Núria Planas

TEACHING MATHEMATICS IN MULTILINGUAL CLASSROOMS

In this paper we present the way in which language issues have become a relevant factor in research which aims to study the socio-cultural aspects of mathematics education in classrooms with a high percentage of immigrant students. Our research on language issues focuses on two aspects, namely the language as a social tool within the mathematics classroom and the language as a vehicle in the construction of mathematical knowledge. We introduce our problem within this area and provide a rationale for our research methodology, not avoiding its drawbacks,but rather giving examples of the kinds of difficulties we encountered. The paper highlights the integrated nature of the social, cultural and linguistic aspects of mathematics teaching and learning, and illustrates the fact that, even if the mathematical language can be considered universal, the language of ‘doing mathematics within the classroom’ is far from being universal.

Bilingual Students using their Languages in the Learning of Mathematics

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 South-American 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.

Modelo para el análisis didáctico en educación matemática

Resumen La finalidad de este artículo es presentar la viabilidad de un modelo teórico para el análisis de procesos de enseñanza y aprendizaje de las matemáticas. Dicho modelo contempla cinco niveles de análisis, los cuales son aplicados conjuntamente a un episodio de clase. Este modelo se ha elaborado para describir (¿qué ha ocurrido aquí?), explicar (¿por qué ha ocurrido?) y valorar (¿qué se podría mejorar?) procesos de instrucción en el aula de matemáticas. Nos basamos en una síntesis teórica de aspectos del enfoque ontosemiótico del conocimiento y la instrucción matemática, que venimos desarrollando desde hace una década. Aunque algunas partes del modelo son específicas de la actividad matemática, investigadores de otras áreas educativas pueden adaptarlas de modo que resulten eficaces en el análisis didáctico de otros tipos de prácticas escolares. El principal resultado esperado de la aplicación del modelo es llegar a una valoración fundamentada de la idoneidad didáctica de procesos de instrucción.

Immigrant Parents' Perspectives on their Children's Mathematics Education

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.

Immigrant Children Learning Mathematics in Mainstream Schools

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).

Social representations as mediators of mathematics learning in multiethnic classrooms

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.RésuméPartant des théories socioculturelles, nous interprétons les normes régulant les pratiques dans les cours de mathématiques comme étant en relation avec les représentations sociales des groupes sociaux dominants et avec la culture de l’école concernant ce qui constitue l’apprentissage des mathématiques. Ayant leurs propres histoires personnelles en tant que membres de certains groupes sociaux, et ayant eu des traditions scolaires différentes de celle qui prédomine la culture d’accueil, les élèves immigrants ont leurs propres images de ce que sont les mathématiques scolaires. Les individus en interaction dans la classe interprètent les différents épisodes sur la base des représentations sociales des groupes avec lesquels ils s’identifient. Dans les classes multiéthniques, différentes réinterprétations d’une même norme entrent en collision. L’absence de négociation fait obstacle à la participation des élèves immigrants dans les conversations mathématiques et ainsi interfere avec les processus d’apprentissage des élèves.

Are Different Students Expected to Learn Norms Differently in the Mathematics Classroom

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.

Mathematical Learning in a Context of Play.

In this article we analyse a didactical situation centred on the creation and use of a symbolic play environment in a class of pupils aged five and six years‐old. The main source of data for this paper comes from an experimentation planned in relation to the following research question: does symbolic play in simulated contexts help pupils to increase their mathematical activity in preschool learning? We draw on the sociocultural teaching and learning theories inspired by Vygostsky. We argue that the creation of and participation in a simulated context in classroom play is an adequate starting point for working on situations of social interaction and for promoting a joint construction of mathematical knowledge. The findings show the evolution of the pupils’ actions during the symbolic game and the progressive incorporation of concrete arithmetical contents into their mathematical thinking. RÉSUMÉ: Dans cet article, nous analysons une situation didactique centrée sur la création et l’utilisation d’un environnement de jeu symbolique dans une classe d’enfants âgés de cinq à six ans. La principale source de données provient d’une expérimentation conçue pour répondre à la question de recherche suivante: est‐ce que le jeu symbolique, dans des contextes de simulation, aide les élèves à accroître leur activité mathématique au sein des apprentissages préscolaires? Nous nous appuyons sur les théories socioculturelles de l’apprentissage et de l’enseignement, inspirées par Vygotsky. Nous avançons que la création et la participation à un contexte de simulation en classe constituent un point de départ adéquat pour travailler sur des situations d’interaction sociale et pour promouvoir une construction conjointe de connaissances mathématiques. Les résultats montrent l’évolution des actions des élèves au cours du jeu symbolique et l’incorporation progressive de contenus arithmétiques concrets dans leur pensée mathématique. ZUSAMMENFASSUNG: In diesem Beitrag wird eine didaktische Situation analysiert, die sich auf die Schaffung und Nutzung einer Umgebung für symbolisches Spiel in einem Klassenzimmer für fünf und sechs Jahre alte Schulkinder zentriert. Die Hauptdatenquelle dabei stammt aus einer Versuchsdurchführung, die in Hinsicht auf folgende Forschungsfrage geplant wurde: Hilft symbolisches Spiel in simulierten Kontexten Schulindern dabei, ihre mathematischen Aktivitäten im Vorschul‐Lernen zu steigern? Wie beziehen uns auf die von Vygotski angeregte Theorie soziokulturellen Lehrens und Lernens. Wir argumentieren, dass die Schaffung von und Partizipation in einem simulierten Kontext im Spiel innerhalb des Klassenzimmers ein angemessener Ausgangspunkt für das Arbeiten an sozialen Interaktionssituationen und für die Förderung einer gemeinsamen Konstruktion mathematischen Wissens ist. Die Ergebnisse zeigen die Entwicklung der Handlungen der Schulkinder während des symbolischen Spiels und die fortschreitende Einarbeitung konkreter arithmetischer Inhalte in ihr mathematisches Denken. RESUMEN: En este artículo analizamos una situación didáctica centrada en la creación y uso de un medio de juego simbólico en una clase de alumnos de 5 y 6 años de edad. La fuente principal de información para este artículo proviene de un experimento planificado en relación a la siguiente pregunta: ¿Ayuda el juego simbólico en contextos simulados a mejorar la actividad matemática en el aprendizaje preescolar? Partimos de teorías de enseñanza y aprendizaje inspiradas en Vygostsky. Argumentamos que la creación y participación en un contexto simulado en el juego de la sala de clases es un punto de partida adecuado para trabajar con situaciones de interacción social y para promover la construcción conjunta del conocimiento matemático. Los resultados muestran la evolución del accionar de los alumnos durante el juego simbólico y la incorporación progresiva de contenidos aritméticos concretos en su pensamiento matemático.

Language identities in students’ writings about group work in their mathematics classroom

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.

Understanding Interruptions in the Mathematics Classroom: Implications for Equity.

The article is based on an extensive microethnographic study (Planas, 2001) that was focused on students aged 15–16 years who exhibited a high number of interruptions in their participation in the mathematics classroom. Our research points to the importance of considering how the students construe normative meanings for the classroom episodes, and how they value others and the knowledge construed. We argue that some interruptions in the students’ participation can be understood as an active contestation to the classroom norms and to the perceived valorisations. Broadening the understanding of the learning opportunities for all the students requires studying further how the classroom sociocultural context and participants’ valorisations mediate both the participation processes and the construction of mathematical knowledge.