Núria Planas | Universitat Autònoma de Barcelona (original) (raw)
Books by Núria Planas
Equity in mathematics education, 2019
For the past decade reform efforts have placed importance on all students being able to participa... more For the past decade reform efforts have placed importance on all students being able to participate in collaborative and productive mathematical discourse as an essential component for their learning of mathematics with deep conceptual understandings. In this book our intent is to support mathematics education researchers, teacher educators, teachers and policy makers in providing positive solutions to the enduring challenge in mathematics education of enabling all participants including diverse students to equitably access mathematical discourse. By diverse learners we mean learners who are minoritized in terms of gender, disability, or/and social, cultural, ethnic, racial or language backgrounds. We aim to increase understanding about what it means to imagine, design and engage with policy and practice which enhance opportunities for all students to participate in productive mathematical discourse. In widening the lens across policy and practice settings we recognize the interplay between the many complex factors that influence student participation in mathematics. The various chapters tell practical stories of equitable practices for diverse learners within a range of different contexts. Different research perspectives, empirical traditions, and conceptual foci are presented in each chapter. Various aspects of diversity are raised, issues of concern are engaged with, and at times conventional wisdom challenged as the authors provide insights as to how educators may address issues of equitable access of minoritized learners to the mathematical discourse within settings across early primary through to high school, and situated in schools or in family and community settings.
This book examines multiple facets of language diversity and mathematics education. It features r... more This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapter draws on research from two or more countries to illustrate important research findings, theoretical developments and practical strategies.
UNIÓN, una revista consolidada, Jan 1, 2008
Page 251. Diciembre de 2008, Número 16, páginas 251-253 ISSN: 1815-0640 L i b r o s L i b r o s L... more Page 251. Diciembre de 2008, Número 16, páginas 251-253 ISSN: 1815-0640 L i b r o s L i b r o s L i b r o s L i b r o s Matemática inclusiva: propuestas para una educación matemática accesible Autor: Àngel Alsina y Núria ...
Articles -English by Núria Planas
ZDM Mathematics Education, 2022
During the last decades, the study of how learners and teachers of mathematics use the resource o... more 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, specifically 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 specifically appear in the realisation of mathematics teaching talk as mediational in the work with mathematics teachers on their classroom teaching.
In the context of refinement of frameworks over the past decades within the domain of mathematics... more 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.
We discuss language diversity in mathematics education research by considering the move from a vi... more 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? Keywords Mathematics education research · Language · Language diversity · Politics of representation · Cultural and postcolonial studies · Circuit of culture
The thinking of language as resource in mathematics education research has been more metaphorical... more 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 this paper, we expand our prior work on mathematics education in contexts of language diversit... more In this paper, we expand our prior work on mathematics education in contexts of language diversity by elaborating on the three perspectives on language described by Ruiz (NABE J 8(2):15–34, 1984): language-as-right, language-as-resource, and language-as-problem. We illustrate our arguments with data taken from research contexts in Catalonia-Spain and South Africa. In these two parts of the world, the language policy in education has long been an issue, with a monolingual orientation that values one language (i.e., Catalan in Catalonia and English in South Africa) over others. Throughout the introduction of specific examples of policy documents, classroom practices, and participants’ reports, our main point is that the right of using the students’ languages makes sense because it is itself more than an intrinsic human right; it is an option that potentially benefits the creation of mathematics learning opportunities. Especially for the instances of classroom practices, our examples can be considered as representative in that they point to a common situation in our data: despite the fact of the language of learning and teaching being fixed, there is room for the learners and the teacher to take or react to a decision on what language to use, with whom, and how in concrete moments of the interaction. However, on the basis of our studies and drawing on the literature in mathematics education and language diversity, we argue that language rights are not sufficiently connected to language as a pedagogical resource. The enactment of these rights is still contributing in many ways to the social and political construction of problems concerning the role of certain languages in classroom interaction. We conclude the paper by discussing some possibilities for framing language as a resource that provide effective support to all students’ learning of mathematics.
The data reported in this article come from a large project whose goal was to explore how Latin A... more 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.
In this article we reflect on the learning of mathematics in bilingual settings from a social and... more In this article we reflect on the learning of mathematics in bilingual settings from a social and a political perspective. In particular we highlight two concepts that are key to our work: language-as-resource and language-as-political. To do so, we draw on classroom data from students of Mexican origin in Tucson, USA, and students from Latin America in Barcelona, Spain. The language policies in our contexts share a message of privileging the language of instruction (English or Catalan) over other languages. Our analysis of the two sets of data points to differences in the mathematical participation of students on the basis of which language they use. We develop the argument that, even if languages other than Catalan and English are accepted and certain pedagogies may be close to a language-as-resource approach, the use of the students' languages is politically mediated in such a way that its pedagogical value (as a medium of communication and learning) is not always taken into account in the bilingual mathematics classroom.
Equity in mathematics education, 2019
For the past decade reform efforts have placed importance on all students being able to participa... more For the past decade reform efforts have placed importance on all students being able to participate in collaborative and productive mathematical discourse as an essential component for their learning of mathematics with deep conceptual understandings. In this book our intent is to support mathematics education researchers, teacher educators, teachers and policy makers in providing positive solutions to the enduring challenge in mathematics education of enabling all participants including diverse students to equitably access mathematical discourse. By diverse learners we mean learners who are minoritized in terms of gender, disability, or/and social, cultural, ethnic, racial or language backgrounds. We aim to increase understanding about what it means to imagine, design and engage with policy and practice which enhance opportunities for all students to participate in productive mathematical discourse. In widening the lens across policy and practice settings we recognize the interplay between the many complex factors that influence student participation in mathematics. The various chapters tell practical stories of equitable practices for diverse learners within a range of different contexts. Different research perspectives, empirical traditions, and conceptual foci are presented in each chapter. Various aspects of diversity are raised, issues of concern are engaged with, and at times conventional wisdom challenged as the authors provide insights as to how educators may address issues of equitable access of minoritized learners to the mathematical discourse within settings across early primary through to high school, and situated in schools or in family and community settings.
This book examines multiple facets of language diversity and mathematics education. It features r... more This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapter draws on research from two or more countries to illustrate important research findings, theoretical developments and practical strategies.
UNIÓN, una revista consolidada, Jan 1, 2008
Page 251. Diciembre de 2008, Número 16, páginas 251-253 ISSN: 1815-0640 L i b r o s L i b r o s L... more Page 251. Diciembre de 2008, Número 16, páginas 251-253 ISSN: 1815-0640 L i b r o s L i b r o s L i b r o s L i b r o s Matemática inclusiva: propuestas para una educación matemática accesible Autor: Àngel Alsina y Núria ...
ZDM Mathematics Education, 2022
During the last decades, the study of how learners and teachers of mathematics use the resource o... more 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, specifically 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 specifically appear in the realisation of mathematics teaching talk as mediational in the work with mathematics teachers on their classroom teaching.
In the context of refinement of frameworks over the past decades within the domain of mathematics... more 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.
We discuss language diversity in mathematics education research by considering the move from a vi... more 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? Keywords Mathematics education research · Language · Language diversity · Politics of representation · Cultural and postcolonial studies · Circuit of culture
The thinking of language as resource in mathematics education research has been more metaphorical... more 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 this paper, we expand our prior work on mathematics education in contexts of language diversit... more In this paper, we expand our prior work on mathematics education in contexts of language diversity by elaborating on the three perspectives on language described by Ruiz (NABE J 8(2):15–34, 1984): language-as-right, language-as-resource, and language-as-problem. We illustrate our arguments with data taken from research contexts in Catalonia-Spain and South Africa. In these two parts of the world, the language policy in education has long been an issue, with a monolingual orientation that values one language (i.e., Catalan in Catalonia and English in South Africa) over others. Throughout the introduction of specific examples of policy documents, classroom practices, and participants’ reports, our main point is that the right of using the students’ languages makes sense because it is itself more than an intrinsic human right; it is an option that potentially benefits the creation of mathematics learning opportunities. Especially for the instances of classroom practices, our examples can be considered as representative in that they point to a common situation in our data: despite the fact of the language of learning and teaching being fixed, there is room for the learners and the teacher to take or react to a decision on what language to use, with whom, and how in concrete moments of the interaction. However, on the basis of our studies and drawing on the literature in mathematics education and language diversity, we argue that language rights are not sufficiently connected to language as a pedagogical resource. The enactment of these rights is still contributing in many ways to the social and political construction of problems concerning the role of certain languages in classroom interaction. We conclude the paper by discussing some possibilities for framing language as a resource that provide effective support to all students’ learning of mathematics.
The data reported in this article come from a large project whose goal was to explore how Latin A... more 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.
In this article we reflect on the learning of mathematics in bilingual settings from a social and... more In this article we reflect on the learning of mathematics in bilingual settings from a social and a political perspective. In particular we highlight two concepts that are key to our work: language-as-resource and language-as-political. To do so, we draw on classroom data from students of Mexican origin in Tucson, USA, and students from Latin America in Barcelona, Spain. The language policies in our contexts share a message of privileging the language of instruction (English or Catalan) over other languages. Our analysis of the two sets of data points to differences in the mathematical participation of students on the basis of which language they use. We develop the argument that, even if languages other than Catalan and English are accepted and certain pedagogies may be close to a language-as-resource approach, the use of the students' languages is politically mediated in such a way that its pedagogical value (as a medium of communication and learning) is not always taken into account in the bilingual mathematics classroom.
Intercultural Education, Jan 1, 2007
This paper provides data from individual interviews conducted with 15 and 16 year-old nonimmigran... more This paper provides data from individual interviews conducted with 15 and 16 year-old nonimmigrant 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 wholeclass 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 article, I explore language identities and processes of negotiation concerning parts of t... more 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 sociopolitical 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.
We analyse social interactions during the first days of class in a secondary mathematics classroo... more 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 sociomathematical 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.
Educational Studies in Mathematics, Jan 1, 2001
In this paper we present the way in which language issues have become a relevant factor in resear... more 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.
For the Learning of Mathematics, Jan 1, 2004
it relates to students from certain ethnic and language groups and economically disadvantaged stu... more it relates to students from certain ethnic and language groups and economically disadvantaged students. We are primarily concerned with seeking ways to develop approaches to mathematics education that are sensitive to the contexts and lived experiences of all learners.
Transitions between contexts of …, Jan 1, 2002
European Journal of Psychology of Education, Jan 1, 2005
Drawing on socio-cultural theory, we understand the norms regulating the practices within the mat... more 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 students, 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.
Revista de Didáctica de las …, Jan 1, 1999
En este estudio<NOTAREF Id="1"/&... more En este estudio<NOTAREF Id="1"/> consideramos todos los alumnos como comunicadores matemáticos en potencia, sin excepción de los alumnos pertenecientes a las minorías étnicas. El cálculo en contexto pone de manifiesto la importancia de las situaciones, ...
Uno: Revista de didáctica de las matematicas, Jan 1, 2002
En este artículo se ilustran dos episodios que sirven poro discutir la diversidad de interpretaci... more En este artículo se ilustran dos episodios que sirven poro discutir la diversidad de interpretaciones de las normas ea el aula de matemáticas. A pesar de que las normas son recursos imprescindibles para garantizar la comunicación y tienen la función de dar seguridad y orden a las ...
Suma, Jan 1, 1999
Acceso de usuarios registrados. Acceso de usuarios registrados Usuario Contraseña. ...
Cuadernos de Pedagogia, Jan 1, 2000
La enseñanza de esta disciplina en la escuela refleja su carácter universal, pero olvida a menudo... more La enseñanza de esta disciplina en la escuela refleja su carácter universal, pero olvida a menudo el bagaje cultural del alumnado y sus necesidades sociales. Los autores reivindican que se aproveche la diversidad como fuente de riqueza para el aprendizaje ...
UNO. Revista de Didáctica de las …, Jan 1, 2006
Este artículo analiza, desde la perspectiva de la formación inicial en Didáctica de las Matemátic... more Este artículo analiza, desde la perspectiva de la formación inicial en Didáctica de las Matemáticas, diversas creencias de los futuros maestros respecto al conocimiento matemático. Algunas de estas creencias son un auténtico obstáculo para avanzar hacia ...
Perspectiva escolar, Jan 1, 2000
... El que diem, el que no diem i el que esperem que passi a l'aula. Autores: Nú... more ... El que diem, el que no diem i el que esperem que passi a l'aula. Autores: Núria Planas; Localización: Perspectiva escolar, ISSN 0210-2331, Nº 242, 2000 (Ejemplar dedicado a: Matemàtiques per a tothom) , pág. 44. Fundación Dialnet. Acceso de usuarios registrados. ...
Suma: Revista sobre …, Jan 1, 2000
UNO. Revista de Didáctica de la …, Jan 1, 2009
En el marco de un proyecto de investigación, hemos iniciado un trabajo en equipo con profesorado ... more En el marco de un proyecto de investigación, hemos iniciado un trabajo en equipo con profesorado de matemáticas para la construcción de un modelo formativo para el aula de didáctica de la matemática. De acuerdo con los principios de una epistemología de la práctica, partimos de la preparación de casos profesionales que puedan usarse como ejemplos de cuestiones relevantes del conocimiento didáctico-matemático que el estudiante de profesor tiene que aprender. En este artículo, destacamos la importancia de colaborar con profesorado de matemáticas en la selección e interpretación de casos * .
En este artículo se reflexiona sobre las competencias profesionales contempladas en el máster que... more En este artículo se reflexiona sobre las competencias profesionales contempladas en el máster que habilita para ejercer de profesor de secundaria y se responde primero a la siguiente pregunta: ¿cómo se concretan las competencias específicas de matemáticas y su didáctica en las tres materias que se contemplan en el máster (complementos para la formación matemática, aprendizaje y enseñanza de las matemáticas, e innovación docente e iniciación a la investigación educativa)? A continuación, se hace una propuesta sobre el papel que deben jugar las prácticas en dicho máster.
El proceso de Boloña pretende dotar a Europa de un sistema universitario de mayor calidad en el q... more El proceso de Boloña pretende dotar a Europa de un sistema universitario de mayor calidad en el que los estudiantes pasan a ser el centro del sistema, y son ellos quienes construyen y autorregulan de forma activa su conocimiento, relacionando nuevos significados con otros ya interiorizados, mientras que el profesor es una ayuda en este proceso de autorregulación.
La finalidad de este artículo es presentar la viabilidad de un modelo teórico para el análisis de... more 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. Palabras clave: Enseñanza y aprendizaje de las matemáticas, enfoque ontosemiótico, prácticas de aula, objetos y procesos matemáticos, normas, conflictos semióticos, idoneidad didáctica.
En este artículo me propongo, por un lado, revisar críticamente la noción de lengua mediante el a... more En este artículo me propongo, por un lado, revisar críticamente la noción de lengua mediante el análisis de prácticas en aulas de matemáticas y, por otro, contribuir a la tarea de conceptualizar dicha noción desde una perspectiva social y pedagógica. Para abordar ambos propósitos, me centro en el caso del aula de matemáticas bilingüe, por ser donde vengo desarrollando mi labor científica más reciente. Sostengo que el uso de una noción demasiado general y teóricamente débil de lengua en educación matemática obstaculiza la comprensión del papel mediador de las lenguas de los estudiantes en el aprendizaje de las matemáticas. Elaboro este supuesto con datos de mi contexto para argumentar la posibilidad de una fundamentación que, a
las metáforas imperantes de la lengua como derecho y como problema, añada la metáfora de la lengua como recurso. La triple caracterización de la lengua como derecho, problema y recurso asume en última instancia que la función básica de las lenguas de los estudiantes en el aula es contribuir a la creación colectiva de oportunidades de aprendizaje.
Para citar: . Iniciación al lenguaje algebraico en aulas multilingües: Contribuciones de un proye... more Para citar: . Iniciación al lenguaje algebraico en aulas multilingües: Contribuciones de un proyecto en desarrollo. Avances de Investigación en Educación Matemática, 3, 25-44 © Sociedad Española de Investigación en Educación Matemática (SEIEM). www.seiem.es Iniciación al lenguaje algebraico en aulas multilingües: Contribuciones de un proyecto en desarrollo Iniciación al lenguaje algebraico en aulas multilingües: Contribuciones de un proyecto en desarrollo
. El papel del contexto en la identificación de argumentaciones matemáticas por un grupo de profe... more . El papel del contexto en la identificación de argumentaciones matemáticas por un grupo de profesores. PNA, 7(4), 155-170.
Cultura y Educaci&# 243; n, Jan 1, 2008
Resumen En este artículo exploramos la noción de práctica educativa teniendo en cuenta cambios en... more Resumen En este artículo exploramos la noción de práctica educativa teniendo en cuenta cambios en el discurso del pro-fesor y en los discursos de los alumnos a raíz de la interacción entre unos y otros en un aula de matemáticas. Partimos de las teorías socioculturales del habla ...
Educación Matemática, Jan 1, 2006
Page 1. Educación Matemática Santillana aliavi@prodigy.net.mx ISSN (Versión impresa): 1665-5826 M... more Page 1. Educación Matemática Santillana aliavi@prodigy.net.mx ISSN (Versión impresa): 1665-5826 MÉXICO 2006 Núria Planas MODELO DE ANÁLISIS DE VIDEOS PARA EL ESTUDIO DE PROCESOS DE CONSTRUCCIÓN ...
Enseñanza de las Ciencias, Jan 1, 2004
Últimamente se viene produciendo un creciente énfasis en aspectos socioculturales y afectivos de ... more 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 microetnográfi ca 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 . Palabras clave. Educación matemática, teorías sociales del aprendizaje, participación, microetnografía, normas, valoraciones, respuestas emocionales.
Revista de Educación, Jan 1, 2004
Las tasas de fracaso escolar más altas en las sociedades modernas se dan entre los alumnos inmigr... more Las tasas de fracaso escolar más altas en las sociedades modernas se dan entre los alumnos inmigrantes. Esta pauta se mantie-ne e incluso incrementa en el caso de las matemáticas escolares. En la actualidad, la proliferación de trabajos en educación matemática en ...
Enseñanza de las Ciencias, Jan 1, 2001
This paper is included in a qualitative research carried out in a classroom with 15-16 year-old m... more This paper is included in a qualitative research carried out in a classroom with 15-16 year-old minority and economically disadvantaged students. The research tries to develop an inclusive approach for integrating both the cognitive and emotional perspective in order to improve the comprehension of the processes of constructing meanings in the classroom microculture. We assume that multicultural classrooms promote more evidence about the variety of meanings and values concerning with the mathematical practice. It is our intention to think over the possible interferences in learning that can be derived from the different interpretations of mathematical norms in the classroom.
Planas, N. (2010). Las teorías socioculturales en la investigación en educación matemática: refle... more Planas, N. (2010). Las teorías socioculturales en la investigación en educación matemática: reflexiones y datos bibliométricos. En M.M. Moreno, A. Estrada, J. Carrillo, & T.A. Sierra, (Eds.), Investigación en Educación Matemática XIV (pp. 163-195). Lleida: SEIEM 163 LAS TEORÍAS SOCIOCULTURALES EN LA INVESTIGACIÓN EN EDUCACIÓN MATEMÁTICA: REFLEXIONES Y DATOS BIBLIOMÉTRICOS Planas, N.
Presentamos una investigación sobre el aprendizaje de isometrías con un programa de geometría din... more Presentamos una investigación sobre el aprendizaje de isometrías con un programa de geometría dinámica. Los datos se han tomado en una clase de secundaria con estudiantes de 14 y 15 años trabajando en un entorno colaborativo. Partiendo de los ejes de cognición matemática, mediación tecnológica y orquestación del profesorado, construimos la noción de «momento clave en el aprendizaje» para desarrollar el análisis. Para este artículo, seleccionamos cuatro ejemplos de momento clave que indican la pertinencia de explorar los ejes anteriores y que, a su vez, apuntan a la necesidad de considerar estos ejes de forma integrada. En futuras investigaciones, tendremos que profundizar en la influencia entre los distintos resultados que ahora destacamos.
La finalidad de este artículo es presentar la viabilidad de un modelo teórico para el análisis de... more 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. Palabras clave: Enseñanza y aprendizaje de las matemáticas, enfoque ontosemiótico, prácticas de aula, objetos y procesos matemáticos, normas, conflictos semióticos, idoneidad didáctica.
La investigación en educación matemática y diversidad lingüística lleva varias décadas desarrollá... more La investigación en educación matemática y diversidad lingüística lleva varias décadas desarrollándose y hay una importante cantidad de literatura científi ca al respecto (ver, por ejemplo, los trabajos compilados por Barwell, 2009). Destaca la reciente creación del 21 Estudio ICMI, 'Mathematics education and language diversity', en 2009, y la organización del congreso asociado en 2011, que suponen un impulso y reconocimiento a este tipo de cuestiones. Como reacción al énfasis dado al aula monolingüe, la Comisión Internacional en Instrucción Matemática -ICMI, por sus siglas en inglés -ha encargado un estudio sobre el estado de la investigación en educación matemática y multilingüismo, con el fi n de promover el análisis de las relaciones entre matemáticas y escenarios de educación multilingües, así como dar a conocer el conocimiento construido en este ámbito en distintos entornos políticos y geográfi cos.
Las tasas de fracaso escolar más altas en las sociedades modernas se dan entre los alumnos inmigr... more Las tasas de fracaso escolar más altas en las sociedades modernas se dan entre los alumnos inmigrantes. Esta pauta se mantiene e incluso incrementa en el caso de las matemáticas escolares. A menudo se supone que los alumnos en situación de riesgo tienen impedimentos inherentes a su condición marginal que dificultan su acceso a las prácticas (matemáticas) escolares. Sin embargo, hasta el momento, importantes proyectos de investigación (ver, por ejemplo, el proyecto QUASAR, Brown et al., 1996) han argumentado que el bajo nivel de participación y éxito en el aula de matemáticas de alumnos con fuerte desventaja socioeconómica no se debe necesariamente a una falta de habilidades o a un déficit cognitivo, sino más bien a la conjunción de múltiples factores de orden sociocultural, algunos originados en la microcultura del aula y otros derivados de la estructura social.
Este informe señala la necesidad de establecer relaciones entre la educación matemática y otras d... more Este informe señala la necesidad de establecer relaciones entre la educación matemática y otras disciplinas cercanas. Se toma la idea de recontextualización introducida por Bernstein y se examina cómo está siendo aplicada para revisar y adaptar el uso en investigación educativa de nociones procedentes de teorías sociales. Se pone el énfasis en tres disciplinas que, desde la década de los ochenta, vienen contribuyendo a la producción de conocimiento en educación matemática: psicología cultural, sociología y antropología. La noción de competencia comunicativa se considera con el propósito de ejemplificar parte de un proceso de recontextualización que está siendo llevado a cabo en nuestra área.
In this report we explore language practices when learning and teaching mathematics in a classroo... more In this report we explore language practices when learning and teaching mathematics in a classroom with bilingual learners and a bilingual teacher. We focus on data from the analysis of the whole class discussions in seven lessons. Up to eight episodes distributed in five of the lessons reveal the fragility of switching languages as a reiterated finding, particularly experienced by those learners whose dominant home language is not the language of instruction. Each time a student "dares" to switch languages there are more or less subtle reactions which affect the course and contents of the discussion. We conclude that individual positions and language practices are resources for research in that their study informs of interpretative and action frames that can be mobilised to explain shifts in the direction of mathematical interactions.
… of the Sixth Conference of the …
In this paper we are interested in the understanding of how the classroom discourse helps to deve... more In this paper we are interested in the understanding of how the classroom discourse helps to develop the students' comprehension of the non ostensive mathematical objects as objects that have "existence". First, we examine the role of the objectual metaphor in the understanding of the mathematical entities as "objects with existence", as well as in some of the conflicts that the use of this type of metaphor can provoke in the students' interpretations. Second, we examine the mathematics discourse from the perspective of the ostensives representing non ostensives that do not exist.
pagines.uab.cat
In the introduction section of the book edited by Schwarz, Dreyfus and Hershkowitz (2009), it is ... more In the introduction section of the book edited by Schwarz, Dreyfus and Hershkowitz (2009), it is argued the importance of analyzing the processes involved in classroom interaction to explore what is under the shared construction of mathematical knowledge. To represent optimal ...
… Group for the …, Jan 1, 2006
2006. In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N.(Eds.). Proceedings 30th Co... more 2006. In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N.(Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, p. 205. Prague: PME. 1-205 WS05: TEACHING AND LEARNING MATHEMATICS IN ...
International Group for the Psychology of …, Jan 1, 2008
A challenge for mathematics education: …, Jan 1, 2004
WORKING GROUP 1/GROUPE DE TRAVAIL 1 14 Teaching mathematics in multicultural classrooms: from dif... more WORKING GROUP 1/GROUPE DE TRAVAIL 1 14 Teaching mathematics in multicultural classrooms: from differences to commonalities Núria Gorgorió, Núria Planas Universitat Autònoma de Barcelona (Spain) Abstract Mathematics teachers find immigrant students to be ...
Proceedings of the 3rd Conference of the …, Jan 1, 2004
Abstract: We interpret immigrant students' learning experience as a transition proce... more Abstract: We interpret immigrant students' learning experience as a transition process between contexts of mathematical practice. Transition processes can be studied through the analysis of the different meanings that the individuals participating in the classroom attach to the ...
Proceedings of the 7th Congress of …, Jan 1, 2011
Language and discursive practices shape the concepts and processes that organize much of the ever... more Language and discursive practices shape the concepts and processes that organize much of the everyday situations in the mathematics classroom. In their work, Enyedy et al. (2008) refer to revoicing as a discursive practice to promote a deeper conceptual understanding of ...
Mathematics Education and …
… of the 33rd Conference of the …, Jan 1, 2009
This paper presents a report on how a group of immigrant bilingual students use their languages i... more This paper presents a report on how a group of immigrant bilingual students use their languages in the learning of mathematics. We have developed our research with immigrant bilinguals in Catalonia, Spain, that arrived at a young age from South-American countries. We ...
International Group for the Psychology of M …, Jan 1, 2005
Proceedings of the …, Jan 1, 2008
We adapt the onto-semiotic approach to research in mathematics education developed by Godino and ... more We adapt the onto-semiotic approach to research in mathematics education developed by Godino and his colleagues (eg, Font, D'Amore & Godino, 2007; Godino, Batanero, & Roa, 2005) in order to better understand certain disparities in the interpretation of classroom ...
CERME 4 Proceedings, Jan 1, 2005
Cultural diversity in mathematics (education): …, Jan 1, 2000
Proceedings of the Second International …, Jan 1, 2000
In this paper we discuss the adequacy of using a collaborative model as a research approach for s... more In this paper we discuss the adequacy of using a collaborative model as a research approach for studying the dynamics of a multicultural mathematics classroom 1 . The goal of the research is the analysis of the immigrant students' processes of adapting to a new cultural context, ...
Advances in mathematics education, 2012
This paper draws on two research studies with similar theoretical backgrounds, in two different s... more 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.
UNO-Revista de Didáctica de las …, 2000
Este artículo desarrolla problemáticas que pueden ser consideradas paralelas a las que actualment... more Este artículo desarrolla problemáticas que pueden ser consideradas paralelas a las que actualmente se presentan en las clases de enseñanza obligatoria en nuestro país y desvela claves de intervención ante grupos de alumnos heterogéneos, donde se ha de impartir un ...
Aula de innovación educativa, 2004
Biblioteca de la Universidad Complutense de Madrid, Base de datos de artículos de revistas, ...
ZDM – Mathematics Education
During the last decades, the study of how learners and teachers of mathematics use the resource o... more 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, specifically the practices of naming and explaining, in mathematics teaching talk. We conclude that the importance of mathematics teaching talk is construed through tensions ...
Research for Educational Change: Transforming researchers' Insights Into Iimprovement in Mathematics Teaching and Learning, 2016
PNA. Revista de Investigación en Didáctica de la Matemática, 2013
En este artículo presentamos datos de un estudio en torno a los discursos sobre la argumentación ... more En este artículo presentamos datos de un estudio en torno a los discursos sobre la argumentación en clase de matemáticas elaborados por un grupo de profesores de secundaria. En concreto, explicamos un resultado que pone de relieve el siguiente fenómeno: al identificar argumentaciones matemáticas en episodios de clase, varios profesores buscaron evidencias del carácter argumentativo en el contexto del aula y de la tarea, relegando aspectos epistémicos más generales. En sus distintas respuestas, estos profesores priorizaron dónde se produjo la argumentación sobre cómo se produjo.The Role of Context in the Identification of Mathematical Argumentations by a Group of TeachersIn this article, we present the data from a study on discourses about argumentation in the mathematics classroom by a group of secondary teachers. In particular, we explain a result that points to the following phenomenon: when teachers identify mathematical argumentations in lesson episodes, some of them search for ...
En este texto, reviso avances de la investigacion en educacion matematica y lengua a fin de compa... more En este texto, reviso avances de la investigacion en educacion matematica y lengua a fin de compartir parte del conocimiento generado en este dominio. Esta tarea de revision ha de servir como recurso para aquellos academicos con interes en construir una cierta comprension sobre que se sabe en la actualidad, especialmente en relacion con el aprendizaje matematico multilingue. Bajo el supuesto de que la produccion de conocimiento siempre se da en el nivel de la teoria, empiezo con consideraciones sobre las teorias sociales de la ensenanza y del aprendizaje de matematicas. Estas son las teorias que estan contribuyendo principalmente, por una parte, a la expansion del dominio y, por otra, a la refinacion de lineas especificas de desarrollo.
This report is a summary of the questions, comments and issues brought up in the ETC4 panel of th... more This report is a summary of the questions, comments and issues brought up in the ETC4 panel of three expert researchers on mathematics and language. The purpose of this panel was to discuss: (1) What do we mean by the language of the learner, of the teacher and of mathematics? (2) What are today the opportunities and challenges of classroom-based research on mathematics and language? The major recommendations and position statements included: (i) Develop more nuanced theoretical frameworks for the understanding of the politics of language use in the mathematics classroom (ii) Re-evaluate conceptualizations of languages and speakers in terms of distinctions, differences, dichotomies and difficulties (iii) Conduct more language-related design research for teaching and learning of specific mathematical content areas.
We begin by briefly examining the relevance of the study of language in mathematics education res... more We begin by briefly examining the relevance of the study of language in mathematics education research, as well as some of the collaborative forms in which TWG09 is moving the study of language forward in the field. To provide reasons for the recent contributions by TWG09, we summarise lines of concern and tendencies that come from our reading of the set of papers and posters presented at CERME9. We build on the review work by Morgan (2013) to argue for the consolidation of such a diversity of lines of concern and tendencies in the contemporary agenda of the domain. The discussion of accomplished goals of the agenda points to a number of challenges and priorities in the context of TWG09 – its participants, their interaction and their activity.
Journal of Communication, 2015
KEYWORDS Translation. Interpretation. Representation. Multiplied Numbers. Language Structure ABST... more 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 un...
The European Society for Research in Mathematics Education (ERME) holds a biennial conference (CE... more The European Society for Research in Mathematics Education (ERME) holds a biennial conference (CERME) in which research is presented and discussed in Thematic Working Groups (TWGs). The initiative, which began in the September 2017 Newsletter, of introducing the working groups continues here, focusing on ways in which European research in the field of mathematics education may be interesting or relevant for research mathematicians. The aim is to extend the ERME community with new participants, who may benefit from hearing about research methods and findings and who may contribute to future CERMEs.
The Second Handbook of Research on the Psychology of Mathematics Education, 2016
Research is always carried out from a standpoint, an epistemological stance that shapes the ontol... more Research is always carried out from a standpoint, an epistemological stance that shapes the ontological assumptions about what is being researched, even though the researchers might be unaware of or unconcerned about what it is. Despite apparently being evident, this assertion needs to be revisited when reviewing the insertion of socio-cultural approaches to mathematics thinking, learning and education in the last 10 years of research in PME.
New ICMI Study Series, 2016