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Building the Foundation : The 23rd ICMI Study.

Bibliographic Details
Main Author: Bartolini Bussi, Maria G.
Other Authors: Sun, Xu Hua.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2018.
Edition:1st ed.
Series:New ICMI Study Series
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • 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
  • 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.
  • 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., &amp
  • 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., &amp.
  • 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
  • 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.
  • 5.3.2 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
  • 5.5 The What and Why of WNA: Towards a Cognitive Dimension
  • References
  • Cited papers from Sun, X., Kaur, B., &amp
  • 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., &amp
  • 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 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., &amp.
  • 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.

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