Mathematics Education and Language Diversity: The 21st ICMI Study (New ICMI Study Series)

Acknowledgments
Contents
Contributors
List of Figures
List of Tables
Chapter 1: Introduction: An ICMI Study on Language Diversity in Mathematics Education
	1.1 History of the Study
		1.1.1 What Do We Mean by Language Diversity and Why Does It Matter for Mathematics Education?
		1.1.2 Outline of the Chapter
	1.2 Changing Perspectives on Mathematics Education and Language Diversity
	1.3 Establishing the Scope of the Study: Preparing the Discussion Document
	1.4 The Study Conference
	1.5 Preparation of This Volume
	1.6 Summary of Research Ideas in This Volume
	1.7 Implications for Policy and Practice
	1.8 Some Issues for Future Research
	1.9 Summary Statement
	References
Chapter 2: Impact of Differing Grammatical Structures in Mathematics Teaching and Learning
	2.1 Introduction
	2.2 The Mathematics Register
		2.2.1 Register Development: Modern European Languages
		2.2.2 Register Development: Multilingual Contexts
	2.3 Grammatical Systems
	2.4 Number
		2.4.1 Syntactic Category
		2.4.2 Transparency and Regularity
	2.5 Logic and Reasoning
		2.5.1 Negation
		2.5.2 Formal Semantics
	2.6 Space and Geometry
		2.6.1 Spatial Frame of Reference
		2.6.2 Topological Language
	2.7 Suggested Directions for Teachers and Researchers
	2.8 Conclusion
	References
Chapter 3: Making Use of Multiple (Non-shared) First Languages: State of and Need for Research and Development in the European Language Context
	3.1 Introduction
	3.2 First Language as a Widely Accepted Resource for Giving Access to Mathematics
	3.3 Cultural and Political Dimension: Presenting the European Language Context
		3.3.1 Multilingualism in Europe and European Schools: Demographic Facts and Emerging Consciousness
		3.3.2 Multiple Languages in European Schools
	3.4 Practical Dimension: Teachers’ Options for Including First Languages in European Classrooms
		3.4.1 Options for First Language Use Under Different Language Conditions
		3.4.2 Cultural Dimensions Beyond Language: Bridging Cultural Gaps
	3.5 Research Dimension: Three Examples of Empirical Studies on Effects on Students’ Learning, Obstacles, and Conditions
		3.5.1 Language and Agency
		3.5.2 Language and Cultures
		3.5.3 Installing Teaching Strategies Against Established Monolingual Classroom Norms
	3.6 Final Remarks
	Acknowledgments
	References
Chapter 4: Mathematics Education in Multilingual Contexts for the Indigenous Population in Latin America
	4.1 Introduction
	4.2 Models of Indigenous Education in History
	4.3 Dynamics and Tensions Between Languages and Cultures
		4.3.1 Language Extinction, Revitalization, and Development
		4.3.2 Tensions Between Oral and Written Registers
	4.4 Relevant Mathematics Education in Indigenous Contexts
		4.4.1 Officializing Ethnomathematics in Peru
		4.4.2 Using Language to De-colonialize Indigenous Education in Colombia
		4.4.3 Problematizing Schooling and Mathematics Education in Brazil
	4.5 Concluding Remarks
	References
Chapter 5: Challenges and Opportunities for Second Language Learners in Undergraduate Mathematics
	5.1 Introduction
	5.2 Linguistic Difficulties in Advanced Mathematics for Multilingual Contexts
		5.2.1 Lexical and Notational Issues
		5.2.2 Logical Issues
	5.3 Examples of Various Multilingual Contexts at University
		5.3.1 A Multilingual Situation in Cameroonian Universities
		5.3.2 The Case of Denmark
		5.3.3 Increasing Linguistic Diversity in France
		5.3.4 The Case of Malawi
		5.3.5 Bilingualism in Russia: The Case of Tatarstan
	5.4 Results of Research Studies
		5.4.1 The Case of Students in New Zealand Who Have English as an Additional Language
		5.4.2 Logical Issues: The Case of Negation of Quantified Statements
		5.4.3 An Ongoing Experiment for Teacher Training in Tatarstan
	5.5 Conclusion
	References
Chapter 6: Language Diversity in Mathematics Teacher Education: Challenges Across Three Countries
	6.1 Different Countries, Similar Challenges
	6.2 The Three Contexts: South Africa, Malawi, and Catalonia-Spain
	6.3 What Do We Know About Mathematics Teacher Educators’ Awareness of the Multilingual Context of their Practice?
		6.3.1 Mathematics Teacher Educators’ Awareness in South Africa
		6.3.2 Mathematics Teacher Educators’ Awareness in Malawi
		6.3.3 Mathematics Teacher Educators’ Awareness in Catalonia
	6.4 What Practices Do Mathematics Student Teachers Get Exposed to in the Preservice Classroom?
		6.4.1 Teacher Education Practices in South Africa
		6.4.2 Teacher Education Practices in Malawi
		6.4.3 Teacher Education Practices in Catalonia
	6.5 Joint Discussion
		6.5.1 Awareness and Implications
		6.5.2 Practices and Implications
	6.6 Concluding Remarks
	References
Chapter 7: Addressing Multi-language Diversity in Mathematics Teacher Education Programs
	7.1 Introduction
	7.2 Raising Awareness of Issues Related to Teaching the English Mathematics Register
		7.2.1 Understanding the Language Context in Which Teachers Work
		7.2.2 Understanding Potential Difficulties with Mathematics Language
	7.3 Facilitating Discourse in English as the LoLT in Mathematics Classrooms
		7.3.1 Dialogic Practices
		7.3.2 The Role of Questioning
		7.3.3 The Practice of Using Code-Switching to Engage in Mathematical Discourse
	7.4 Incorporating Mathematics Language and Literacy into the Teacher Preparation Program
		7.4.1 Developing Language Modules to Integrate into Methods Courses
		7.4.2 Simultaneous Interpreting Between English and an Indigenous Language as a Tool in Teacher Education
		7.4.3 Using Mathematics Educator Reflective Communities to Collaboratively Plan to Integrate Language in Mathematics Instruction
	7.5 Conclusion
	References
Chapter 8: Mathematics in the Hands of Deaf Learners and Blind Learners: Visual–Gestural–Somatic Means of Doing and Expressing Mathematics
	8.1 Introduction
	8.2 The Rise, Fall and Rise of Sign and Gesture
	8.3 Sensory Modalities and Knowledge Mediation
	8.4 Language Resources of Deaf Mathematics Students
		8.4.1 Example 1: The Visual Modality in Arithmetic Calculations
		8.4.2 Example 2: Bringing Dynamism to Mathematical Discourse
		8.4.3 Traces of Enactments in the Signs and Gestures of Deaf Mathematics Learners
	8.5 Visual–Gestural Expressions of Blind Mathematics Students
		8.5.1 Example 3: Embodied Abstractions in the Gestures of a Blind Student
	8.6 Mathematics in Our Hands
	References
Chapter 9: Student Agency and Counter-Narratives in Diverse Multilingual Mathematics Classrooms: Challenging Deficit Perspectives
	9.1 Introduction
	9.2 Vignettes of Counter-Narratives in the Experiences of Emergent Bilinguals in Mathematical Classrooms
		9.2.1 Vignette 1: Mispronunciation as Wordplay
		9.2.2 Vignette 2: Teenagers and Counting Words
		9.2.3 Vignette 3: Open-Ended Tasks
	9.3 Concluding Thoughts
	References
Chapter 10: Tensions in Teaching Mathematics in Contexts of Language Diversity
	10.1 Introduction
	10.2 Tensions in Mathematics Classrooms in Contexts of Language Diversity
	10.3 Bakhtin’s Theory of Language
	10.4 Case 1: Mathematics in a Multilingual Mathematics Classroom in South Africa
	10.5 Case 2: Using an International Language to Teach Mathematics in Malaysia
	10.6 Case 3: Immigrant Students Learning Mathematics in a Sheltered Language Program
	10.7 Case 4: Immigrant Students and Teacher in a Mathematics Class in South Africa
	10.8 Discussion and Conclusions
	References
Chapter 11: Purposefully Relating Multilingual Registers: Building Theory and Teaching Strategies for Bilingual Learners Based on an Integration of Three Traditions
	11.1 Introduction
	11.2 Relating Registers for Common Multiples: Snapshot from India
		11.2.1 Tasks and Situation in the Camp Lessons
		11.2.2 Code-Switching Between Registers for Better Explanation
		11.2.3 Use of Gestures and Nonverbal Cues
		11.2.4 Use of Technical and Everyday Registers
	11.3 Revisiting Three Traditions of Reflecting on Linguistic Transitions
		11.3.1 Transitions Between First and Second Languages: Code-Switching
		11.3.2 Transitions Between Everyday and Technical Language
		11.3.3 Transitions Between Different Mathematical Representations: Relating Mathematical Registers
		11.3.4 Integrating Three Transitions Between Languages, Registers, and Representations
	11.4 Theoretical Exploration: Representations, Registers, or Languages?
		11.4.1 Different Conceptualizations
		11.4.2 Registers with Different Representations
		11.4.3 Some Teaching Implications
	11.5 Transitions Between Registers for Developing Conceptual Understanding of Fractions: Snapshot from Germany
		11.5.1 Research Context
		11.5.2 The Case of Amir and Ekim: Challenges and Insights While Relating Registers
	11.6 Final Remarks
	References
Chapter 12: Using ICTs to Facilitate Multilingual Mathematics Teaching and Learning
	12.1 Consideration of Language Diversity in the Literature on ICTs for Mathematics Teaching and Learning
		12.1.1 ICTs-Mediated Human Communication for Mathematics Learning
		12.1.2 With and Beyond the Language in Learning Tools
	12.2 Multilingualism in the ICT Literature
		12.2.1 Mathematics Learning Tools with Some Multilingualism
		12.2.2 Search Engines: Beyond a Dictionary of Translations
	12.3 Supporting Mathematics Teaching and Learning in Multilingual Environments
		12.3.1 Language Switch
		12.3.2 Multilingualism in Dynamic Geometry Systems
		12.3.3 Multilingualism in Computation Tools
		12.3.4 Learning Resources Repositories
		12.3.5 Communication Tools
		12.3.6 Reference Tools
	12.4 Outlook
	References
Chapter 13: Language Diversity and New Media: Issues of Multimodality and Performance
	13.1 Language Diversity and New Media
		13.1.1 Humans-with-Media
		13.1.2 Multimodality
		13.1.3 Performance for a Wider Audience
	13.2 Case Studies
		13.2.1 Case A: Grades 2 and 4 Students in Canada Explore Optimization
		13.2.2 Case B: Brazilian Students Explore Sequences and Series of Numbers
	13.3 Audience, Multimodal Communication, and Language Diversity
	13.4 Concluding Remarks
	References
Chapter 14: Language Diversity in Research on Language Diversity in Mathematics Education
	14.1 Identifying the Problématique: Language(s) of Education, and of Research
	14.2 The Problématique and Its Meta-Language
	14.3 Motivating Case: “Researching Mathematics Teacher Education”
	14.4 Contributions to the ICMI 21 Study Conference: Overall Analysis
	14.5 Personal Case 1 (Faïza)
	14.6 Personal Case 2 (Hien)
	14.7 Personal Case 3 (Carl)
	14.8 Conclusions
	References
Chapter 15: Research Rationalities and the Construction of the Deficient Multilingual Mathematics Learner
	15.1 Introduction
	15.2 Examining Research Rationalities
	15.3 The Logic of Achievement Gaps Research
	15.4 The Logic of Classroom Research
	15.5 Concluding Remarks
	References
ICMI Study 21 Discussion Document:Mathematics Education and LanguageDiversity
	Executive Summary
	Discussion Document
		Focus of the Study
		Rationale for the Study
		Framing Multilingualism
		Mathematics Education and Multilingualism
		Orientation
		Themes for the Study
		Participation in the Study
		Study Timeline
		Inquiries
		Members of the International Programme Committee
Index