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

• Superior document: ICME-13 Monographs
• Author: 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
• Physical Description: 1 online resource (369 pages)

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.