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Altres ajuts: EIN2019-103213536 Altres ajuts: PID2019-104964GBI00 Classroom research into mathematics and language has studied issues of context specificity such as cultures of explanation or the impact of language policies on practice. More recently, researchers in the domain have started to study issues of content specificity aimed at performing language-responsive mathematics teaching for the learning of precise mathematical content. Progress in the conceptualization of language as resource for mathematics teaching and learning makes it necessary to strengthen the discussion of the contexts of culture and interaction along with the linguistic demands given by the specificity of the mathematical content at play. In this paper, I introduce a sociocultural framing for a mathematical-linguistic view of grammar as resource with the focus on explicitness in communication. I then report developmental work with two teachers on their teaching of algebraic concepts, and address the question of how to learn to communicate explicit meanings for these concepts in classroom mathematical talk. The structuring principle adopted for this work was to critically distinguish and choose or produce instances of teacher talk that overtly communicated conceptual meaning within the algebra of equations. I conclude with preliminary evidence of the effectiveness of the work with the teachers.

Based on an ethnographic study, we explore the potential of experimenting with multiple languages for number words as part of young children’s mathematical activity. Data from a preschool classroom activity on ‘number words in “other” languages’ exemplify a complex process of discursive identity-work and dialogism amongst children, parents, teacher, and researchers. The focus is on the case of little Mariah, a Pakistani immigrant girl in Greece, who experiences participation by sharing number knowledge in her mother tongue Urdu, and highlights how gendered, racial, or language-related discourses weave her learner identity in a multilingual preschool classroom.

The thinking of language as resource in mathematics education research has been more metaphorical than conceptual so far. This article provides grounds and reasons for the theorization of language as resource. Based on views from sociolinguistics and functional grammar, I propose a theorization that considers the social languages of learners and the systems of language as discursive dialectical sites of potential/actual and shared/non-shared meaning production. I illustrate the analysis of a text of a student group work in order to inform the discussion. The approach to data analysis seeks out tensions between potentially realizable and actual meaning in the immediacy of situations embedded in cultures of school mathematics and the official language of instruction. In the midst of social and personal relationships and diverse experiences in/of the world, language is a shifting resource for the communication of tensions regarding languages of learners and the creation of newer situations toward the production of meaning taken as mathematical and shared.

In the context of refinement of frameworks over the past decades within the domain of mathematics education research on language, the development of more nuanced theories is a challenge. In this issue of ZDM, a number of researchers present their work of exploration and elaboration of theories for the study and understanding of language in mathematics education. Since various relevant frameworks are present in the collection of papers, we use them to consider and evaluate the existing ontology. We aim to answer the following questions: What theories and concepts are visible in the papers? What are the works of some of the authors and terms that seem to be interpreted differently? What does this complexity imply for research in mathematics education? From the answers to these questions, we conclude that the domain can be characterised by its complexity, diversity, and contention. All three phenomena together seem to have the potential to be a strength for the progress of the domain.

The main idea behind the title of this chapter is that there is something about language diversity which is tied to mathematics learning in a way that justifies a detailed investigation. I take the theoretical lens of language-as-resource to examine how certain uses of language and representations of speakers are voiced in ways that positively mediate the emergence and restoration of mathematics learning opportunities. Overall, I frame language as a powerful resource in the mathematics classroom whose resourcing for mathematics learning implies a multiplicity of languages (and, hence, discourses and voices) about language modeling and group identification. This position statement goes beyond dominant ideologies of language. It challenges historically well-established frames for mathematics education research on language and provides new ways to think about language, what we do with it in research and practice, and why.

The data reported in this article come from a large project whose goal was to explore how Latin American students in Catalonia, Spain use their two languages—Spanish and Catalan—to support their learning of mathematics in small groups with other students who are Spanish- or Catalan-dominant. For 5 years, lessons from bilingual mathematics classrooms in three public secondary schools were video-recorded and transcribed. In the presentation of findings, I discuss three language practices that emerged from the analyses of several classroom instances as follows: (1) caution with mathematical vocabulary, (2) invention of terms, and (3) word-for-word translation. One example is chosen to represent each practice and some of its situated effects. The first two examples support the view that the experience of language difficulties, either real or presumed, contributes to generating opportunities that may be beneficial to mathematics learning. The third example, where the focus on the mathematics is hindered, points to a contrasting finding. Unlike other studies in the field, which have reported the difficulties and obstacles that arise in learning and teaching due to bilingualism in the classroom, I propose a change of focus through the conceptualization of language as a potential for thinking and doing, and particularly for learning and teaching mathematics.

The gap between the worlds of academic research and school practice has been treated from a diversity of theories and cultures of mathematical pedagogy (Adler, 2005; Garcia, Sanchez, Escudero, & Llinares, 2006; Jaworski, 1998; Krainer & Zehetmeier, 2013; Lubienski, 2008). In a context in which the study of barriers between research and practice in mathematics teacher education is a major topic, the argument by Kieran, Krainer and Shaughnessy (2013) for more research on how to interact in ways that lead to positive synergies is very relevant:The challenge now for all of us in the international mathematics education community is to consider how further to promote and systematize collaborative research work among teachers, with or without university researchers [. . .] A case can be made that all countries should consider implementing a systematic integration of linked research and practice.

In this article, I explore language identities and processes of negotiation concerning parts of these identities as seen by a group of students from a bilingual mathematics classroom. A collection of 10 students’ individual writings on the questions ‘What language do you use during group work in your mathematics class and why?’ is examined from a socio-political perspective. My data emphasize the importance of addressing the complexity of the identity work that goes on in the students’ texts. Through their writings and despite the perception of limits, students negotiate complementary language identities that are contrary to the established monolingual ideologies in the research context. Students show distinct degrees of agency in their responses as they attempt to produce language identities that are much more complex than those politically ascribed to them.

This article centers on a professional development project with a group of high school mathematics teachers in Barcelona. The eight participating teachers taught in low-income schools with a high percentage of immigrant students. Our model of professional development is based on the involvement of the teachers as co-researchers of their local contexts and practices. In this approach, our concept of social justice is tied to the notion of empowerment, both for teachers and for their immigrant students. Our analysis of data from twelve sessions with the teachers shows the development of a shared awareness of their local situation that leads to their questioning of their practices followed by a reconstruction of those. Teachers worked together to move from talking to action. Our analysis of data from the implementation of one lesson in a classroom shows that action, and illustrates signs of empowerment in the teacher and the students, such as students’ challenging of aspects of the task and taking on a more participatory role and the teacher’s reflection on the overall experience.

This chapter provides the introduction to this ICMI Study 21 volume. It includes: a discussion of the place of this study and its topic within ICME; a discussion of what is meant by the study title; and a brief historical account of research on this topic in mathematics education. The chapter also recounts the various stages of the study, including the development of the discussion document, the study conference, and the preparation of this volume. The latter parts of the chapter include syntheses of some key research ideas emerging from the volume, implications for policy and practice and issues for further research.

This paper provides data from individual interviews conducted with 15 and 16 year‐old non‐immigrant students from a highly multiethnic secondary urban school in Barcelona, Spain. In this school, mixed classrooms (immigrant and local) and small linguistically heterogeneous working groups are frequent in the mathematics lessons. The focus is on the non‐immigrant students’ perspectives on the notion of learning. Findings show that these students interpret certain whole‐class and small‐group interactions among local and immigrant students as not constitutive of learning. In particular, I explore some of the meanings associated with the representation of the multiethnic classroom as a conflictive place for learning.

In this paper we present and exemplify our interpretation of some theoretical constructs that have proved useful to our understanding of the complexity of multicultural mathematics classrooms. Constructs such as culture, cultural distance, cultural conflict and identities-in-construction have oriented our study of the complexity of highly multicultural mathematics classrooms in Barcelona. The purpose of this paper is to discuss how cultural distance arising from the different meanings that students, being local or immigrant, inevitably bring to the mathematics classroom may turn into cultural conflicts when cultural interaction is not facilitated through classroom discourse. The lack of cultural interaction and communication may give rise to strong negative feedings and refusal to participate on the side of the students. Students' nonparticipation can be understood as an active response to cultural distance and negative opinions in order to safeguard the identities they (wish to) construct within a context that they perceive as hostile.

This paper draws on two research studies with similar theoretical backgrounds, in two different settings, Barcelona (Spain) and Tucson (USA). From a sociocultural perspective, the analysis of mathematics education in multilingual and multiethnic classrooms requires us to consider contexts, such as the family context, that have an influence on these classrooms and its participants. We focus on immigrant parents’ perspectives on their children’s mathematics education and we primarily discuss two topics: (1) their experiences with the teaching of mathematics, and (2) the role of language (native language and second language). The two topics are explored with reference to the immigrant students’ or their parents’ former educational systems (the “before”) and their current educational systems (the “now”). Parents and schools understand educational systems, classroom cultures and students’ attainment differently, as influenced by their sociocultural histories and contexts.

Drawing on socio-cultural theory, we understand the norms regulating the practices within the mathematics classroom as resulting from the social representations of the socially dominant groups and of the school culture related to what constitutes learning mathematics. Immigrant studients, having their own personal histories as members of particular social groups, and having been in school traditions other than the one predominant in the host society, have their own images of what mathematics in school is about. Individuals interacting in the classroom are all re-interpreting the different episodes from the perspective of the social representations of the larger groups with which they identify themselves. In multiethnic classrooms different re-interpretations of the same norms clash. The lack of negotiation gives rise to obstacles to immigrant students’ participation in the mathematical conversations and, therefore, interferes with the students’ learning process.

We analyse social interactions during the first days of class in a secondary mathematics classroom (15 and 16-year-olds) with a high percentage of immigrant students. Our analyses show the co-existence of different models for both the interpretation and the use of classroom social norms and socio-mathematical norms. Valorising some behaviours over others appears as part of the discursive practices of mathematics classrooms. Local and immigrant students are not expected to behave in the same way, nor are they treated in the same way. The teacher and some students, who are familiar with the prevailing norms, cancel certain norms for a while in such a way that some immigrant students are excluded from fully participating in the mathematical discussion.

In the article originally published in 2005 we addressed immigrant parents’ perspectives of the teaching of mathematics in two geographic contexts, Barcelona (Spain) and Tucson (USA). The article illuminates two specific aspects of marginalization of those who move to a new country with hopes of a better life, including education, for their children. Since then we have expanded upon our work in these two specific aspects—parents’ perceptions about the teaching and learning of mathematics and the role of language in mathematics instruction. We argue that these two issues are central to the marginalization of immigrant parents’ and therefore, their children in the area of mathematics education. Therefore it is critical for educators to understand and address these issues to improve the mathematics education of immigrant students.

In his chapter, Barwell draws on the Bakhtinian notion of co-existing voices, heteroglossia, to point to the experience of four tensions in linguistically diverse mathematics classrooms, namely: 1) school versus home languages, 2) formal versus informal language in mathematics, 3) language policy versus mathematics classroom practices, and 4) a language for learning mathematics versus a language for getting on in the world. To further explore Barwell’s points, I bring up the metaphor of orchestration. My idea of orchestration refers to the manner in which various voices are individually used to produce coordinated results. As in the case with instruments in an orchestra, the final production requires successful individual practices with instruments that successfully interact with each other. My main argument here is that heteroglossia needs adequate practical orchestration, on the part of all members in a class: they all need to learn what the others can and cannot do, what distributions of work sound more adequate at each time, why is it that some of the ideas and contributions sound different depending on who introduces them, etc. By interpreting orchestration as something that includes all participants, not only the actions and choices by the teacher, it becomes clearer that students and teachers have lots in common.

We understand the schooling of the immigrant children as a transition process, because when they arrive into a new country they have to cope with the many changes involved in moving from one culture to another. In particular, they have moved from one school culture into another, if they have attended school, or perhaps they have moved from a ‘no-schooling’ culture into a school culture. We regard immigrant students as having the need to build a bridge from the meanings of their initial situation to those of the present one. All of them have the right to be offered the opportunity to develop their potentialities to the full, regardless of their country of origin or the reasons for their migration. We believe that school should contribute to help them create a continuity between their home and the host culture’s meanings. From that point of view, and not avoiding the researchers’ commitments to society and particularly to teachers and students, the goal of our study is to find teaching approaches that contribute to co-construct the students’ transition in order to make it as smooth as possible. We say ‘co-constructing the transitions’ because a one-sided construction would not be complete, since the meanings a child brings to a situation, as Bruner states, ‘are not to his own advantage unless he can get them shared with others’ (1990, p. 13). Everyone involved in the dynamics of the mathematics classroom has to participate in the negotiation of the meanings associated with the diverse situations, in order to ensure a real sharing of them (Kao & Tienda, 1998).

Este documento se incluye en una investigación cualitativa llevada a cabo en un aula con estudiantes minoritarios y en desventaja económica de entre 15 y 16 años. La investigación intenta desarrollar un enfoque inclusivo para integrar las perspectivas cognitiva y emocional a fin de mejorar la comprensión de los procesos de construcción de significados en la microcultura del aula. Suponemos que las aulas multiculturales promueven más evidencia sobre la variedad de significados y valores relacionados con la práctica matemática. Nuestra intención es pensar en las posibles interferencias en el aprendizaje que pueden derivarse de las diferentes interpretaciones de las normas matemáticas en el aula. Los resultados de nuestros análisis deberían ser una contribución para una mejor comprensión de este fenómeno.

KEYWORDS Translation. Interpretation. Representation. Multiplied Numbers. Language Structure ABSTRACT This paper reports on data collected from African language-speakers in South Africa whose experience of mathematics teaching takes place in a language that is not their own. The work is theoretically underpinned in the social and situated perspectives of mathematics learning. Major findings from the case of two African language- speakers reported here provide a strong argument for the consideration of the role and structure of language in the teaching and learning of multiplication to African speaking learners in the multilingual classroom. The importance of paying attention to the difference that diverse language speakers attach meaning to multiplied numbers is highlighted in order to ensure that their representation in not lost in the translation. The paper also suggest alternative ways of expressing multiplied numbers in African languages in ways that will not compromise their understanding of this operation, particularly those involving algebraic terms.

This paper is about how immigrant bilingual students use their languages in the learning of mathematics. Our research has been with immigrant bilinguals in Catalonia, Spain, who arrived at a young age from SouthAmerican countries. We use a critical sociolinguistic approach, which draws on social theory in the analysis of how language is involved in the construction of teaching and learning opportunities. Our data point to the differences in the ways that the Spanish dominant bilingual students use their two languages during their engagement in mathematical activity. The shifts from Catalan to Spanish, and from Spanish to Catalan, coincide with shifts in the complexity of the students’ mathematical practices. The students tend to use the two languages for different purposes, depending on the complexity of the mathematical practices, and in relation to different social settings that coexist within the classroom. What does it mean to learn mathematics in a language that is not your first language in a country that is not your own? This is the situation in many immigrant bilingual mathematics classrooms in Catalonia, Spain. A majority of immigrant students in these classrooms have Spanish as a first language. However, they learn mathematics in Catalan, which is the official language for learning and teaching mathematics in Catalonia. How do these Spanish dominant bilingual students use languages during mathematics teaching and learning in Catalan classrooms? Do they switch languages during mathematical activity? If so, what are some of the factors that promote their language switching within the context of specific lessons? In this paper we explore those questions. We do this by drawing on a wider study involving immigrant bilingual children attending a Catalan school who were either born in Catalonia or went there at a young age from South-American countries such as Ecuador, Bolivia, Peru and Colombia. Our analysis highlighted two recurrent themes in regard to which language was used by the students: 1) the impact from acquiring specific vocabulary in the second language; and 2) the development of mathematical argumentations in the first language. We argue that the shifts from Catalan to Spanish coincided with shifts in the complexity of the students’ mathematical practices. The students tended to use the two languages for different