International Reflections on the Netherlands Didactics of Mathematics : : Visions on and Experiences with Realistic Mathematics Education.

International Reflections on the Netherlands Didactics of Mathematics : : Visions on and Experiences with Realistic Mathematics Education.

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Bibliographic Details
Superior document:ICME-13 Monographs
:
van den Heuvel-Panhuizen, Marja.
Place / Publishing House:Cham : : Springer International Publishing AG,, 2019.
©2020.
Year of Publication:2019
Edition:1st ed.
Language:English
Series:ICME-13 Monographs
Online Access:
Physical Description:1 online resource (369 pages)
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Table of Contents:
  • International Reflections on the Netherlands Didactics of Mathematics
  • Preface
  • Contents
  • 1 Seen Through Other Eyes-Opening Up New Vistas in Realistic Mathematics Education Through Visions and Experiences from Other Countries
  • 1.1 Introduction3pc
  • 1.2 Making Acquaintance with RME3pc
  • 1.2.1 Personal Encounters3pc
  • 1.2.2 Narratives of First RME Experiences3pc
  • 1.2.3 Outstanding Features of RME3pc
  • 1.3 Processes of Implementation of RME3pc
  • 1.4 Challenges in Implementing RME3pc
  • 1.5 Adaptations of RME3pc
  • 1.6 Criticisms of RME and Dissenting Views3pc
  • 1.7 RME Flavours in Foreign Curricula, Textbooks, Instructional Materials, and Teaching Methods3pc
  • 1.8 A Reflection to Conclude3pc
  • 2 From Tinkering to Practice-The Role of Teachers in the Application of Realistic Mathematics Education Principles in the United States
  • 2.1 Introduction3pc
  • 2.1.1 The Role of Teachers in Advancing RME in the United States3pc
  • 2.1.2 Attractive Features of RME to U.S. Teachers3pc
  • 2.2 Introduction of RME in the United States: Late 1980s-Mid 1990s3pc
  • 2.2.1 The Whitnall Study3pc
  • 2.2.2 Going to Scale with Mathematics in Context3pc
  • 2.2.3 Assessing RME3pc
  • 2.2.4 Two Other Collaborations3pc
  • 2.2.5 FIUS: Developing RME Networks in the United States3pc
  • 2.3 Guided Reinvention of High School Mathematics: Fred Peck's Personal Account3pc
  • 2.4 Summary Remarks3pc
  • References
  • 3 Searching for Alternatives for New Math in Belgian Primary Schools-Influence of the Dutch Model of Realistic Mathematics Education
  • 3.1 Traditional Mathematics3pc
  • 3.2 New Math3pc
  • 3.3 Critique on New Math3pc
  • 3.4 The 'Realistic' Alternative3pc
  • 3.5 Math Wars3pc
  • 3.6 Future Developments?3pc
  • References
  • 4 The Impact of Hans Freudenthal and the Freudenthal Institute on the Project Mathe 2000
  • 4.1 Introduction3pc.
  • 4.2 Developmental Research3pc
  • 4.3 The View of Mathematics3pc
  • 4.4 A Genetic View of Teaching and Learning3pc
  • 4.5 Mathematics Education as a Research Domain3pc
  • References
  • 5 Reflections on Realistic Mathematics Education from a South African Perspective
  • 5.1 Introduction3pc
  • 5.2 The Essences of REMESA3pc
  • 5.3 Vision Geometry3pc
  • 5.4 Global Graphs3pc
  • 5.5 Conclusion3pc
  • References
  • 6 Learning to Look at the World Through Mathematical Spectacles-A Personal Tribute to Realistic Mathematics Education
  • 6.1 At the Beginning It Was Symbol Crunching, but with a Bit of Spice3pc
  • 6.2 Starting to Look at the World with Mathematical Spectacles3pc
  • 6.3 Meeting RME3pc
  • 6.4 Developing a 'Mathematical Gaze'-From Instructional Design to a Learning Goal3pc
  • 6.5 Coda3pc
  • References
  • 7 Graphing Linear Equations-A Comparison of the Opportunity-to-Learn in Textbooks Using the Singapore and the Dutch Approaches to Teaching Equations
  • 7.1 Introduction3pc
  • 7.2 A Study of Teaching Graphing Linear Equations in Textbooks Using the Singapore and Dutch Approach3pc
  • 7.2.1 Objective of This Chapter3pc
  • 7.2.2 Backgrounds of the Contexts of Textbooks Examined3pc
  • 7.2.3 Framework for Analysing the OTL in the Textbooks3pc
  • 7.3 Data and Results3pc
  • 7.3.1 The Sequencing of the Content on Graphing Equations in the Two Textbooks3pc
  • 7.3.2 Classroom Activities Proposed on Graphing Equations in the Two Textbooks3pc
  • 7.3.3 Complexity of the Demands for Student Performance on Graphing Equations in the Two Textbooks3pc
  • 7.4 Findings and Discussion3pc
  • 7.4.1 Sequencing of Content3pc
  • 7.4.2 Classroom Activities3pc
  • 7.4.3 Complexity of the Demands for Student Performance3pc
  • 7.5 Reflections of Two Singapore Mathematics Teachers3pc
  • 7.5.1 Profiles of the Two Teachers3pc.
  • 7.5.2 How Do You Teach Graphing Equations to Your Students?3pc
  • 7.5.3 Has the Dutch Approach Textbook Provided You with an Alternative Perspective?3pc
  • 7.5.4 Would the Dutch Approach Work in Singapore Classrooms? What Would It Take for It to Work in Singapore Classrooms?3pc
  • 7.6 Concluding Remarks3pc
  • References
  • 8 Low Achievers in Mathematics-Ideas from the Netherlands for Developing a Competence-Oriented View
  • 8.1 Introduction3pc
  • 8.2 Mathematics Education in Special Education in Germany3pc
  • 8.3 Looking at the Netherlands: Looking at a Competence-Oriented Approach3pc
  • 8.3.1 Realistic Mathematics Education3pc
  • 8.3.2 Diagnostic Procedures: New Assessment Formats3pc
  • 8.3.3 Students' Own Productions: Open Problems3pc
  • 8.3.4 Making Connections Between Problems: Patterns and Structures3pc
  • 8.4 Research in Germany3pc
  • 8.4.1 Competence-Oriented Diagnosis3pc
  • 8.4.2 Students' Own Productions: Open Problems3pc
  • 8.4.3 Making Use of Picture Books for Learning Mathematics3pc
  • 8.4.4 Primary Students' Preconceptions of Negative Numbers3pc
  • 8.5 Conclusions and Perspectives3pc
  • 8.5.1 Competence-Oriented Diagnosis and Instruction3pc
  • 8.5.2 Own Productions and Open Problems3pc
  • 8.5.3 Support of Own Strategies3pc
  • 8.5.4 Role of Mistakes3pc
  • 8.5.5 Last but Not Least3pc
  • References
  • 9 From the Bottom Up-Reinventing Realistic Mathematics Education in Southern Argentina
  • 9.1 Introduction3pc
  • 9.1.1 Curricular Innovation in Mathematics Education3pc
  • 9.1.2 Initial Attempts at Bringing Realistic Mathematics Education to Argentina3pc
  • 9.1.3 San Carlos de Bariloche, Birthplace of the Grupo Patagónico de Didáctica de la Matemática3pc
  • 9.2 First Phase (2000-2004): Contexts, Situations, Models, and Strategies3pc
  • 9.2.1 Fractions, Decimals, and Percentages3pc
  • 9.2.2 City Buses3pc.
  • 9.2.3 From Necklaces to Number Lines3pc
  • 9.2.4 The Function of Contexts in RME3pc
  • 9.2.5 Mental Arithmetic: Models and Strategies3pc
  • 9.3 Second Phase (2005-2009): Deepening and Solidifying3pc
  • 9.3.1 Mathematising Within the GPDM3pc
  • 9.3.2 Making Connections3pc
  • 9.3.3 Fall Seminar: Teachers Teaching Teacher Educators3pc
  • 9.3.4 In the Meanwhile, in Pre-service Teacher Education3pc
  • 9.3.5 Thinking Aloud Together3pc
  • 9.4 Third Phase (2011-2015): The GPDM, an Ever-Expanding Endeavour3pc
  • 9.4.1 More Publications and Translations3pc
  • 9.4.2 Research Projects3pc
  • 9.5 Closure3pc
  • References
  • 10 Realistic Mathematics Education in the Chinese Context-Some Personal Reflections
  • 10.1 Historical Review3pc
  • 10.1.1 Hans Freudenthal's Visit to China3pc
  • 10.1.2 Chinese Scholars' Visits to the Freudenthal Institute3pc
  • 10.1.3 Two Forums on the Theory and Practice of RME Held in China3pc
  • 10.2 The Influence of RME in the Chinese Context3pc
  • 10.2.1 The Influence of RME on Curricular Policy Making3pc
  • 10.2.2 The Influence of RME on Textbook Design3pc
  • 10.2.3 The Influence of RME on Classroom Teaching3pc
  • References
  • 11 The Enrichment of Belgian Secondary School Mathematics with Elements of the Dutch Model of Realistic Mathematics Education Since the 1980s
  • 11.1 Papy and Freudenthal: Opposite Views on Mathematics Education in Neighbouring Countries3pc
  • 11.2 Critique on New Math in Belgium and Search for Alternatives3pc
  • 11.3 How During the Middle 1980s and 1990s New Developments in Neighbouring Countries Reached the Community of Flemish Mathematics Teachers3pc
  • 11.3.1 Rounding off the Rough Edges of New Math3pc
  • 11.3.2 A Second Wave of Changes3pc
  • 11.3.3 Consolidation3pc
  • 11.4 Some Topics that Underwent a True Metamorphosis3pc
  • 11.5 Conclusion3pc
  • References.
  • 12 Echoes and Influences of Realistic Mathematics Education in Portugal
  • 12.1 Introduction3pc
  • 12.2 Influences on Research Studies3pc
  • 12.2.1 Whole Numbers and Operations3pc
  • 12.2.2 Mental Calculation3pc
  • 12.2.3 Rational Numbers3pc
  • 12.2.4 Algebra3pc
  • 12.2.5 Geometry3pc
  • 12.3 Influences on Curriculum Documents3pc
  • 12.4 Conclusion3pc
  • References
  • 13 Supporting Mathematical Learning Processes by Means of Mathematics Conferences and Mathematics Language Tools
  • 13.1 The Santa Claus Problem3pc
  • 13.2 The Guiding Principle of Progressive Mathematisation3pc
  • 13.3 Using Mathematics Conferences3pc
  • 13.3.1 Learning to Subtract in the Number Domain up to 10003pc
  • 13.3.2 Task-Related Exchange with the Help of Mathematics Conferences3pc
  • 13.3.3 Tools for Organising Mathematics Conferences3pc
  • 13.4 Learning to Describe and Explain by Using Mathematics Language Tools3pc
  • 13.4.1 Mathematics, More Than Calculating3pc
  • 13.4.2 Sums of Consecutive Natural Numbers3pc
  • 13.4.3 Mathematics Language Tools3pc
  • 13.5 Numbers Can Be Realistic Too3pc
  • References
  • 14 Reinventing Realistic Mathematics Education at Berkeley-Emergence and Development of a Course for Pre-service Teachers
  • 14.1 Reinventing Realistic Mathematics Education at Tel Aviv University: Dor's Story3pc
  • 14.2 Meanwhile, in New York City: Betina's Story3pc
  • 14.2.1 At the Graduate Center of City University of New York3pc
  • 14.2.2 Mathematics in the City: Learning and Practicing Realistic Mathematics Education3pc
  • 14.2.3 At Brooklyn College3pc
  • 14.3 Reinventing Algebra Brick by Brick: A Graduate Level Pre-service Mathematics Teaching Course3pc
  • 14.3.1 Paradigmatic Didactical-Mathematical Problematic Situations3pc
  • 14.3.2 The 'Brick Pyramid' Problem3pc
  • 14.3.3 Reinventing Algebra by Thinking Aloud Together About the Brick Pyramid and Beyond3pc.
  • 14.4 An Undergraduate Course for Pre-service Mathematics Teachers3pc.

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