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Background: The focus on translanguaging practices in multilingual classrooms can be seen, by and large, as responding to risks of violence entailed in diverse contexts of language use, including the teaching and learning of mathematics. However, the practice of translanguaging alone cannot counteract the hegemonic authority of our relation to language curricula being present through interactions among teachers, students, and researchers, as well as material resources. Purpose: Drawing on Bakhtin’s philosophy of language, we discuss dialogicality as a critical and democratic organizing principle for the pervasive polyphony that characterizes every utterance constituting heteroglossia. Dialogicality reconstitutes our relation to language through the “other” and the need to see any utterance as a nonteleological process among subjects and objects. As such, the aim is to explore how acts of dialogicality may address the potential risks of onto/epistemic violence in translanguaging practices. Focusing on either emergent or orchestrated translanguaging in three European states: Greece, Catalonia and Sweden, we discuss how dialogicality allows for alternative accounts of language use in complex classroom events. Method: Methodologically, we start by encountering the sociopolitical context of monolingual and monologic curricula in Europe, where the three cases we theorize take place, along with our considerations for dialogicality in the realm of translanguaging. Our theorizing-in-practice unfolds a double effort in reading. First, what can we read today as risks of onto/epistemic violence in each of these cases? And second, what is the potential of dialogic translanguaging across the cases and within the boundaries of state monolingual policy and monologic discursive culture of school mathematics? Findings: The present article contributes by discussing dialogicality as a relational onto/epistemology toward addressing translanguaging practices. Concerning the first question, our theorizing-in-practice shares evidence of the inevitable presence of onto/epistemic violence in every utterance. The limited scope of a crude mathematisation process through language appears continuously in mathematics classrooms, serving to place either the object or the subject into fixed narratives. Regarding the second question, our dialogical reading of translanguaging denotes the importance of the importance of minor responding(s) to such moments of violent risk. We understand them as “cracks” in the authoritative status of monolingual and monologic mathematics curricula; we argue that such minor, yet crucial, cracks are of great significance for creating acts of dialogicality from “below,” disrupting the hegemonic authority of an assumed neutral mathematical language. Conclusions/Recommendations: The risk of onto/epistemic violence is inevitable in any discursive and embodied encounter in multilingual mathematics classrooms, including the translanguaging practices. The study suggests that acts of dialogicality become minor responses to violence in ways that both counteract oppressive monologic discourse and open toward a relational onto/epistemology with mathematics, children, teachers, material resources, and researchers. Remembering how Bakhtin insisted that “language is never unitary” and “dialogue” is not a panacea, we emphasize the need for a continuous focus on creating acts of dialogicality with language and discourse.

Speculations about the relation between mathematics and language are age old and ever popular. Galileo famously claimed that the universe is written in mathematical language. There is no lack of cl...

Altres ajuts: acords transformatius de la UAB Altres ajuts: the South African Research Chairs Initiative of the Department of Science and Technology and the National Research Foundation, Grant no. 71218 at the University of the Witwatersrand; and the School of Education, University of Malawi. During the last decades, the study of how learners and teachers of mathematics use the resource of language has contributed to our understanding of mathematics teaching and learning in a variety of classrooms and cultures. Developmental work with mathematics teachers on the particular resource of mathematics teaching talk is more recent. In order to explore responses related to the importance of this talk, in this paper we consider three sites of practice in mathematics education-research, professional development and teaching-and illustrations of data from or about them, including studies from the literature, and work with secondary school mathematics teachers in Catalonia-Spain and Malawi around the teaching of angles. We argue that tensions permeate these sites of practice when a focus is placed on word use, specifcally the practices of naming and explaining, in mathematics teaching talk. We conclude that the importance of mathematics teaching talk is construed through tensions with other resources in language and teaching. Tensions specifcally appear in the realisation of mathematics teaching talk as mediational in the work with mathematics teachers on their classroom teaching.

Últimamente se viene produciendo un creciente énfasis en aspectos socioculturales y afectivos de la educación matemática. Este artículo presenta un enfoque inclusivo a estos aspectos para mejorar la comprensión del problema de la alternancia entre participación y no-participación en el aula de matemáticas. Se describe una metodología cualitativa microetnográfica basada en tres categorías: a) la cultural, relativa a diferencias en la interpretación de las normas del aula; b) la social, relativa a valoraciones dadas a las diferentes interpretaciones; y c) la afectiva, relativa a respuestas emocionales dadas por los alumnos a normas y valoraciones. Para probar la adecuación de un enfoque inclusivo al problema mencionado, se exponen con detalle métodos interpretativos que han sido usados en Planas (2001). Recently, there has been an increasing emphasis on socio-cultural and affective issues in mathematics education research. This paper presents an interrelated approach to these issues in order to better understand the alternance between participation and non-participation in the mathematics classroom. The methodology exposed is micro-ethnographic and based on three main categories: a) the cultural, related to differences in the interpretation of classroom norms; b) the social, related to valorizations given to different interpretations; and c) the affective, related to emotional responses given by the students to both norms and valorizations. Some interpretive methods that have been used in a recent work (Planas, 2001) are shown in detail as a way to prove the adequacy of the interrelated approach.

Altres ajuts: Agencia Nacional de Investigación y Desarrollo / Beca Chile Magíster Profesionales de la Educación 77200019 En este artículo resumimos un estudio exploratorio sobre el conocimiento de contenidos de la materia de educación matemática en un entorno de formación inicial de profesorado; desde nuestro posicionamiento sociocultural, nos fijamos en el papel mediador de las lenguas matemáticas utilizadas en la instrucción y en los materiales curriculares, y escogemos contenidos relativos a lenguas matemáticamente relevantes para la enseñanza y el aprendizaje de la relación entre área y volumen. Con base en respuestas a un cuestionario, primero examinamos qué saben o anticipan las futuras maestras acerca de la función de la lengua en la enseñanza y el aprendizaje del contenido matemático específico. Luego amplificamos el análisis con entrevistas selectivas guiadas por respuestas al cuestionario. Los resultados muestran estudiantes con una comprensión débil de contenidos de la materia que habrán de enseñar -conceptos de área y volumen-, a la vez que iniciándose en la construcción de contenidos sobre cómo enseñar la materia -lenguas matemáticas para enseñar la relación entre área y volumen. In this article, we report an exploratory study about the knowledge of mathematics education subject content in a setting of education preservice training; within our sociocultural positioning, we focus on the mediating role of mathematical languages used in instruction and curricular material, and choose content relative to mathematically-relevant languages for the teaching and learning of the relationship between area and volume. Based on responses from a questionnaire, we first examine what primary school student teachers know or anticipate of the function of language when teaching and learning the specific mathematical content. We then amplify the analysis by means of selective interviews guided by responses to the questionnaire. Our results show student teachers with weak understanding of contents of the subject to be taught -concepts of area and volume- while becoming initiated in the construction of contents on how to teach the subject -mathematical languages for teaching the area-volume relationship.

Varios ejemplos extraídos del aula demuestran que hacer matemáticas es hablar, escribir, leer y escuchar matemáticas de forma combinada con hablar, escribir, leer y escuchar lengua. Comprender la complejidad lingüística que entrañan las matemáticas puede contribuir a entender mejor las dificultades de su aprendizaje. Decía el matemático Henri Poincaré que las matemáticas no son sino un lenguaje bien hecho. Aun así, en el ámbito escolar continúa manteniéndose la distinción entre Lengua y Matemáticas, sobre todo en las edades más avanzadas (afortunadamente, los currículos de los más pequeños se refieren de forma amplia al aprendizaje global de lenguajes). El distanciamiento institucional entre la enseñanza de las Matemáticas y la enseñanza de la Lengua tiene varios orígenes y se argumenta de modos muy diversos. Uno de los argumentos recurrentes es la universalidad del lenguaje matemático en comparación con la arbitrariedad atribuida a los denominados lenguajes ordinarios. Sin embargo, a pesar de los aspectos universales en el código de las matemáticas, el lenguaje matemático es, en la práctica, un lenguaje mixto con elementos de los lenguajes ordinarios. Para entender significados expresados por medio del lenguaje matemático, éstos se tienen que interpretar desde fórmulas lingüísticamente híbridas de conocimiento que conjuguen vocabulario específico, vocabulario especializado, sintaxis específica y sintaxis especializada. Pero ¿qué se entiende por cada una de estas expresiones? Los ejemplos que siguen contribuyen a comprenderlas y a situarlas en el contexto de la enseñanza y el aprendizaje de las matemáticas en la escuela

Explicamos el desarrollo y algunos resultados de una investigación en un aula de matemáticas de una escuela que acoge estudiantes sordos en Bogotá, Colombia. Examinamos la actividad matemática en un grupo de estudiantes con distintos grados de compromiso auditivo durante la resolución de una tarea aritmética. Con base en el análisis del video de clase y de transcripciones de momentos de la actividad, generamos tres temas que informan sobre aspectos comunicativos y matemáticos del trabajo en el grupo, que son además aspectos constatados para otros grupos y sesiones de clase. Los temas son: 1) referencia al contexto extra-matemático del enunciado; 2) uso tentativo de razonamientos inductivos y deductivos; y 3) ambigüedad conceptual y léxica con vocabulario técnico. A raíz de la discusión de los temas, señalamos implicaciones para la enseñanza de las matemáticas con estudiantes sordos y oyentes We explain the conduction and some results of an investigation in a mathematics class of a school for deaf students in Bogotá, Colombia. We examine the mathematical activity within a group of students, with different levels of auditory processing, during their resolution of an arithmetic task. Drawing on the analysis of the video and transcripts of some moments of the activity, we generate three themes regarding communicational and mathematical issues of the work in the group, which in turn have been found for other groups and lessons. The themes are: 1) reference to the extra-mathematical context of the wording; 2) tentative use of inductive and deductive reasoning; and 3) conceptual and lexical ambiguity around technical vocabulary. From the discussion of the themes, we come to implications for mathematics teaching to deaf and hearing students.

This chapter provides a commentary on multilingual mathematics classroom research over the last two decades in order to look toward the next decades with a focus on issues of policy and practice. I select some of the theoretical nuances and concerns that have shaped the domain with respect to the critical relationships between: (1) monolingually oriented educational policies and progress in multilingual mathematics classroom research; and between (2) this progress and its implications for mathematics teacher education policies and pedagogies. To this end, I undertake a threefold interpretation of progress in the research domain. I argue that three meta-theoretical concerns have challenged, not without frictions and back-and-forth fluctuations, monolingually oriented policies, practices, and theories. I start with domain research grounded on language as tool of communication and on codeswitching as encoder of accurate meaning in multilingual mathematics teaching and learning. I follow with research that interrogates the ideal of meaning accuracy, and then end with the most recent line of translingual domain research with implications for the broader field and the work of teacher educators and researchers.

La multiculturalidad en aumento en nuestras aulas es una realidad que exige investigar en búsqueda de un currículo integrador y de un modelo metodológico adecuado para todos. Cualquier alumno, sea cual sea su procedencia cultural, posee en potencia recursos y estrategias para enfrentarse a problemas y situaciones matemáticas. La legitimación del conocimiento matemático de origen no escolar favorece la interpretación de las matemáticas como producto cultural. Por otro lado, la aceptación de valores y expectativas asociados a las matemáticas y un enfoque 'enculturizador' en el aula repercuten positivamente en todos los alumnos independientemente del grupo cultural al que pertenecen

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.

La práctica de argumentación matemática es parte esencial de la formación de los estudiantes en las distintas etapas escolares y, por tanto, también debe ser tenida en cuenta en la formación de los futuros maestros. En este escrito mostramos datos sobre algunas de las carencias en el conocimiento práctico y teórico de la argumentación matemática en un pequeño grupo de estudiantes de Titulaciones de Magisterio. Estos datos nos llevan a reflexionar sobre las implicaciones que las dificultades de los maestros tienen en el aprendizaje de sus alumnos The practice of mathematical argumentation is a key component in the students' development during their different school periods. Hence, it needs to be considered in the future teachers' academic development. In this text we draw on data concerning the lack of practical and theoretical knowledge on the notion of mathematical argumentation in a small group of students from a primary teacher education grade. This data leads to further reflection on some of the implications that the teachers' difficulties may have on their students' learning

En el marco del consumo responsable, la educación matemática juega un papel fundamental. Esta es la premisa que guía dos experiencias llevadas a cabo en aulas de ESO del IES Ramón Casas i Carbó, en Palau-solitá y Plegamans (Barcelona). En una de ellas se plantean cuestiones sobre los mensajes matemáticos de anuncios de automóviles con la temática medioambiental de fondo; en la otra, se estudian dos envases en los que se comercializan un mismo producto. Ambas experiencias tienen en común el que : están relacionadas con situaciones de contexto real y facilitan conexiones entre contenidos matemáticos y la Educación para el Consumo. Cataluña Madrid (Comunidad Autónoma). Servicio de Formación del Profesorado. CRIF Las Acacias; Calle General Ricardos, 179; 28025 Madrid; Tel. +34915250893; Fax +34914660991; SRPPIDE@madrid.org ESP

Se presenta una actividad que pretende desarrollar el pensamiento crítico en los alumnos a través de la comparación de distintos productos denominados light. Esta actividad tiene lugar en el aula de matemáticas y pretende que los alumnos aprendan a distinguir entre opiniones y razonamientos, y que a su vez desarrollen razonamientos progresivamente más profundos, precisos y claros, incluso llegando a cuestionar lo que presuponen, hasta el punto de plantear objeciones. Cataluña Madrid (Comunidad Autónoma). Servicio de Formación del Profesorado. CRIF Las Acacias; Calle General Ricardos, 179; 28025 Madrid; Tel. +34915250893; Fax +34914660991; SRPPIDE@madrid.org ESP

Los procesos de aprendizaje y los de construcción de identidad son realidades distintas e inseparables. La educación se convierte en un recurso positivo para las personas cuando es capaz de conjugar ambos procesos de modo que avanzar en unos también suponga avanzar en los otros. En el caso de los alumnos inmigrantes, las dificultades de adaptación a una nueva cultura escolar acostumbran a complicar los procesos de construcción de su identidad grupal e individual.

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.

This chapter argues that the progress of mathematics education and language research is taking place through a complex expansion rather than an overthrow of the linguistic paradigm, with an increase in the scope of the domain and in the spread of cultural and social claims. It addresses the following questions: What is the scope of the research on mathematics education and language? How can we map and link the newer approaches in the domain of mathematics education and language to classical approaches? What has been achieved in the last two decades of research? The chapter analyses research reported at Congress of European Research in Mathematics Education (CERME) since 1998 as a benchmark for assessing the phenomenon of increasing complexity as well as the relationship between continuity and complexity in the European Society for Research in Mathematics Education (ERME) domain.

This study explores how a teacher’s use of revoicing promotes students’ mathematical thinking and, more generally, mathematical learning opportunities. We analyzed four lessons where 12-year-old students solved geometry problems. We identified episodes that illustrate how the teacher’s actions supported students’ explanations during mathematical discussions. In this chapter we show two examples, from one of the lessons, where the teacher’s use of revoicing created spaces where students strengthened their understanding of the concept of distance between two points and its relation with the Pythagorean Theorem. Our theoretical approach to revoicing leads us to distinguish and examine three dimensions: linguistic, discursive and mathematical. The integrated view of such dimensions serves to find emergent relationships among talk, classroom discourse, and learning opportunities.

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.

We discuss language diversity in mathematics education research by considering the move from a view of language as representation that strives to correlate concepts, ideas, codes and signs towards addressing the representation politics of language. Language as representation of mathematics has framed the discursive construction of language diversity over the years in published research in our field. We argue that the representation politics of language as grounded in cultural and postcolonial studies enables us to see the meanings attributed to language diversity as resulting from a complex 'circuit of culture' in the realm of global and local identity politics. Three questions help us in this endeavour: (1) What are assumed as commonly shared meanings about language diversity? (2) How do they become present in prevailing discourses about the languages of mathematics, teachers and learners? (3) How may a view of language diversity as part of the 'circuit of culture' disturb the normative presence of such assumptions?