Mamokgethi Setati Phakeng Universidad de Sudáfrica Pretoria, Sudáfrica Martha Villavicencio Ubillús Ministerio de Educación Lima, Perú. Universidad Autónoma de Barcelona Barcelona, Cataluña-España Universidad de Sudáfrica Pretoria, Sudáfrica Universidad Paola Valero Aalborg Aalborg, Dinamarca.
Introduction: An ICMI Study on Language Diversity in Mathematics Education
- History of the Study
- What Do We Mean by Language Diversity and Why Does It Matter for Mathematics Education?
- Outline of the Chapter
- Changing Perspectives on Mathematics Education and Language Diversity
- Establishing the Scope of the Study: Preparing the Discussion Document
- The Study Conference
- Preparation of This Volume
- Summary of Research Ideas in This Volume
- Implications for Policy and Practice
- Some Issues for Future Research
- Summary Statement
In the final report of the symposium (UNESCO, 1974), the lack of research on the relationship between language and mathematics was noted. This assumption proved to be the case, as can be seen from several chapters in this volume.
In many countries, the official language of instruction is a world language that is considered important to the economy of the country as a whole. Therefore, one of the outcomes of this volume should be that we as researchers need to find ways to engage with politicians and bureaucrats productively so that they are aware of what the research says and work with them to ensure the continuation of such dialogue.
Impact of Differing Grammatical Structures in Mathematics Teaching and Learning
Introduction
This chapter examines the features of the mathematical register and the development of the mathematical register for a few selected languages. In most of the cases discussed, the impact of grammatical structures on mathematics teaching and learning has not been empirically investigated.
The Mathematics Register
- Register Development: Modern European Languages
- Register Development: Multilingual Contexts
The language of modern mathematics is part of the continuum of technical language development that had begun in Europe at least in the seventeenth century. A particularly notable feature of the mathematics register is nominalization, where processes, originally verbs, become wrapped up in nouns (Halliday, 2004).
Grammatical Systems
Where a mathematical function is not encoded in the grammar, articulating the function can be more difficult. It can also be difficult for speakers to accept adding function to a language if it involves adding to a closed class.
Number
- Syntactic Category
- Transparency and Regularity
Number systems can also differ in the correspondence of their names to the base system used, and whether this in turn corresponds to the symbolic written notation. The base-ten written notation is dominant in the world today, but even some languages that predominantly use a base-ten system have irregularities.
Logic and Reasoning
- Negation
- Formal Semantics
A sentence such as 'the group is not large' is translated ehara te rōpū i te nui. What can be said about the convergence of the string (un) if:. a) Equation (E) has no solution.
Space and Geometry
- Spatial Frame of Reference
- Topological Language
Anaphora contributes to the misunderstanding of the sentence and to difficulties in using it in inferences. Discussing the implications of the favoring of the intrinsic frame of reference in Mopan, a Mayan language, Danziger (1996) discussed mental rotation activities often given as spatial math problems in schools, such as deciding whether pictured cubes are the same or not.
Suggested Directions for Teachers and Researchers
Johnston and Slobin (1979) studied the order of acquisition of certain spatial terms in English, Italian, Turkish and Serbo-Croatian, finding a similar order for each language but different ages of acquisition which they attributed to linguistic factors such as morphological complexity and, in the case of Turkish, to the fact that these terms are 'postpositions' in Turkish and not prepositions. Tāua (the two of us) includes the speaker and listener, while māua (the two of us) includes the speaker, another person but excludes the listener.
Conclusion
Encouraging my students to do science and math lessons in practical ways, focusing on the actual performance of the small rituals of quantifying with hands, eyes, water, string and rulers as well as with utterances, proved to be a useful and generative way of dealing with the generative tensions between English and Yoruba logics of numbering. Some Aspects of Sociolinguistic Interactions between Linguistics and Mathematics Education: Final Report of the Symposium Sponsored by UNESCO, CEDO and ICMI, Nairobi Kenya, September 1-11, 1974.
Making Use of Multiple (Non-shared) First Languages: State of and Need for Research
Language Context
- Introduction
- First Language as a Widely Accepted Resource for Giving Access to Mathematics
- Cultural and Political Dimension: Presenting the European Language Context
- Multilingualism in Europe and European Schools
- Multiple Languages in European Schools
- Practical Dimension: Teachers’ Options for Including First Languages in European Classrooms
- Options for First Language Use Under Different Language Conditions
- Cultural Dimensions Beyond Language: Bridging Cultural Gaps
- Research Dimension: Three Examples of Empirical Studies on Effects on Students’ Learning, Obstacles,
- Language and Agency
- Language and Cultures
- Installing Teaching Strategies Against Established Monolingual Classroom Norms
- Final Remarks
This is why it is often argued that it is necessary to use the many first languages 1. Instead, we refer to the first languages of minorities or immigrants and focus on practical matters in the mathematics class. The usual model is to enable or encourage first language use (second and third columns of the table) without obligations.
Mathematics Education in Multilingual Contexts for the Indigenous Population
- Introduction
- Models of Indigenous Education in History
- Dynamics and Tensions Between Languages and Cultures
- Language Extinction, Revitalization, and Development
- Tensions Between Oral and Written Registers
- Relevant Mathematics Education in Indigenous Contexts
- Offi cializing Ethnomathematics in Peru
- Using Language to De-colonialize Indigenous Education in Colombia
- Problematizing Schooling and Mathematics Education in Brazil
- Concluding Remarks
In some cases, religious conversion and the exoticization of the "savage" native led to the extermination of indigenous people. In the first quarter of the nineteenth century, independence from the European empires took place. Their strategies lead to the vitality of indigenous languages and their articulation with the Spanish language.
Challenges and Opportunities for Second Language Learners in Undergraduate
- Introduction
- Linguistic Difficulties in Advanced Mathematics for Multilingual Contexts
- Lexical and Notational Issues
- Logical Issues
- Examples of Various Multilingual Contexts at University
- A Multilingual Situation in Cameroonian Universities
- The Case of Denmark
- Increasing Linguistic Diversity in France
- The Case of Malawi
- Bilingualism in Russia: The Case of Tatarstan
- Results of Research Studies
- The Case of Students in New Zealand Who Have English as an Additional Language
- Logical Issues: The Case of Negation of Quantified Statements
- An Ongoing Experiment for Teacher Training in Tatarstan
- Conclusion
It is also spoken in nearby areas of the Littoral and Western provinces, as well as in urban centers. The language of choice is Ewondo, one of the main languages in the Yaoundé area. In the first part of the chapter, we gave some a priori considerations to describe the specific forms.
Language Diversity in Mathematics Teacher Education: Challenges Across Three Countries
- Different Countries, Similar Challenges
- The Three Contexts: South Africa, Malawi, and Catalonia-Spain
- What Do We Know About Mathematics Teacher Educators’ Awareness of the Multilingual Context
- Mathematics Teacher Educators’ Awareness in South Africa
- Mathematics Teacher Educators’ Awareness in Malawi
- Mathematics Teacher Educators’ Awareness in Catalonia
- What Practices Do Mathematics Student Teachers Get Exposed to in the Preservice Classroom?
- Teacher Education Practices in South Africa
- Teacher Education Practices in Malawi
- Teacher Education Practices in Catalonia
- Joint Discussion
- Awareness and Implications
- Practices and Implications
- Concluding Remarks
We now address ways in which mathematics teachers think about language diversity in the teaching and learning of mathematics. The mathematics teachers saw their responsibility as fulfilling this role in the classroom and the mathematics student teachers saw themselves as recipients of this knowledge. Research in the three countries under discussion shows that mathematics teacher training focuses mathematics students' attention on becoming mathematics teachers and on acquiring mathematical knowledge.
Addressing Multi-language Diversity
- Introduction
- Raising Awareness of Issues Related to Teaching the English Mathematics Register
- Understanding the Language Context in Which Teachers Work
- Understanding Potential Diffi culties with Mathematics Language
- Facilitating Discourse in English as the LoLT in Mathematics Classrooms
- Dialogic Practices
- The Role of Questioning
- The Practice of Using Code-Switching to Engage in Mathematical Discourse
- Incorporating Mathematics Language and Literacy into the Teacher Preparation Program
- Developing Language Modules to Integrate into Methods Courses
- Simultaneous Interpreting Between English
- Using Mathematics Educator Refl ective Communities to Collaboratively Plan to Integrate Language
- Conclusion
Teachers' questioning can be used in the development of students' learning and their own use of language as a means of reasoning. In addition, teachers are becoming more aware of the need to teach mathematical language, both in the native language and in English. Language practices in mathematics teaching and learning: a case study of three mathematics teachers in multilingual schools.
Mathematics in the Hands of Deaf Learners and Blind Learners: Visual–Gestural–Somatic
Introduction
In the case of blind mathematics students, on the other hand, considering linguistic resources of a visual-spatial nature, such as gestures, may seem wrong, since such resources will not be seen. Perhaps the clearest example of this devaluation can be found in the history of Sign in the education of the deaf. In the next section, to examine how the attention paid to visual and nonverbal forms of communication has changed over time, we begin by summarizing moments from this history.
The Rise, Fall and Rise of Sign and Gesture
It was only in the 1960s and 1970s that this dominance began to be challenged, especially after the scientific recognition of American Sign Language (and consequently the sign languages of other countries around the world) as a true and natural language (Stokoe. It was only in the mid-1980s that gestures began to be considered as an integral part of language, with McNeill (1985) showing how they are used during speech to constitute the conceptual content of an utterance.as in the field of linguistics, such recognition has only recently gained ground.
Sensory Modalities and Knowledge Mediation
This means that gestures are just as much a part of the set of linguistic resources used to share experiences of the world as they are components of spoken and sign language. Material and semiotic tools not only enable cognitive activity; they are part of the act of thinking and of what is thought about (cognition). In the light of the previous discussion, our goal in presenting these examples is threefold: to explore the characteristics of mathematical activity that favor visual-motor-somatic forms of expression; consider the relationships between lexical expressions (either sign or spoken) and gestures; and, more generally, to seek evidence of how mathematical activity and understanding are (and are) shaped by different ways of perceiving and doing, and different ways of trying to share these experiences with others.
Language Resources of Deaf Mathematics Students
- Example 1: The Visual Modality in Arithmetic Calculations
- Example 2: Bringing Dynamism to Mathematical Discourse
- Traces of Enactments in the Signs and Gestures of Deaf Mathematics Learners
5 The names of the students whose work is presented in the paper have been changed. They were then specifically asked to compare the areas of the different polygons in the figures. Examples include the signs for rectangles, isosceles and right triangles, and some of the signs used to make equations.
Visual–Gestural Expressions of Blind Mathematics Students
- Example 3: Embodied Abstractions in the Gestures of a Blind Student
This example focuses on the strategies of one of the students, Leandro, when he tried to determine the area and perimeter of the triangle. Moreover, just as the sign for "rectangle" in MSL emphasizes defining properties of the shape, so did Leandro's gesture. Caio: Ah, but the sides of the triangle are not equal (traces the circumference with his fingers).
Mathematics in Our Hands
Thus, as in the case of deaf math students, it seems that for blind students too, the visual-gesture-somatic modality brings dynamism to math discussions and practices and the ubiquity of such expressions, even among those who do not see them. suggest that they are an integral part of the process of learning and doing math. Our view is that words, signs and gestures, all forms of what Vygotsky called symbolic language, are constructs rooted in the sensory experiences of the pupils who produce them. Sign Language Structure: An Overview of the Visual Communication System of American Deaf People.
Student Agency and Counter-Narratives in Diverse Multilingual Mathematics
Classrooms: Challenging Defi cit Perspectives
Introduction
Deficit perspectives also come from existing literature on language learning and development that is framed with a monolingual bias, which not only obscures competence in children's native languages, but also how children can use native and emerging languages productively to support communication in the language . of teaching (Gort, 2006; Moschkovich, 2002. In the remainder of this chapter, we draw on these ideas to examine several vignettes that highlight creative and productive uses of emerging multilingual resources available. In doing so, we hope to counter-narratives that both challenge deficit perspectives and offer a promising approach to advance research in the teaching and learning of mathematics in linguistically heterogeneous classrooms that captures the full range of students' competencies.
Vignettes of Counter-Narratives in the Experiences of Emergent Bilinguals in Mathematical Classrooms
- Vignette 1: Mispronunciation as Wordplay
- Vignette 2: Teenagers and Counting Words
- Vignette 3: Open-Ended Tasks
Anna changed the direction of the math discussion based on the girls' interest in teenagers, a change initiated by the students. The open-ended nature of the classroom discussion determined the possible ways students could act (Cotton & Hardy, 2004. With the help of the group, Ciara uses will and cognitive elasticity to develop a diagram and present her ideas (Figure 9.2.
Concluding Thoughts
Secada (Eds.), Changing faces of mathematics: Perspectives on multiculturalism and gender equality (pp. 85–93). Twice Less: Black English and Black Student Performance in Math and Science. Fuglestad (Eds.), Proceedings of the Twenty-eighth Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 37–54).
Tensions in Teaching Mathematics in Contexts of Language Diversity
- Introduction
- Tensions in Mathematics Classrooms in Contexts of Language Diversity
- Bakhtin’s Theory of Language
- Case 1: Mathematics in a Multilingual Mathematics Classroom in South Africa
- Case 2: Using an International Language to Teach Mathematics in Malaysia
- Case 3: Immigrant Students Learning Mathematics in a Sheltered Language Program
- Case 4: Immigrant Students and Teacher in a Mathematics Class in South Africa
Given the reported decline in Malaysian students' English language proficiency and the belief that "teaching subjects in scientific disciplines in English would accelerate the acquisition of scientific knowledge in order to develop a scientifically literate nation by 2020". the government introduced the new language policy for mathematics and science education (Choong, 2004, p. 2). The existence of the classe d'accueil is the result of centripetal linguistic forces in the Quebec education system. The aim is that after one year they will be able to communicate in French enough to be able to be in a regular classroom […] The two main thrusts of the program are communication in French and integration into their new environment.
