Language and Communication in Mathematics Education · International Perspectives by Moschkovich, Judit -- Read -- Imperial Library of Trantor

Index

Contents Overviews of Language and Communication Research in Mathematics Education 1 International Perspectives on Language and Communication in Mathematics Education

Abstract 1 Background 2 Language and Communication in Relation to the Field 3 This Volume References

2 Sixty Years (or so) of Language Data in Mathematics Education

Abstract 1 Introduction 2 Word Problems 3 Classroom or Research Events and Their Records: Making a Thing of Things 4 The ICME-13 TSG 31 Panel Talk Itself (July 26th, 2016) 5 In Conclusion Acknowledgements References

3 Subject-Specific Academic Language Versus Mathematical Discourse

Abstract 1 The Development of a Linguistic Perspective on the Learning of Mathematics 2 Multilingual Contexts—From Deficit to Resource 3 Summary References

4 Recommendations for Research on Language and Learning Mathematics

Abstract 1 Introduction 2 Recommendation #1: Draw on Interdisciplinary Approaches and Methodologies 3 Recommendation #2: Define Central Theoretical Constructs and Connect Those to a Theoretical Framework 4 Recommendation #3: Build on Existing Methodologies to Focus on Both Language and Mathematical Activity 5 Recommendation #4: Recognize Central Distinctions, but Avoid Dichotomies

5.1 Conversation Analysis and Discourse Analysis 5.2 Every-day and Academic Language 5.3 Kinds of Communication and Talk

6 Methodological Issues in Designing Research 7 Closing: Why These Issues Matter to Me References

Learner Focused Research 5 Making Student Explanations Relevant in Whole Class Discussion

Abstract 1 Introduction 2 The Structure of Classroom Interaction 3 Methods 4 Findings

4.1 Teachers Explicitly Requiring an Explanation 4.2 Giving a Dispreferred Response 4.3 Students Continuing Their Turn

5 Conclusion References

6 How Learners Communicate Their Mathematics Reasoning in Mathematics Discourse

Abstract 1 Introduction 2 Literature Review

2.1 Communicating Mathematics Reasoning 2.2 Communicating Mathematics Reasoning in a Multilingual Classroom

3 Theoretical Perspective 4 Research Design and Methodology 5 Findings from the Study 6 Conclusions and Recommendations References

7 Dealing with Function Word Problems: Identifying and Interpreting Verbal Representations

Abstract 1 Introduction 2 Theoretical Background and Research Questions

2.1 Dealing with Function Word Problems 2.2 Connecting Representations of Functional Relationships 2.3 Language Demands When Dealing with Function Word Problems 2.4 Research Question

3 Research Design 4 Selected Results from the Analysis

4.1 Brief Summary of the Case of Alexandra and Tatjana 4.2 Brief Summary of the Case of Fynn and Svenja 4.3 Brief Summary of the Case of Mike and Nils 4.4 Brief Summary of the Case of Altin and Jona 4.5 Summary

5 Conclusion References

8 The Interplay of Language and Objects in the Process of Abstracting

Abstract 1 Introduction 2 Basic Assumptions on Mathematics Learning

2.1 About the Setting: Mathematics Learning as a Social Process 2.2 About the Content: Mathematics Learning as Abstracting

3 Background Theories on Language and Objects

3.1 Functions of Language (Bruner, 1974) 3.2 Language as a Means of Recontextualization (Aukerman, 2007) 3.3 Objects as Actors (Latour, 2005)

4 Methods 5 Connecting Theories

5.1 Result I: The Interplay of Language and Objects 5.2 Result II: The Interplay of Language and Objects in the Process of Abstracting

References

9 Intersecting Language Repertoires When 4-Year-Olds Count

Abstract 1 Context 2 An Apparently Mathematical Situation

2.1 Mathematical Situations from the Perspective of Positioning Theory

3 Analytic Approach 4 Language Repertoires in the Situation 5 Discussion Acknowledgements References

10 Explaining as Mathematical Discursive Practices of Navigating Through Different Epistemic Fields

Abstract 1 Introduction: The Importance of the Discursive Level of Language in Mathematics Education 2 Theoretical Perspectives: Conceptualisation of Explaining Practices in Whole-Class Discussions

2.1 Explaining in Interactional Discourse Analysis 2.2 Explaining from an Interactionist Perspective in Mathematics Education 2.3 Explaining from an Epistemological Perspective in Mathematics Education 2.4 Synthesis: Conceptualisation of Explaining as Multiple Practices of Navigating Through Different Epistemic Fields 2.5 Insights into the Process of Identifying Explaining Practices

3 Conclusion Grant Information References

Teacher Focused Research 11 Interactional Processes in Inclusive Mathematics Teaching

Abstract 1 Starting Point: Inclusion and the German School System 2 Theoretical and Methodological Foundations 3 Research Project 4 Methodological Procedure of Data Analysis 5 Presentation and Analysis of a Selected Scene

5.1 Description of the Situation 5.2 Selected Transcript Extracts 5.3 Summary Interactional Analysis 5.4 Answering the Research Questions

6 Summary Results and Perspectives References

12 A Teacher’s Use of Revoicing in Mathematical Discussions

Abstract 1 Introduction 2 Our Approach to Revoicing 3 Participants, Task and Methods 4 Analysis of Two Episodes

4.1 Episode 1: Distance Between Two Points 4.2 Episode 2: The Pythagorean Theorem

5 Some Final Remarks Acknowledgements References

13 Authority and Politeness: Complementary Analyses of Mathematics Teaching Episodes

Abstract 1 Introduction 2 Positioning and Authority 3 Politeness Theory and the Notion of Face 4 Connections Between Politeness and Positioning Theories 5 Context and Methodology 6 Complementary Analyses 7 Discussion—An Attempt to Reconcile References

14 The Use of Language in the Construction of Meaning for Natural Number

Abstract 1 Introduction 2 Theoretical Framework

2.1 Thinking and Language 2.2 The Teaching of Division with Natural Numbers 2.3 Lesson Study and Language Use 2.4 Shared Thinking

3 Method

3.1 A Case Study Related to Lesson Study 3.2 Research Participants 3.3 Tools

3.3.1 First Joint Session with Teachers 3.3.2 The Design of Mathematics Lessons

4 Results

4.1 Arithmetic Problems with Natural Numbers Posed by Karina 4.2 Work in Teams 4.3 Closing the Lesson

5 Analysis

5.1 The Multi-grade Classroom 5.2 The Lesson 5.3 Joint Working Sessions with Teachers

6 Conclusions References

15 “I Am Sorry. I Did Not Understand You”: The Learning of Dialogue by Prospective Teachers

Abstract 1 About Communication in Mathematics Education 2 About Dialogue in Mathematics Education 3 A Possible Context to the Learning of Dialogue 4 “Yes, I Have Heard What They Said”: Isabela’s Practice of Dialogue 5 Data About Data: Isabela’s Point of View About Her Own Practice 6 About Learning of Dialogue 7 Dialogue as a Move Towards the Other 8 Final Remarks References

Language Diversity Research 16 Teacher Knowledge and Teaching Practices in Linguistically Diverse Classrooms

Abstract 1 Motivation and Goal 2 Literature Background 3 Methodology

3.1 Measures 3.2 Mathematical Knowledge for Teaching (MKT) Instrument 3.3 Pedagogical Content Knowledge for Teaching Mathematics to ELLs (PCK-MELL) Instrument 3.4 Mathematical Quality of Instruction Observational Protocol 3.5 Quality of Linguistically Diverse Teaching 3.6 Sample and Data Collection

4 Data Analysis and Results

4.1 Scoring Quality of Instruction and MKT 4.2 Data Analysis and Results

5 Conclusions Acknowledgements References

17 Podcasts in Second Language Mathematics Teaching as an Instrument for Measuring Teachers’ Language Awareness

Abstract 1 Introduction 2 Theoretical Backgound

2.1 Language and Mathematics Learning 2.2 Teacher Language Awareness 2.3 Podcasts as Research Instruments

3 Methods

3.1 Settings and Research Questions 3.2 Pilot Study 3.3 Methods Used in the Main Study

3.3.1 Semi-structured Interviews

4 Data Analysis

4.1 Podcasts 4.2 Semi-structured Interviews

5 Preliminary Results 6 Discussion Acknowledgements Appendix: German Version of the Interview Guidelines References

18 Exploring How a Grade 7 Teacher Promotes Mathematical Reasoning in a Multilingual Mathematics Class of English Second Language Learners

Abstract 1 Introduction 2 Theoretical Framework and Literature Review 3 Methodology

3.1 A Brief Description of the Lesson Observed 3.2 The Teacher’s Role in Promoting Mathematical Reasoning 3.3 How Did the Teacher Develop Mathematical Proficiency?

3.3.1 Conceptual Understanding 3.3.2 Procedural Fluency 3.3.3 Strategic Competence 3.3.4 Adaptive Reasoning 3.3.5 Productive Disposition

3.4 Probing the Learners to Talk About Mathematics

4 Summary of the Findings

4.1 Did the Teacher Encourage Mathematical Reasoning? How Did the Way in Which the Teacher Interacted with the Learners Enable or Constrain Mathematical Reasoning?

5 Conclusions and Recommendations References

19 The Meaning of ‘Number’ in Kaiabi Language: Indigenous Teachers’ Identity Discourses in a Multilingual Setting

Abstract 1 Introduction 2 Saying “Number” in Their Native Language: Aspects of Kaiabi Identity from Xingu Park 3 Final Remarks References

Contributor Biographies

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