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EB

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Cham : Springer International Publishing AG, 2018

1 online resource (548 pages)

ISBN 9783319635552 (electronic bk.)

ISBN 9783319635545

New ICMI Study Ser.

Print version: Bartolini Bussi, Maria G. Building the Foundation: Whole Numbers in the Primary Grades Cham : Springer International Publishing AG,c2018 ISBN 9783319635545

Chapter 2: Social and Cultural Contexts in the Teaching and Learning of Whole Number Arithmetic -- 2.1 Introduction -- 2.2 The Context Form: Design -- 2.3 The Context Form: Data -- 2.3.1 The General Structure of Education Systems for Early Years Mathematics -- 2.3.2 Inclusiveness in Education -- 2.3.3 Textbooks -- 2.3.4 National Curriculum Standards and Assessment -- 2.3.5 Teachers’ Qualification and Teacher Education and Development -- 2.4 Conclusion -- References -- Chapter 3: Language and Cultural Issues in the Teaching and Learning of WNA -- 3.1 Introduction -- 3.1.1 Reflections on Language and Culture Before, During and After the Macao Conference -- 3.1.2 Some Everyday Language Issues in Number Understanding -- 3.2 Place Value in Different School Languages and Cultures -- 3.2.1 Some Reported Difficulties in Understanding Place Value ---

3.2.2 Transparency and Regularity of Number Languages: Some European Cases.

Chapter 2: Social and Cultural Contexts in the Teaching and Learning of Whole Number Arithmetic -- 2.1 Introduction -- 2.2 The Context Form: Design -- 2.3 The Context Form: Data -- 2.3.1 The General Structure of Education Systems for Early Years Mathematics -- 2.3.2 Inclusiveness in Education -- 2.3.3 Textbooks -- 2.3.4 National Curriculum Standards and Assessment -- 2.3.5 Teachers’ Qualification and Teacher Education and Development -- 2.4 Conclusion -- References -- Chapter 3: Language and Cultural Issues in the Teaching and Learning of WNA -- 3.1 Introduction -- 3.1.1 Reflections on Language and Culture Before, During and After the Macao Conference -- 3.1.2 Some Everyday Language Issues in Number Understanding -- 3.2 Place Value in Different School Languages and Cultures -- 3.2.1 Some Reported Difficulties in Understanding Place Value ---

Intro -- Foreword -- Preface -- ICMI Study 23: Primary Mathematics Study on Whole Numbers -- Attenders at the Study Conference Held in Macao (SAR China) in June 2015 -- Contents -- Contributors -- List of Abbreviations -- List of Figures -- List of Tables -- Part I: Introductory Section -- Chapter 1: Building a Strong Foundation Concerning Whole Number Arithmetic in Primary Grades: Editorial Introduction -- 1.1 Introduction -- 1.2 The ICMI Study 23 -- 1.2.1 The Rationale of the Study -- 1.2.2 The Launch of the Study -- 1.2.3 The Discussion Document -- 1.2.4 The Study Conference -- 1.2.5 The Study Volume -- 1.3 Merits of the Study -- 1.4 Impact of the Study -- 1.5 Limits of the Study -- 1.6 The Implications of This Study -- 1.6.1 A Message for Practitioners -- 1.6.2 A Message for Curriculum Developers and Policymakers -- 1.7 Concluding Remarks -- 1.8 Processes and Acknowledgements -- References ---

5.2.2.1 Early Numeration Practices -- 5.2.2.2 The Invention of the Counting Principle -- 5.2.2.3 The Pre-structures of Number Naming -- 5.2.3 The Conceptual Development of Numeral Systems -- 5.2.3.1 Tally Systems -- 5.2.3.2 Additive Systems -- 5.2.3.3 Multiplicative-Additive System -- 5.2.3.4 Decimal Place Value System -- 5.2.3.5 Modern Theoretical Approaches -- 5.2.4 Epistemological and Pedagogical Insights from History -- 5.2.4.1 Pedagogical Insights from the Pre-history of Numbers -- 5.2.4.2 Understanding Numerals’ Uses: To Write, to Compute, to Talk -- 5.2.4.3 Understanding the Conceptual Changes in the Development of the Decimal Place Value System -- Memorising the Multiplication Table -- Unit Conversions -- 5.3 Foundational Ideas from Language and Culture -- 5.3.1 Whole Number Naming: Universal vs Cultural ---

5.5 The What and Why of WNA: Towards a Cognitive Dimension -- References -- Cited papers from Sun, X., Kaur, B., & -- Novotna, J. (Eds.). (2015). Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers. Retrieved February 10, 2016, from www.umac.mo/fed/ICMI23/doc/Proceedings_ICMI_STUDY_23_final.pdf -- Chapter 6: Reflecting on the What and Why of Whole Number Arithmetic: A Commentary on Chapter 5 -- 6.1 Introduction -- 6.2 Problematics of Place Value Notation -- 6.3 Algebraic Structure and the Power of Place Value Notation -- 6.4 Possible Lessons for Education -- 6.5 Comments on Particular Sections of Chapter 5 -- 6.5.1 Comments on Section 5.3.1 -- 6.5.2 Comments on Section 5.3.1.2 -- 6.5.3 Comments on Section 5.4.2 -- 6.6 Conclusion -- References -- Cited papers from Sun, X., Kaur, B., & ---

3.2.3 Post-colonial Cases: Africa and Latin America -- 3.2.3.1 Algeria -- 3.2.3.2 The Guatemalan Case -- 3.2.3.3 Tanzania and Other East African Countries -- 3.2.4 Towards Transparency: The Chinese Approach -- 3.3 The Chinese Approach to Arithmetic -- 3.3.1 The Ancient History -- 3.3.2 Chinese Language Foundation to Place Value -- 3.3.2.1 Base 10 and the Conversion Rate for Measurement -- 3.3.2.2 Classifiers -- 3.3.2.3 Radicals and the Part-Part-Whole Structure -- 3.3.3 Conceptual Naming of Fractions -- 3.3.4 Arithmetic Operations -- 3.3.5 Mathematical Relational Thinking: Equality -- 3.3.5.1 The History of the Equal Sign ’=’ in Europe -- 3.3.5.2 The History of the Equal Sign ’=’ in China -- 3.3.5.3 Chinese Approaches to the Relational Meaning of Equality -- 3.4 Educational Implications -- 3.4.1 Place Value and Whole Number Operations -- 3.4.2 Cardinal Numbers and Measure Numbers -- 3.4.3 Fraction Names -- 3.4.4 Arithmetic Operations -- 3.4.5 Mathematical Relational Thinking: Equality or Sameness -- 3.4.5.1 Some Reported Difficulties in the Understanding of Equality -- 3.4.5.2 Variation Problems in China and Italy -- 3.5 Concluding Remarks -- References -- Cited Papers from Sun, X., Kaur, B., & -- Novotna, J. (Eds.). (2015). Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers. Retrieved February 10, 2016, from www.umac.mo/fed/ICMI23/doc/Proceedings_ICMI_STUDY_23_final.pdf -- Chapter 4: On Number Language: A Commentary on Chapter 3 -- 4.1 Introduction -- 4.2 What Is Written and What Is Said -- 4.3 On Place Value -- 4.4 Count Nouns and Mass Nouns: The Question of Units -- 4.5 Cardinal, Ordinal and Fractional: Three Interlocking Linguistic Subsystems -- 4.6 A Few Concluding Remarks -- References -- Cited papers from Sun, X., Kaur, B., &.

Chapter 7: Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches -- 7.1 Introduction -- 7.1.1 What Was Presented at the Conference: Overview -- 7.1.2 The Discussion of the Working Group -- 7.1.3 About the Chapter -- 7.2 Neuro-cognitive Perspectives -- 7.2.1 A ’Starter Kit’ for Early Number -- 7.2.2 Neuropsychology and the Triple-Code Model -- 7.2.3 Transcoding Numerals (Symbols) to Number Words -- 7.3 Beyond Neuro-cognitive Approaches: Quantitative Relations, SFOR and an Awareness of Patterns and Structures -- 7.3.1 Children’s Early Competencies in Quantitative Relations -- 7.3.2 Spontaneous Focusing on Numbers (SFON) and Quantitative Relations (SFOR) -- 7.3.3 An Integrated Perspective Focused on Patterns and Structures -- 7.4 Exemplars of Classroom Studies from Cognitive Perspectives -- 7.4.1 Ordinal Awareness in Learning Number -- 7.4.2 Part-Whole Relations and Structure Sense -- 7.4.2.1 Hands and Fingers: An Important Embodied Structure -- 7.4.2.2 Use of Artefacts for Fostering the Development of Structure Sense: The Importance of Sharing Strategies -- 7.4.3 Additive Relations -- 7.4.4 Cross-Cultural Study of Number Competence -- 7.4.5 Counting and Representations of Number -- 7.5 Methodological Issues and Recommendations -- 7.5.1 Study Designs -- 7.5.1.1 Assessing Strategy Use with Cross-Sectional Studies -- 7.5.1.2 Tracing Individual Development with Longitudinal Studies -- 7.5.1.3 Evaluating Teaching Approaches with Intervention Studies -- 7.5.2 Task Designs -- 7.5.3 Conclusions: Methodological Issues -- 7.6 General Conclusions and Implications -- 7.6.1 General Conclusions -- 7.6.2 Implications for Further Research and Practice -- References -- Cited papers from Sun, X., Kaur, B., &.

Novotna, J. (Eds.). (2015). Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers. Retrieved February 10, 2016, from www.umac.mo/fed/ICMI23/doc/Proceedings_ICMI_STUDY_23_final.pdf.

5.2.2.1 Early Numeration Practices -- 5.2.2.2 The Invention of the Counting Principle -- 5.2.2.3 The Pre-structures of Number Naming -- 5.2.3 The Conceptual Development of Numeral Systems -- 5.2.3.1 Tally Systems -- 5.2.3.2 Additive Systems -- 5.2.3.3 Multiplicative-Additive System -- 5.2.3.4 Decimal Place Value System -- 5.2.3.5 Modern Theoretical Approaches -- 5.2.4 Epistemological and Pedagogical Insights from History -- 5.2.4.1 Pedagogical Insights from the Pre-history of Numbers -- 5.2.4.2 Understanding Numerals’ Uses: To Write, to Compute, to Talk -- 5.2.4.3 Understanding the Conceptual Changes in the Development of the Decimal Place Value System -- Memorising the Multiplication Table -- Unit Conversions -- 5.3 Foundational Ideas from Language and Culture -- 5.3.1 Whole Number Naming: Universal vs Cultural ---

5.3.1.1 The Danish Case: The History of Number Names in Denmark -- 5.3.1.2 The Algerian Case: Language Diversity in the Post-colonial Era.

5.5 The What and Why of WNA: Towards a Cognitive Dimension -- References -- Cited papers from Sun, X., Kaur, B., & -- Novotna, J. (Eds.). (2015). Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers. Retrieved February 10, 2016, from www.umac.mo/fed/ICMI23/doc/Proceedings_ICMI_STUDY_23_final.pdf -- Chapter 6: Reflecting on the What and Why of Whole Number Arithmetic: A Commentary on Chapter 5 -- 6.1 Introduction -- 6.2 Problematics of Place Value Notation -- 6.3 Algebraic Structure and the Power of Place Value Notation -- 6.4 Possible Lessons for Education -- 6.5 Comments on Particular Sections of Chapter 5 -- 6.5.1 Comments on Section 5.3.1 -- 6.5.2 Comments on Section 5.3.1.2 -- 6.5.3 Comments on Section 5.4.2 -- 6.6 Conclusion -- References -- Cited papers from Sun, X., Kaur, B., & ---

Novotna, J. (Eds.). (2015). Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers. Retrieved February 10, 2016, from www.umac.mo/fed/ICMI23/doc/Proceedings_ICMI_STUDY_23_final.pdf.

3.2.3 Post-colonial Cases: Africa and Latin America -- 3.2.3.1 Algeria -- 3.2.3.2 The Guatemalan Case -- 3.2.3.3 Tanzania and Other East African Countries -- 3.2.4 Towards Transparency: The Chinese Approach -- 3.3 The Chinese Approach to Arithmetic -- 3.3.1 The Ancient History -- 3.3.2 Chinese Language Foundation to Place Value -- 3.3.2.1 Base 10 and the Conversion Rate for Measurement -- 3.3.2.2 Classifiers -- 3.3.2.3 Radicals and the Part-Part-Whole Structure -- 3.3.3 Conceptual Naming of Fractions -- 3.3.4 Arithmetic Operations -- 3.3.5 Mathematical Relational Thinking: Equality -- 3.3.5.1 The History of the Equal Sign ’=’ in Europe -- 3.3.5.2 The History of the Equal Sign ’=’ in China -- 3.3.5.3 Chinese Approaches to the Relational Meaning of Equality -- 3.4 Educational Implications -- 3.4.1 Place Value and Whole Number Operations -- 3.4.2 Cardinal Numbers and Measure Numbers -- 3.4.3 Fraction Names -- 3.4.4 Arithmetic Operations -- 3.4.5 Mathematical Relational Thinking: Equality or Sameness -- 3.4.5.1 Some Reported Difficulties in the Understanding of Equality -- 3.4.5.2 Variation Problems in China and Italy -- 3.5 Concluding Remarks -- References -- Cited Papers from Sun, X., Kaur, B., & -- Novotna, J. (Eds.). (2015). Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers. Retrieved February 10, 2016, from www.umac.mo/fed/ICMI23/doc/Proceedings_ICMI_STUDY_23_final.pdf -- Chapter 4: On Number Language: A Commentary on Chapter 3 -- 4.1 Introduction -- 4.2 What Is Written and What Is Said -- 4.3 On Place Value -- 4.4 Count Nouns and Mass Nouns: The Question of Units -- 4.5 Cardinal, Ordinal and Fractional: Three Interlocking Linguistic Subsystems -- 4.6 A Few Concluding Remarks -- References -- Cited papers from Sun, X., Kaur, B., &.

5.3.2 The Incompatibilities Between Spoken Numbers, Written Numbers and Numeration Units Within 100 -- 5.3.3 Links and Incompatibilities Between Numeration and Calculation -- 5.3.4 How to Bridge the Incompatibility: Some Interventions -- 5.4 Foundational Ideas Influenced by Multiple Communities -- 5.4.1 The Influence of Economics and Business: A Case from Ancient China -- 5.4.2 The Influence of Academic Mathematics: A Case from the Mathematics Community in Israel -- 5.4.3 The Influence of Science and Technology: A Case from the New Math Reform in France -- 5.4.4 The Influence of Public and Private Stakeholders: A Case from Current Curriculum Reform in Canada -- 5.4.5 Foundational Ideas Summary: Understanding the Unpredictable Long-Term Effects of Change ---

Chapter 7: Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches -- 7.1 Introduction -- 7.1.1 What Was Presented at the Conference: Overview -- 7.1.2 The Discussion of the Working Group -- 7.1.3 About the Chapter -- 7.2 Neuro-cognitive Perspectives -- 7.2.1 A ’Starter Kit’ for Early Number -- 7.2.2 Neuropsychology and the Triple-Code Model -- 7.2.3 Transcoding Numerals (Symbols) to Number Words -- 7.3 Beyond Neuro-cognitive Approaches: Quantitative Relations, SFOR and an Awareness of Patterns and Structures -- 7.3.1 Children’s Early Competencies in Quantitative Relations -- 7.3.2 Spontaneous Focusing on Numbers (SFON) and Quantitative Relations (SFOR) -- 7.3.3 An Integrated Perspective Focused on Patterns and Structures -- 7.4 Exemplars of Classroom Studies from Cognitive Perspectives -- 7.4.1 Ordinal Awareness in Learning Number -- 7.4.2 Part-Whole Relations and Structure Sense -- 7.4.2.1 Hands and Fingers: An Important Embodied Structure -- 7.4.2.2 Use of Artefacts for Fostering the Development of Structure Sense: The Importance of Sharing Strategies -- 7.4.3 Additive Relations -- 7.4.4 Cross-Cultural Study of Number Competence -- 7.4.5 Counting and Representations of Number -- 7.5 Methodological Issues and Recommendations -- 7.5.1 Study Designs -- 7.5.1.1 Assessing Strategy Use with Cross-Sectional Studies -- 7.5.1.2 Tracing Individual Development with Longitudinal Studies -- 7.5.1.3 Evaluating Teaching Approaches with Intervention Studies -- 7.5.2 Task Designs -- 7.5.3 Conclusions: Methodological Issues -- 7.6 General Conclusions and Implications -- 7.6.1 General Conclusions -- 7.6.2 Implications for Further Research and Practice -- References -- Cited papers from Sun, X., Kaur, B., &.

Novotna, J. (Eds.). (2015). Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers. Retrieved February 10, 2016, from www.umac.mo/fed/ICMI23/doc/Proceedings_ICMI_STUDY_23_final.pd -- Part II: Working Group Chapters and Commentaries -- Chapter 5: The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes -- 5.1 Introduction -- 5.1.1 Conference Presentations: Overview -- 5.1.1.1 Historical Background -- 5.1.1.2 Language Foundation of WNA: Regularity, Grammar and Cultural Identity -- 5.1.1.3 Foundational Ideas Underlying WNA -- 5.1.1.4 Different Expected Learning and Teaching Goals for WNA -- 5.1.2 Working Groups’ Discussions -- 5.1.3 The Structure of This Chapter -- 5.2 Foundational Ideas that Stem from History -- 5.2.1 Introduction: The Hindu-Arabic Numeral System -- 5.2.2 Knowledge of Pre-numeral Systems ---

001895173

express

(Au-PeEL)EBL6422753

(MiAaPQ)EBC6422753

(OCoLC)1066178491