher 3 is in a support role in this section as she follows the discourse and affirms Student 6’s question while in the same course leads her to the correct approach for the next tasks according to Teacher 1’s utterances. Student 6 uses Teacher 3’s affirmation to point to Student 7’s mistakes in his marking of the bar and his fraction in comparison with her own solution – Student 6’s question is therefore a request for the reinsurance before she shows Student 7 his mistakes. This is quite striking as Teacher 2 did not mention the correct solution for the task until that point: The ongoing discourse in German is not about whether the mathematical solution is right or not, it is about the way to get to the solution using fraction-bars and thus, about how to employ graphical representations for mathematical tasks.The students are used to a Syrian educational culture of mathematics that focuses primarily on mathematical procedures and not so much on graphical representations of mathematical operations, as we learned both from discussions with our student assistants from Syria and from analyses of Syrian math books (Redder et al. in press.). Here, they use notwithstanding those representations as a genuine part of solving a mathematical task. Meanwhile, the Arabic language serves them as a shortcut to the correct solution of the fraction and to the part of learning mathematics as they know it. So, whereas Teacher 2 talks about graphical representations, Student 6 is interested in the correct symbolic solution. And as she is already aware that Teacher 2 wants them to use the fraction-bars and discuss the symbolic solution later, Student 6 refers to Teacher 3 in her more familiar language of instruction, Arabic.But there is more to the difference of educational cultures: The practice of Teacher 2 of lettting the students explain their solutions to task – no matter if wrong or right and thus to enable them to discover their mistakes themselves – can be seen a practice that is well established in the German educational culture. This can be seen as a form of “Socratic dialogue” which also proves to be efficient in multilingual constellations (Redder et al. 2018: 94–152). By means of the systematic usage of Arabic, this potential obstacle can be overcome easily. Moreover, it could be seen that Student 6 even made use of this constellation strategically and solve the symbolic part of the task that is more important to her faster than the graphical part that is important for Teacher 2.It could be seen that the acting of Teacher 3 provides the students with an additional resource of understanding through speech actions, namely by simply providing them with the possibility to ask questions concerning the progression of the session in their well-developed classroom and family language when they struggle in understanding Teacher 2. In this very case, Arabic as an available linguistic resource enables a discursive interaction between the students that would otherwise probably not happen. Even more so, having a teacher present that is fluent in the well-known language of instruction can help to avoid misunderstandings and possible frustration that can occur when being confronted with different educational cultures.5DiscussionIn this paper we have illustrated how multilingual profiles can provide a basis for implementing multilingual teaching and learning in subject-matter classrooms as well as for linguistic analyses of multilingual discourses. They can help to differentiate between groups of multilinguals and shed light on the necessity to treat and teach different groups of multilingual students according to their group-specific needs and prerequisites – a necessity that is even more important when it comes to the integration of adolescent migrants. The discourse analytic results can help for a recursive refinement of the multilingual profiles with respect to German as medium of instruction, family language as medium of instruction and the very linguistic quality of subjects’ knowledge. Hence, this concept can both build on and enrich the research on translanguaging pedagogy (e. g. García and Kleyn 2016). Knowledge of the multilingual profile of a certain group and thus their expectations, abilities and presuppositions, enables to take the particular linguistic and mental peculiarities into account and to adapt education accordingly, i. e. by implementing different types of teaching formats.To show this, two groups of multilinguals have been characterized exemplarily: German-Turkish Multilingual Germans and new migrants from Arabic-speaking countries. Two qualitative analyses on bilingual sessions on fractions have illustrated how the linguistic differences between the groups can affect multilingual teaching and learning. In Analysis 2, we have shown how the use of the family language (even if usually not used for teaching and learning) enables a special form of knowledge transfer and acquisition. Drawing on the family language allows the teacher to activate everyday-knowledge and experiences for educational purposes. Utilizing this knowledge can help the acquisition of subject-matter content, such as mathematical conceptualizations, as well as an expansion of the family language to a level appropriate for schools. Including the Multilingual Germans’ family language level seems to lead to empowerment and further inclusion (Barwell 2009; Schüler-Meyer et al. 2019).In the case of new migrants, the analysis of the Arabic-German session in Analysis 3 has shown that other prerequisites have to be met. In addition to the conceptual differences determined by different languages, differences of the educational cultures (to which students are more or less accustomed) can also be taken into consideration as they may cause different expectations on methodological issues. If students don’t manage to cope with these differences, they might get lost in the educational system. Hence, multilingual education that meets these challenges can allow teachers to take students’ prior experiences into account and at the same time to promote the further acquisition of the target-language to an academic level. Therefore, multilingual education can be seen as an integration tool (cf. Rehbein 2013).Our results from the above small-scale study with homogenous groups show that we can shed light on the complexity of the challenges teachers face in classrooms every day, as they are teaching different groups of multilinguals and monolinguals in the same class and a separation of the different groups is not intended in our perspective. Moreover, we see it as beneficial for every student to be in contact with (other) multilingual students and their linguistic and cultural prerequisites. By comparing German-Turkish-speaking Multilingual Germans with new migrants, we have shown that new migrants do not really pose new challenges, but need to be approached slightly different when it comes to successful implementation of multilingual teaching and learning: In the case of German-Turkish-speaking students, Turkish has to be pushed in order to bypass their presuppositions and expectations and to achieve a more balanced multilingualism – at least in a phase of transition from mono- to multilingual teaching. But it seems to be obvious that these observations cannot be transferred to the case of Arabic-speaking new migrants. Here, German has to be pushed without abandoning Arabic. Moreover, Arabic has to be seen and used as both, an additional and foundational resource of teaching and learning and thus for understanding. The adolescent migrants’ prior knowledge, which is learned via and bound in the language(s) of the home country, could be activated by incorporating the language(s) in education in the target country. We are convinced: Even in subjects with – often falsely assumed – low requirements for language, such as mathematics, students can profit from multilingual education. Teachers need to be aware of these possibilities. By approaching their multilingual students with the knowledge of their multilingual profile, the teachers can organize and plan the teaching accordingly and, ideally, in more beneficial ways.6ConclusionThe data we presented in this paper provides brief and specialized insights into possible constellations of multilingual teaching and learning: The teachers in our data were multilingual themselves and, with the exception of one teacher who needed the support of an additional teacher to teach the Arabic-speaking students, thus were able to follow the multilingual discourses of the students. This was a meaningful approach to enable us to understand how the multilingual resources of the students can be activated and put to use for teaching mathematics, but it leads to some restrictions: Of course, it is easier to foster family languages and target languages at the same time, when all participants are able to speak and understand them. But this constellation is more less never the case in a regular classroom. A monolingual teacher can face some difficulties in comparable situations, especially when it comes to the question of assessment of the students’ knowledge presented in a different language. Hence, it is important to create possibilities for the students in which they are allowed to use any language they know without limitations, to enable the students to access their full mental capacities and conceptual knowledge, whilst maintaining a classroom discourse that allows the teachers to assess the students’ knowledge and foster them individually. The effects of this approach are currently under investigation through further discourse analyses (Wagner et al. in press).Looking at Germany and its long history of migration, it becomes obvious that new migrants do not really pose new challenges, but the solutions should be innovative: By employing multilingual teaching and learning. But there is still a lot of work to be done, as our study can only scratch the surface of what a sustainable implementation of multilingualism in accordance with the complex heterogeneity of classrooms can look like. In the next steps it is necessary to look further into the question of how multilingual profiles recursively refined by discourse analysis can help teachers to plan and conduct multilingual teaching formats and, even further, to determine the benefits of multilingual teaching in regular classrooms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png European Journal of Applied Linguistics de Gruyter

New migrants, new challenges? – Activating multilingual resources for understanding mathematics: institutional and interactional factors

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de Gruyter
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
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2192-953X
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10.1515/eujal-2020-0017
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Abstract

1IntroductionThe integration of migrants into European societies is among the most profound societal challenges of today although migration is not a challenge that only occurred recently. For at least 60 years now, and even though this fact has often been denied, western European countries can be viewed as countries of immigration, their societies as societies of immigration with varying shapes. Germany, too, faced various phases of migration. These include the invited immigration of so-called “guest workers”In Germany migrant workers were called “Gastarbeiter”, which translates verbatim into “guest workers”. This denomination implies the expectation the workers will only stay temporarily without settling and bringing their families and will be going back to their origin country after the work was done. from Italy, Spain, Greece, former Yugoslavia and Turkey from 1955 until 1973; the refugees from the Yugoslavian civil war in the 1990 s and refugees from various conflicts in the Middle Eastern and African countries followed in recent years.This list is by no means complete and has no intent to marginalize the refugees and other migrants from Asia, Eastern Europe, or elsewhere. Despite this German history of immigration, integration has not always or mainly been subject of societal and political discussions, especially not with respect to the integration of migrant students in the educational system. This has significantly changed in the last decade (cf. Hoßmann and Karsch 2011).In Germany, successful integration into an educational system is predominantly discussed as being based on learning German – alongside with extensive and expensive programs for integrating German-Russian ‘Spätaussiedler’ at the turn of the century. However, it should never be underestimated that migrants bring an extensive linguistic knowledge with them – which is not necessarily limited to a single language. For example, a Syrian refugee from northern Syria might actually be raised with Arabic, Kurdish and French plus potential school languages such as English. Moreover, “Arabic” has to be differentiated into its numerous regional varieties and dialects (in our exemplarily case here into Syrian Arabic and Modern Standard Arabic), as these differ greatly from each other (cf. Versteegh 1997: 189–208). Given the linguistic capabilities and affordances of migrants, limiting the discourse on linguistic integration to the acquisition of the target language would mean to marginalize the communicative and epistemic resources of migrants and thus to reduce their chance of participation in school.Efforts to foster bilingual education or education in the heritage languages started in Germany in the mid-1980’s (cf. BAGIV 1985) and have been revived recently (Benholz et al. 2010). Instead, we join the position that providing possibilities for using all available linguistic resources, in language learning as well as subject learning, leads to a more successful and accelerated integration into an educational systemWe would further argue that opening monolingual structured educational systems for other languages besides the target language could also have ripple effects on other domains of society (cf. Rehbein 2013).. To put it simply: ‘use multilingualism as resource’ is an educational principle that is key to integration as it incorporates individual language-related capabilities into the societal educational system, as the research on Translanguaging also suggests (e. g. García 2009).But even though most migrants are either already multilinguals or have to become multilinguals at least to some degree, not all multilinguals can be treated the same way when participating in a multilingual learning environment. Different backgrounds call for different means to fully unfold the respective potential. This can be seen when looking at specific groups of multilingual students. In this paper, we will focus on new migrants from Arabic speaking countries, as an example of one of the largest groups of migrants that has recently sought to take part in the educational system. This group will be compared here with the most present one in the German educational system, namely the third generation of migrant workers from Turkey, who are classified as native resident multilingual students by virtue of the fact that they are born in Germany and raised with both German and Turkish to various degrees, though faced with the domain of classroom discourse being shaped by German only (in the following abbreviated as: Multilingual Germans).We will narrow down the group of interest by focusing on the group of adolescents of twelve to fourteen years, an age group that rarely is put into focus of educational research (SVR research report 2018). Even more so, adolescent migrants are mostly overlooked, even though they face very distinct and complex linguistic challenges when arriving in the target country of their migrationWe are aware of the very heterogenous and often difficult experiences during the process of migration that constitute complex challenges of their own. However, here we will mostly focus on the linguistic aspects of these challenges.. Most importantly, adolescent migrants have often already been schooled in a language other than the language(s) of the target country and thus have language-specific subject knowledge at their disposal.So far the benefits of multilingual education in maths, even when introduced at a late stage of the student’s school careers, have been shown for Multilingual Germans (i. e. Prediger and Redder 2020; Schüler-Meyer et al. 2019; Redder et al. 2018; Wagner et al. 2018). With these students, incorporating their entire linguistic and cognitive repertoire does not serve as an integration tool but rather as a means to foster subject-related understanding and thus to improve their performance in school. Of course, compared to newly arrived adolescent migrants, these students face different challenges in the mathematics classroom (Prediger et al. 2018). Hence, the question is, how the insights from a multilingual education of Multilingual Germans can be transferred to the case of adolescent refugees, and, referring to the title of this paper, in which way this group of new migrants provides the teachers with new and unique challenges.In this paper, we will introduce the concept of ‘multilingual profiles’ both as a broad theoretical input and a more refined outcome of discourse analyses. The concept comprises the ‘linguistic repertoires’ (Gumperz 1972) and additionally integrates a set of further aspects of linguistic knowledge from an action theoretical point of view (see below). A multilingual profile thus serves as a methodological instrument that makes the differences between groups of multilingual students more tangible and enables didactics as well as linguistic analyses to fully take them into account (as shown for the didactical analysis in Prediger et al. 2019b). The aim of ‘multilingual profiles’ is to focus the students’ individual language proficiency in terms of not only linguistic means that manifest as linguistic signs but the full range of qualifications for linguistic action including language-specific mental processes (cf. Rehbein 1977; Ehlich 2013). All these linguistic qualifications serve as the students’ prerequisites for any participative action in classroom discourse. This can subsequently provide teachers with more specific information on how to approach multilingual teaching and learning. This will be achieved by focusing on linguistic knowledge as a subjective dimension of the concept of the ‘constellation’ (Rehbein 1977; Bührig 2005) which is central for linguistic action in general and for multilingual action in particular. Constellations are shaped by specific needs that call for the individual’s linguistic action to fulfill them and pursue respective purposes (cf. Bührig 2005: 148). Hence linguistic action is treated to systematically mediate conditions of the non-linguistic reality for both interactants, speaker and hearer, with their (productive and receptive) linguistic knowledge acquired by socialization processes and their common discursive management up to a certain result determined by their purposes.In consequence, linguistic repertoire and sociolinguistic domain are linked together on a meso-level of analysis.In the following, we will offer some insights into the conceptual ideas behind our notion of multilingual profiles and the categories we included therein, as based within the framework of Functional PragmaticsAlso known as “functional-pragmatic discourse analysis” (cf. Bührig 2005: 144).. After a subsequent elaboration of functional-pragmatic methodology and the data we are working with, we will conduct three analyses in which we will show the benefit of incorporating multilingual profiles in a linguistic analysis of authentic data from mathematicsMathematics is chosen as a subject that often is seen as the subject that requires the lowest language proficiency, because it mostly is said to rely on mathematical symbols – an assumption that could not be further apart from the reality (cf. Prediger et al. 2018). classroom interaction with multilingual students. We will conclude the chapter with a discussion of our findings in these analyses with a distinct prospect on the implications for teaching and learning with multilingual students.2Conceptual background and approachHouse and Rehbein (2004) identify the concept of ‘multilingual communication’ to be the nucleus for treating individual as well as societal multilingualism. In a theoretical reflection of empirical findings, Franceschini (2011) makes the case for ‘discursive multilingualism’ to be taken into account for innovative research. And most recently, Li Wei (2017) calls for an ‘action theory’ to cope with multilingualism. In accordance to these positions, we will approach our data from a functional-pragmatic perspective, using its well-developed action-theoretical and psycholinguistic shape as opposed to, for instance, systemic functional linguistics (i. e. Halliday 1978) which seems to be the closest alternative approach.cf. Redder (2008), as well as Gruber (2012), for a critical comparison of Functional Pragmatics and Systemic Functional Linguistics that highlights the differences between the approaches. Gruber points out that Functional Pragmatics is more focused on the action character of communication while SFL is more focused on the semiotization of it. In doing so, we pursue our research on fostering subject-matter understanding by means of multilingual classroom discourse, which already led to the reconstruction of supportive and non-supportive linguistic strategies on part of teachers and on part of students (Redder et al. 2018).2.1Multilingual profiles in theoryTo specify the respective linguistic knowledge of students as being actors in classroom discourse and hence to specify linguistic knowledge as a distinguishable and outstanding dimension of the interactive constellation, we introduce the concept of ‘multilingual profiles’. As has been pointed out above, simply speaking of multilingual students and thus assuming a homogeneity of a vastly heterogeneous group of students would be naive and could lead to problems in the educational process. The mere consciousness and naming of more than the official language in classroom discourse can initiate the process of overcoming a monolingual habitus. For going beyond this step, teachers should identify their students’ multilingual resources in the first place. For this purpose, García et al. (2017) have developed the “Bilingual Student Identification and Profile” (García et al. 2017: 31) to support teachers to “systematically collect information about who their students are, the languages they speak, their cultural practices, their experiences, and the world that they know” (García et al. 2017: 31). The institutional aim of their idea is to go beyond the three categorizations of children in the U. S. that differentiate “English Language Learners, former English Language Learners and fully English proficient” (García et al. 2017: 31) and instead put the students’ individual linguistic resources into focus and to use these resources for teaching and learning. Thus, a checklist for teachers as well as a form for bilingual student profiles was developed, comprising five aspects: Bilingual use at home, bilingual friends, bilingual exposure in the life of student, education in the LOTE (= Language other than English) and literacy in LOTE (García et al. 2017: 170). The results of the checklist are then to be included in the more concrete bilingual student profiles that consist of six aspects: LOTE spoken or heard consistently at home, countries where the student has lived since birth, countries where the student has gone to school since birth, nativity and residence, education in English, education in LOTE (cf. García et al. 2017: 171).Despite this approach being helpful to create an awareness of the individual linguistic resources of the students and thus to get an idea which of these resources might be helpful in everyday teaching and learning, we suggest that the approach would benefit from further development. These suggestions come as a spring-off from detailed discourse analyses in several constellations of free choice for multilingualism in classroom discourse. As we found out, it is not self-evident to foster subject understanding by any kind of opening the floor for multilingual action or any teacher’s strategy to cope with such interaction formats (cf. Redder et al. 2018). Multilingual discourse has to be evolved far beyond any turn-taking mechanism or surface structure of utterances. However, it still remains to be analyzed how multilingual knowledge processing works on a micro-level and how it can be fostered before this can be applied for educational purposes.Thus, a linguistic analysis (especially an interaction-centered analysis) requires as much meta-data about the students as possible, i. e. their individual multilingualism, their language proficiency and their situational language use in education. Here, we intend to develop the concept of multilingual profiles further beyond the meta-data and make it usable for linguistic analyses.Multilingual profiles are understood as the focalization of those factors of an individuals’ linguistic capability which affect his or her participation in educational discourses. Individual knowledge and capabilities, the mechanisms of perception, evaluation and belief as well as motivation constitute, as Rehbein (1977) spelled out in his theory of action, are the main factors of the mental or “subjective” dimension of a constellation as being distinct from the objective ones (namely: field of action, interactive space, field of control and system of purposes, see Rehbein 2007: 441). Hence an action-centered discourse analysis should take them into account.The idea guiding this approach is not to conduct an individualistic sociological research of every students’ biography, but to identify factors for characterizing groups of students by means of interfaces and similarities in their biography which appear to have impact on the implementation of multilingual teaching and learning formats. This also implies the possibility to modify and extend the multilingual profiles recursively with and after discourse analyses. The aim of multilingual profiles is not so much to provide a basis for multilingual subject-matter teaching but to identify the general possibility for multilingual teaching through an identification of the students’ linguistic resources; hence multilingual profiles go a step further than the concept of García et al. 2017 and differentiate between the language of instruction and subject-related language(s). Thus, our concept goes beyond a mere identification of languages spoken but take, in the long run, language-bound mental processes of knowledge formation as well as the illocutionary dimension of knowledge processing into account. With respect to those mental processes, multilingual profiles exceed explicit or implicit relations to the semiotic-based concept of multilingual repertoires (i. e. Creese and Blackledge 2010). Through this, the concept of multilingual profiles sets to enable a more differentiated view towards the falsely assumed homogeneity of multilingual students. This is necessary to enable for example the differentiation of Multilingual Germans who are raised as multilinguals but are not treated as multilinguals in the educational system and of newly migrated students who turn into emergent multilinguals in Germany as they have been formerly schooled in other languages than German.2.2Shaping multilingual profilesFollowing these general remarks on the concept of multilingual profiles, we now turn to a more concrete reflection of it. The different profiles derive from previous research on Multilingual Germans (cf. Redder al. 2018; Wagner et al. 2018; Prediger et al. 2019a) and the attempt to transfer the respective results to the case of new adolescent migrants in Germany, as will be elaborated in more detail in the methods section of this chapter.The notion behind multilingual profiles is hermeneutic in nature. The core aspects of the profiles were identified through empirically based, functional-pragmatic discourse analyses and serve as a foundation for tailor-made multilingual teaching models as well as further research that might lead to more precise differentiations not considered as of now.Multilingual profiles can be understood as a methodological tool to approach the heterogenous group of multilingual students and shed light on their respective needs in classrooms. Thus, multilingual profiles explicitly seek not to marginalize individual or group-specific differences but to emphasize and operationalize them in a way that allows for taking them into account when developing multilingual teaching models.At the core of multilingual profiles are the languages as a linguistic knowledge of individual actants on how to interact verbally as a common member of a language society.Our action-theoretical categorization of the given capacity is appropriate to overcome any additional type of pragmatics when coping with the simple distinction of language system (langue) and language use (parole). Here we focus on a certain group of verbal actants and the characteristics of its or their linguistic action in the various constellations of everyday life. Different constellations require different usages of languages. Primarily, this concerns linguistic action forms rather than lexical-semantic or grammatic structures. This follows pragmatic and sociolinguistic positions and findings that a conceptualization of language as an ensemble of lexicon and grammar that is regulated by conventions does not fit to linguistic reality.For the purpose of this paper, the reconstruction and operationalization of the multilingual profiles of Arabic speaking adolescent migrants and Multilingual Germans helps to identify them as two distinguishable groups of linguistic actants that require different teaching methods; especially we focus on the following (intertwining and correlating) aspects: (1) the type of acquisition of the German language, (2) the students’ constellation-specific language proficiencyLanguage proficiency, in the sense of this paper, is mainly determined by an individual’s capacity for linguistic action (see Bührig 2005: 147, on the relation of Functional Pragmatics and the speech act theory of Austin 1962). Rehbein and Karakoç 2004, specify the complexity of this notion of language proficiency for multilinguals. and (3) the way subject-specific knowledge is acquired.The type of acquisition of German (as a second language)It is a well-known difference if a language is acquired as a second language or as a foreign language, or if two languages are acquired simultaneously or successively (e. g., Meisel 2019). For many Multilingual Germans, it is often not decidable which language is L1 and which L2. In contrast, new adolescent migrants have to go through an accelerated acquisition of German as a second language. In school, already the mere observation of a students’ type of acquisition of German could lead teachers to activate their knowledge about second language acquisition processes, if available, and opt for certain discourse strategies – not only in language classrooms but also in subject-matter classrooms. In particular, the type of acquisition has an effect on the differences between the new migrants’ and Multilingual Germans’ constellation-specific language proficiency.Constellation-specific language proficiencyAs mentioned above, different constellations require different forms of linguistic acting. In multilingual societies with predominant monolingual school systems such as Germany, this often means that only one language within the multilinguals’ repertoire is activated and academically developed to a certain level – in this case German.This of course does not count for every single multilingual student in Germany, but for the major part it does. There are schools that teach family languages, but only very few. For example, in Hamburg, only 8 out of 411 schools offer Turkish language classes (see https://bildungsserver.hamburg.de/tuerkisch/unterricht/schulen/; retrieved 1/25/21) Thus, Multilingual Germans usually use the German language in schools whereas their family language remains undeveloped on the academic or pre-academic level (cf. Redder et al. in press; Gilham and Fürstenau 2020). Sometimes, writing and reading in the family language is not acquired at all. The wide and recently growing range of family languages in Germany do have their domain mostly in the family and in non-institutional constellations (cf. Rehbein and Grießhaber 1996: 76 f. for the German situation).Compared to Multilingual Germans, new adolescent migrants have of course developed their family language to a high degree, but participating in a German-only classroom discourse is a big challenge, as German is still in the process of acquisition. Subject-matter learning is restricted by these limitations.Linguistic quality of subject-specific knowledgeAs the Multilingual Germans’ family languages are usually not systematically used for learning in school, especially not in subject-matter classrooms (beyond any CLIL-enterprise), subject-specific knowledge is usually bound in the language of schooling, namely German, only. But the family language usually allows a rather tangible or, as based on everyday-knowledge, practically concrete approach to subject-related issues by means of everyday language.Here again, with new adolescent migrants these relations present themselves to be very different. Due to previous schooling in their home country, their knowledge acquired so far is bound in the family language for the most part, whereas the level of proficiency in German enables to a rather pragmatic, concrete approach to subject matter.A reflection of these issues regarding a certain group of multilingual students bears a risk of leading to a grossly simplified and undifferentiated treatment for the individual. However, the identified factors can provide the basis for an assessment of the abilities to perform and linguistically act in school as well as the development of fitting teaching models.Another major issue that impacts the multilingual profiles is the students’ experiences with different educational cultures. Students with individual experience of migration might have been schooled in more than one country in course of seeking refuge, for instance in Iraq, Turkey, Greece or Italy before reaching Germany. But there is few research on the differences of educational cultures; especially no comparative research of the German and the (Syrian-)Arabic educational culture exists. We know from comparative, German-Italian analyses on academic discourse at universities (Thielman, Redder and Heller 2015) that teaching and learning in Germany does significantly involve a lot of verbal interaction amongst students, of talking about the epistemic status of knowledge at hand, as well as of the ability to explain and to exchange arguments. Hence educational cultures imply certain expectations with respect to linguistic action formats for knowledge processing in classroom discourse.When looking at the group of new migrants, two possible additional aspects have to be addressed that differ from the needs from Multilingual Germans:–First-hand experience of migration. Individual migration experience can induce psychological stress or even traumatization which strongly determine the individuals’ ability for linguistic action in classroom discourse as it influences the individual action space and hence the selection of possible and adequate actions.–Continuous education from at least age six. Whereas in Germany, every child is obliged to attend a school from the age of six for at least ten years, other countries have limited compulsory education or lack its monitoring. Additionally, the journey of refugees even lacks school attendance or a structured curriculum, notwithstanding the quality of schooling. In terms of language proficiency, this aspect helps to outline the pragmatic capacities of the students including their accordance to institutional determinations. Also their educational level might deviate significantly from same-age classmates in the target country.These two aspects of multilingual profiles will not be object of our analysis in this paper, but still have to be mentioned as teachers have to be aware that possibly traumatized students as well as students that never attended school could participate in their classrooms. To deal with this is not object of linguistics, but it highlights the need to identify possible challenges of new groups of students across disciplinary boarders.To sum up our discussion so far, the multilingual profiles for Multilingual Germans and new adolescent migrants can be displayed in a matrix (cf. Fig. 1).Fig. 1Aspects of the multilingual profiles of two different groups of students (basic model, recursively extendable by further analyses)The matrix illustrates a first-step exposition as starting-point for deeper investigation by indicators that can be recursively refined by identifying more specific linguistic qualifications in the course of research. It shows that multilingual students indeed have different challenges prerequisites into the classroom. Moreover, the groups of German-Turkish Multilingual Germans and Arabic-German new migrants differ massively from each other in most aspects and can even be regarded as diametrically opposed with respect to their multilingual profiles.3MethodsThe data we rely on with our concept of multilingual profiles is taken from an interdisciplinary research project (MuM Multi I and II) in which mathematics education researchers (Susanne Prediger) and linguists collaborate (Angelika Redder and, in the first phase, also Jochen Rehbein). In the first phase of the project (2014–2017) we developed and investigated a bilingual intervention. Its aim was to support multilingual students with low achievements in mathematics by allowing and enabling them to use their family language in the mathematics classroom. For this purpose, 41 Multilingual Germans in 7th grade were taught on the subject of fractions in a total of 11 groups with 2–5 students each over the course of 5 sessions. The sessions took place during school hours in the cooperating schools. The multilingual teachers were provided by our project and were schooled with regard to dealing with multilingualism. For this purpose, we adapted language-responsive teaching material on the subject of fractions (Prediger and Wessel 2013) to Turkish and provided it in German and Turkish.For the investigation, we used a mixed-methods design that incorporated a randomized control trial to compare a monolingual and a bilingual intervention (as independent variable), tested students’ conceptual understanding of fractions as the dependent variable, and language proficiency in German and Turkish, SES and fluid intelligence as control variables (see Schüler-Meyer et al. 2019). In the randomized control trial, we could show that our material and the intervention can be beneficial for Multilingual Germans (see Schüler-Meyer et al. 2019). The qualitative analysis of the video-recorded and transcribed teaching learning processes reveals interesting insights into typical mathematical learning pathways (Prediger et al. 2019a) and teachers’ as well as student’ strategies (Redder et al. 2018).Building on these insights, the second phase of the project (2017–2020) was dedicated to transferring our experience with German-Turkish Multilingual Germans with multilingual teachers to a different group of multilinguals, the so-called “new migrants” who came to Germany after September 2015 from Arabic-speaking countries. For this phaseThe overlaying goal of the project is to identify strategies to realize multilingual teaching and learning in regular mathematics classrooms with linguistically heterogeneous students., we translated and adapted the teaching material to Arabic and for the needs of the new migrants.As there was already quantitative data on the effectiveness of our intervention, we opted for a small-scale qualitative study with 8 groups of students from Syria with a total of 25 students in the age of 12–16. In this phase, different formats of multilingual teaching were developed: Bilingual teachers with an educational background in Germany as well as co-teaching formats with two teachers, one only speaking German and the other Arabic, hence acting in a supportive role as an expert in the family language of the students or as a second teacher.All sessions were videotaped with at least two cameras, additional audio equipment was used to ensure an adequate sound quality. Prior to recording, all students took a 90-minute mathematics test, a language test and additional questionnaires on their individual history of migration and situation-specific language usage.All students were participating at their free will and in accordance with the parentsWe provided the information about the project and the data collection in German and Arabic., the teachers, the schools as well as the ministriesIn the process of authorization of the projects, we adhered to all ethical standards and the anonymization of the students’ private data. and agreed to the data collection including video recording as a basis for transcriptions, the analyses of anonymized transcription as well as using the anonymized transcriptions for publications and in the process of archiving.The video-data was transcribed using the HIAT-conventions (Ehlich 1993). The special characteristic of HIAT is that transcribed data is presented in score areas, inspired by musical scores. This allows both to capture and display the simultaneity of spoken language as well as of nonverbal actions. In addition to a speaker’s verbal utterances, the nonverbal communication and actions are noted in their processual relation to the verbal utterances in own tiers. HIAT uses standard orthography. The only special characters are “•“ for pauses of 0.25 seconds, ”...” for indicating verbal terminations and ”/” for indicating repairs. The Arabic utterances were transcribed using the DMG-transliteration (Brockelmann et al. 1935) with specific modifications to enable the transliteration of spoken Syrian-Arabic (as elaborated in Krause 2018).In the following we will provide three analyses of our data:–In analysis 1 we will provide a quantitative overview of a bilingual German-Turkish session (lasting 90 minutes, recorded in the first phase of the project). Like his students, the 30-year-old Teacher 1 is a German-Turkish-speaking Multilingual German of 3rd generation. He speaks Turkish on a very elaborated level, currently takes his Master studies in German, Mathematics and Social Studies and has an additional education in multilingualism. For this quantitative overview (fully explored in Schüler-Meyer et al. 2019), the transcribed utterances were annotated according to surface-related criteria of language used, in this case “German”, “Turkish” or “Mixed” (if both languages were used in one utterance by code-switching etc.) as well as “not identified” if no definite annotation was possible. The snapshot provides the overview on frequencies of language use. It is then related to the qualitative analysis of the language constellations following the multilingual profiles in Figure 1.–In analysis 2, we provide a hermeneutic, functional-pragmatic discourse analysis of a bilingual German-Turkish mathematics session with German-Turkish-speaking Multilingual Germans. The 28-year-old Teacher 2 is also a German-Turkish bilingual and holds a teaching certificate with master degree for German and Mathematics. He was involved in the development of the bilingual teaching sessions.–In analysis 3 we provide another hermeneutic, functional-pragmatic discourse analysis, for comparison of an Arabic-German bilingual session with new migrants, three students who immigrated from Syria two and a half years ago and have learned German for about one year and ten months. The same Teacher 2 was involved and additionally Teacher 3, a 20-year-old Multilingual German who is born and raised in Germany with German and Lebanese Arabic (as Lebanon is part of Levantine, her dialect is very similar to the students’ Syrian dialect, cf. Fischer and Jastrow 1980). She is in her Bachelor studies for becoming a teacher in Mathematics, German and English. The teachers who held the sessions were trained in multilingual teaching and learning according to the findings of the preceding research project (cf. Redder et al. 2018).4Analyses4.1Analysis 1: A quantitative overview and its explanation by the multilingual profilesMultilingual learning situations can be analyzed on a surface level by just considering frequencies of languages used. The diagram in Figure 2 provides an example from one German-Turkish bilingual session of 90 minutes. Altogether the discourse consists of 2104 utterances.The whole corpus consists of a total of 67032 utterances with a total duration of 33 hours and 45 minutes. Out of these Teacher 1 uttered 1347, Student 1 384 and Student 2 373. The utterances per person were annotated according to the language they occurred in. The graphs show striking differences between the teacher’s and the students’ language use. Whereas the teacher uses both languages at approximately the same frequency (51.2 % German and 44.1 % Turkish), both students speak German in a much higher frequency than Turkish (84.6 % to 8.6 % and 76.4 % to 15.8 %).Fig. 2Frequency of Language Use in a German-Turkish bilingual sessionFor a quantitative analysis of a bigger dataset, see Schüler-Meyer et al. (2019).A hasty analysis could conclude that introducing multilingual teaching has no positive effect in the sense that the entire linguistic repertoire of the students is being activated more or less automatically, simply because they don’t speak much Turkish. But this conclusion neglects the specificity of the Multilingual Germans’ multilingual profile and how it is shaped by their linguistic experience: The students experience school as mainly monolingual, as most classrooms only allow German. This experience is included in the students’ presupposition and thus shapes their expectations towards tuition in general, especially when it takes place inside a school building during school hours. Every deviation from these expectations must be experienced by the students as an oddity. Thus, the students’ presuppositions, which are an effect of their multilingual profile, serve as an argument for the explanation of the distribution of languages. The presuppositions and the related expectations cause the mental activation of German to a much higher degree than Turkish, so that German still serves as the basal language. The students speak Turkish to a lesser degree not because they are not able to but because they find themselves in a constellation where their Turkish linguistic repertoire usually is not being asked for.In this way we could illustrate how the analysis of multilingual profiles can contribute to explaining quantitative surface data of frequency of language use. The two following analyses will reveal how the different language constellations coagulated into multilingual profiles which unfold in the classroom and thus affect both, the modelling of multilingual teaching and the linguistic analysis of these constellations. For this we will compare the Multilingual Germans with those of newly migrated studentsIt also has to be taken into consideration that the linguistic structures of the respective languages also play a significant role in concept formation and the course of multilingual teaching and learning and thus in the processing of mathematical knowledge. A few studies have already been conducted on this question (cf. Redder 2019 for German and Prediger et al. 2019 a for German and Turkish) however research on these aspects cannot be seen as completed..4.2Analysis 2: German-Turkish speaking Multilingual GermansThe profiles of five Multilingual Germans in the following excerpt correspond to the general consideration on Multilingual Germans: Their experiences with mainly monolingual schools in Germany have an immediate effect on their multilingual profile. Regarding their linguistic capabilities, German is usually developed to an educational level, but Turkish is not. The use of their family language is limited to everyday – often non-institutional – interactions, such as talking with friends and family after school. Therefore, their subject-related knowledge as well as the related linguistic knowledge is available in German but not in their family language. Nevertheless, the family language can serve as a means for gaining insights or for reasoning. But it does so in a rather concrete fashion.Multilingual teaching for Multilingual Germans takes advantage of the special character of the family language proficiency to develop subject-specific knowledge and understanding – accessible with the entire linguistic potential – based upon a tangible or graphic understanding of subject contents. The following excerpt documents such a case in an early stage of a German-Turkish mathematics session on fractions. The students are just getting adapted to using Turkish as a means to solve mathematical tasks and to reason about related problems and meanings. The transcript starts when students discuss whether a fictional students’ answer of 5/3 is an adequate mathematization for a graphical representation of 3/5. In Turkish, 3/5 are expressed as “five therein three”, here they discuss the inverse fraction “three therein five”.source: corpus MuM-Multi © Angelika RedderThe problem at hand here addresses a central difference between German and Turkish patterns for the wording of fractions: While in German, similar to English, the numerator is mentioned first followed by the denominator, in Turkish it is exactly the other way around (three fifths – drei Fünftel – beşte üç“Beşte üç” (Beş-te üç, Five-LOK three) translates verbatim to “Five therein three”.). The wording pattern, which uses a so-called locative suffix (-te in “beşte”) in addition to the word order, expresses a completely different conceptualization of fractions from the German one (Wagner et al. 2019 a; Prediger et al. 2018). The locative causes an integrated conception of the elements of a fraction, where the numerator is contained in the denominator, while the German formulation sets the elements apart from each other. The Turkish wording belongs to a rather technical register and is only receptively familiar to the students. In addition, the different patterns sometimes lead to difficulties in naming fractions. The pupils swap numerators and denominators in German and Turkish.The teacher works on exactly this problem. He does so by letting the students evaluate a fictional statement: “If in a fraction bar 5 of 3 boxes are colored green, this is the fraction 3/5.” After reading the statement in Turkish the students disagree whether or not it is correct. So, the teacher steps in, works up the solution first and then ties it back to the Turkish verbalization of fractions. He does so by drawing on the students’ everyday knowledge and language.The first step the teacher takes is to secure and explain the correct evaluation of the problematic statement. He therefore repeats the answer given beforehand – “Üçte beş olmuyo demiştiniz, demi?” (Three therein five does not work you said, right?; score area 63) – and gives an explanation that particularly emphasizes the aspect of the conceptualization of fractures expressed by the locative morpheme, i. e. the idea that one element is contained within the other: “Üçün içine beş girmiyo [...].” (Five doesn’t fit into three [...].; score area 63 f.). The emphasis is generated by the nominal phrase (Üçün içine – into three) and the verb (girmek – to enter, to come in). Both the nominal and the verbal phrase carry the notion of ‘something being placed or moved into something else’. The verbal phrase does so via the semantics of ‘girmek’ (to enter), which in this case is negated via the suffix -mi- (gir-mi-yo(r) – enter-NEG-PRS – It does not enterThe 3rd person suffix does not exist in Turkish.); the nominal phrase via the semantics of the root of “içine”„Üçün içine” (Üç-ün iç-in-e – Three-GEN inside-POSS-DAT) translates verbatim to “into the inside of (the) three”. (iç – the inside/ interior of something) combined with the dative suffix (-e), which also expresses an orientation towards a goal. In this way, one of the central notions of the Turkish conceptualization of fractions is carried out by means of everyday language.In the following step, the teacher chooses a similar approach. With the utterance “Yani o yüzden beşte üç oluyo, ama üçte beş, üçten beş...” (Well, therefore five therein three does work, but three therein five, of three five...; score area 64 f.) he gives the fraction that would be correct in connection with the statement (beşte üç – five therein three) and contrasts it to the wrong fraction (ama üçte beş – but three therein five). Afterwards he again reformulates the notion carried out by the wording pattern of fractions by using the ablative case (üçten beş – of three five). The ablative, usually labeling something as a point of departure in a tangible or abstract sense, here is used to express the notion that a certain number of pieces are being extracted from an accumulation of equal pieces. This use of the ablative case is very common in everyday situations where something has to be shared or divided amongst a group of individuals, or where an individual has to choose from an array of possibilities. With the following utterance, he gives an example of just one of these types of situations, again using the ablative case (üç tane arabadan – of three cars) to verbalize the relation between part and whole: “Mesela desem • • sana üç tane arabadan beş tane verecem.” (If I say for example, • • of three cars I give you five.; score area 66 f.). In line with the grammatical structure, the example is chosen from a more or less everyday situation.Regarding the conceptualization of numbers, here, the so-called ablative case carries out a rather concrete idea. Whereas the locative case causes a conceptualization of the numerator and denominator being integrated to a certain degree, the ablative case leads to a delimiting relation between part and whole.In this excerpt, the teacher transfers subject-specific knowledge (here conceptualizations of fractions) into everyday language and everyday experience. By doing so, he shifts the focus of understanding from an academic to a more accessible level and creates a “pivot” (Redder et al. 2018: 50 f.) in the students’ understanding and thus develops the conceptualizations and the respective linguistic means relying on the student’s family language. To help the student conceptually develop and understand the subject matter, the knowledge about problem solving in everyday live is actively put to use, by verbalizing it in the language the students’ usually or often use in these everyday situations. By this approach, the mental concept of the respective mathematical objects is tied to a concrete action, as already pointed out as beneficial for students by Gal‘perin (1989).4.3Analysis 3: German-Arabic Co-TeachingThe next excerpt is taken from a German-Arabic teaching session with two teachers in a co-teaching format: Teacher 2 acts as the main German-speaking teacher. He is experienced in terms of bilingual teaching, but in Turkish-German teaching. Teacher 3 acts as a co-teacher and is fluent in both, German and Arabic, both written and spoken. In the session, three students from Syria are present, but in the following excerpt only Student 6 and Student 7 are speaking.The excerpt of the transcript is taken from the very first session in which one might suspect the students to have troubles adapting to the unfamiliar situation of multilingual teaching with two teachers while at the same time having to adapt to an approach to mathematics that incorporates handling of graphical representations and everyday language resources as a means for conceptual understanding. But contrary to the expectations, the students handled the situation quite well and accepted the Arabic-speaking assistant teacher very fast and referred to her for obstacles in understanding.The students have to solve the following task: ‘One boy, Yassir, wants to share one bar of chocolate with his friends fairly. For this purpose, he creates a spreadsheet that includes fractions and also fraction bars to visualize the fractions, in which he marks the part of the chocolate he would get if he was to share the chocolate among 1, 2, 3 or 4 other children.’ The task is supposed to be solved in two ways: The fraction bars have to be marked correctly and the mathematical expression for the fraction must be given. The students begin by writing down the fractions and then turn to the marking of the bars – the latter being an approach to mathematics they just learned about. As expected, some problems with marking the bars occur: Instead of marking the part of the bar that visualizes the part Yassir would get, the students mark the part that the other children would get. From Teacher 2’s point of view, this is an unexpected and unusual approach but it still shows conceptual understanding, even if not in line with the phrasing of the task. After this was identified and understood – this process takes up quite a lot of time and leads to some confusion amongst the students and the teachers – Teacher 2 tries to dissolve the confusion and wants to make sure that the students solve the task accordingly afterwards. This is where the following transcript starts.source: corpus MuM-Multi II © RedderTeacher 2 admits that the students’ solution is also correct (score area 245 f.) and then wants to make sure the students solve the next task accordingly. However, Student 6 still wonders whether her mathematical solution is correct. Instead of asking the German-speaking Teacher 2, she asks Teacher 3 in Arabic (score area 249). One might interpret this question as an indicator that Student 6 could not follow the slightly confusing utterance of Teacher 2, perhaps even because of the lack of language proficiency. But looking more closely, it is really more of a reinsurance – for affirming of her own solution – that she needs for carrying on with the task and, as can be seen in score area 250 f., also for transferring parts of this knowledge to Student 7 and thus possibly clearing some of his problems in the process. Teacher 3 is in a support role in this section as she follows the discourse and affirms Student 6’s question while in the same course leads her to the correct approach for the next tasks according to Teacher 1’s utterances. Student 6 uses Teacher 3’s affirmation to point to Student 7’s mistakes in his marking of the bar and his fraction in comparison with her own solution – Student 6’s question is therefore a request for the reinsurance before she shows Student 7 his mistakes. This is quite striking as Teacher 2 did not mention the correct solution for the task until that point: The ongoing discourse in German is not about whether the mathematical solution is right or not, it is about the way to get to the solution using fraction-bars and thus, about how to employ graphical representations for mathematical tasks.The students are used to a Syrian educational culture of mathematics that focuses primarily on mathematical procedures and not so much on graphical representations of mathematical operations, as we learned both from discussions with our student assistants from Syria and from analyses of Syrian math books (Redder et al. in press.). Here, they use notwithstanding those representations as a genuine part of solving a mathematical task. Meanwhile, the Arabic language serves them as a shortcut to the correct solution of the fraction and to the part of learning mathematics as they know it. So, whereas Teacher 2 talks about graphical representations, Student 6 is interested in the correct symbolic solution. And as she is already aware that Teacher 2 wants them to use the fraction-bars and discuss the symbolic solution later, Student 6 refers to Teacher 3 in her more familiar language of instruction, Arabic.But there is more to the difference of educational cultures: The practice of Teacher 2 of lettting the students explain their solutions to task – no matter if wrong or right and thus to enable them to discover their mistakes themselves – can be seen a practice that is well established in the German educational culture. This can be seen as a form of “Socratic dialogue” which also proves to be efficient in multilingual constellations (Redder et al. 2018: 94–152). By means of the systematic usage of Arabic, this potential obstacle can be overcome easily. Moreover, it could be seen that Student 6 even made use of this constellation strategically and solve the symbolic part of the task that is more important to her faster than the graphical part that is important for Teacher 2.It could be seen that the acting of Teacher 3 provides the students with an additional resource of understanding through speech actions, namely by simply providing them with the possibility to ask questions concerning the progression of the session in their well-developed classroom and family language when they struggle in understanding Teacher 2. In this very case, Arabic as an available linguistic resource enables a discursive interaction between the students that would otherwise probably not happen. Even more so, having a teacher present that is fluent in the well-known language of instruction can help to avoid misunderstandings and possible frustration that can occur when being confronted with different educational cultures.5DiscussionIn this paper we have illustrated how multilingual profiles can provide a basis for implementing multilingual teaching and learning in subject-matter classrooms as well as for linguistic analyses of multilingual discourses. They can help to differentiate between groups of multilinguals and shed light on the necessity to treat and teach different groups of multilingual students according to their group-specific needs and prerequisites – a necessity that is even more important when it comes to the integration of adolescent migrants. The discourse analytic results can help for a recursive refinement of the multilingual profiles with respect to German as medium of instruction, family language as medium of instruction and the very linguistic quality of subjects’ knowledge. Hence, this concept can both build on and enrich the research on translanguaging pedagogy (e. g. García and Kleyn 2016). Knowledge of the multilingual profile of a certain group and thus their expectations, abilities and presuppositions, enables to take the particular linguistic and mental peculiarities into account and to adapt education accordingly, i. e. by implementing different types of teaching formats.To show this, two groups of multilinguals have been characterized exemplarily: German-Turkish Multilingual Germans and new migrants from Arabic-speaking countries. Two qualitative analyses on bilingual sessions on fractions have illustrated how the linguistic differences between the groups can affect multilingual teaching and learning. In Analysis 2, we have shown how the use of the family language (even if usually not used for teaching and learning) enables a special form of knowledge transfer and acquisition. Drawing on the family language allows the teacher to activate everyday-knowledge and experiences for educational purposes. Utilizing this knowledge can help the acquisition of subject-matter content, such as mathematical conceptualizations, as well as an expansion of the family language to a level appropriate for schools. Including the Multilingual Germans’ family language level seems to lead to empowerment and further inclusion (Barwell 2009; Schüler-Meyer et al. 2019).In the case of new migrants, the analysis of the Arabic-German session in Analysis 3 has shown that other prerequisites have to be met. In addition to the conceptual differences determined by different languages, differences of the educational cultures (to which students are more or less accustomed) can also be taken into consideration as they may cause different expectations on methodological issues. If students don’t manage to cope with these differences, they might get lost in the educational system. Hence, multilingual education that meets these challenges can allow teachers to take students’ prior experiences into account and at the same time to promote the further acquisition of the target-language to an academic level. Therefore, multilingual education can be seen as an integration tool (cf. Rehbein 2013).Our results from the above small-scale study with homogenous groups show that we can shed light on the complexity of the challenges teachers face in classrooms every day, as they are teaching different groups of multilinguals and monolinguals in the same class and a separation of the different groups is not intended in our perspective. Moreover, we see it as beneficial for every student to be in contact with (other) multilingual students and their linguistic and cultural prerequisites. By comparing German-Turkish-speaking Multilingual Germans with new migrants, we have shown that new migrants do not really pose new challenges, but need to be approached slightly different when it comes to successful implementation of multilingual teaching and learning: In the case of German-Turkish-speaking students, Turkish has to be pushed in order to bypass their presuppositions and expectations and to achieve a more balanced multilingualism – at least in a phase of transition from mono- to multilingual teaching. But it seems to be obvious that these observations cannot be transferred to the case of Arabic-speaking new migrants. Here, German has to be pushed without abandoning Arabic. Moreover, Arabic has to be seen and used as both, an additional and foundational resource of teaching and learning and thus for understanding. The adolescent migrants’ prior knowledge, which is learned via and bound in the language(s) of the home country, could be activated by incorporating the language(s) in education in the target country. We are convinced: Even in subjects with – often falsely assumed – low requirements for language, such as mathematics, students can profit from multilingual education. Teachers need to be aware of these possibilities. By approaching their multilingual students with the knowledge of their multilingual profile, the teachers can organize and plan the teaching accordingly and, ideally, in more beneficial ways.6ConclusionThe data we presented in this paper provides brief and specialized insights into possible constellations of multilingual teaching and learning: The teachers in our data were multilingual themselves and, with the exception of one teacher who needed the support of an additional teacher to teach the Arabic-speaking students, thus were able to follow the multilingual discourses of the students. This was a meaningful approach to enable us to understand how the multilingual resources of the students can be activated and put to use for teaching mathematics, but it leads to some restrictions: Of course, it is easier to foster family languages and target languages at the same time, when all participants are able to speak and understand them. But this constellation is more less never the case in a regular classroom. A monolingual teacher can face some difficulties in comparable situations, especially when it comes to the question of assessment of the students’ knowledge presented in a different language. Hence, it is important to create possibilities for the students in which they are allowed to use any language they know without limitations, to enable the students to access their full mental capacities and conceptual knowledge, whilst maintaining a classroom discourse that allows the teachers to assess the students’ knowledge and foster them individually. The effects of this approach are currently under investigation through further discourse analyses (Wagner et al. in press).Looking at Germany and its long history of migration, it becomes obvious that new migrants do not really pose new challenges, but the solutions should be innovative: By employing multilingual teaching and learning. But there is still a lot of work to be done, as our study can only scratch the surface of what a sustainable implementation of multilingualism in accordance with the complex heterogeneity of classrooms can look like. In the next steps it is necessary to look further into the question of how multilingual profiles recursively refined by discourse analysis can help teachers to plan and conduct multilingual teaching formats and, even further, to determine the benefits of multilingual teaching in regular classrooms.

Journal

European Journal of Applied Linguistics – de Gruyter

Published: Mar 4, 2022

Keywords: multilingualism; migration; integration; classroom discourse; functional pragmatics; mathematics; teaching and learning; Arabic; Turkish; discourse analysis

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