National Reflections on the Netherlands Didactics of Mathematics : : Teaching and Learning in the Context of Realistic Mathematics Education.

• Superior document: ICME-13 Monographs
• Author: Van den Heuvel-Panhuizen, Marja.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2020.; ©2020.
• Year of Publication: 2020
• Edition: 1st ed.
• Language: English
• Series: ICME-13 Monographs
• Physical Description: 1 online resource (348 pages)

Table of Contents

Intro -- Preface -- Contents -- 1 A Spotlight on Mathematics Education in the Netherlands and the Central Role of Realistic Mathematics Education -- 1.1 Introduction -- 1.2 The Focus on a Particular Type of Tasks -- 1.3 Usefulness as a Key Concept -- 1.4 Common Sense and Informal Knowledge -- 1.5 Mathematical Content Domains Subject to Innovation -- 1.6 The Systemic Context of Dutch Education -- 1.7 The Implementation of RME -- 1.8 The Context of Creating a New Approach to Mathematics Education -- Reference -- 2 Mathematics in Teams-Developing Thinking Skills in Mathematics Education -- 2.1 Introduction -- 2.2 The Emergence of Mathematics in Teams to Develop Mathematical Thinking -- 2.2.1 Secondary Education -- 2.2.2 Primary Education -- 2.3 Characteristics of the Mathematics A-lympiad and the Mathematics B-day Assignments -- 2.3.1 Example from the Mathematics A-lympiad: 'Working with Breaks' -- 2.3.2 Example from the Mathematics B-day: 'How to Crash a Dot?' -- 2.4 The Role of the Teacher -- 2.5 The Student Perspective -- 2.6 The Future of Mathematical Thinking in Secondary Mathematics Education -- References -- 3 Task Contexts in Dutch Mathematics Education -- 3.1 The Prevalent Use of Real-Life Contexts in Dutch Mathematics Tasks -- 3.2 Categories for Mathematical Tasks and Their Relation to Reality -- 3.3 Tasks Contexts in a Dutch Secondary Education Mathematics Textbook -- 3.4 Contexts in Dutch Secondary Education National Mathematics Examinations -- 3.5 Conclusion on Contexts in Dutch Mathematics Education -- References -- 4 Mathematics and Common Sense-The Dutch School -- 4.1 Introduction -- 4.2 Common Sense of Young Students -- 4.3 A 'Math Mom' at Work with a Small Group -- 4.4 A Russian Pioneer Within the Dutch School -- 4.5 A World of Packages -- 4.6 A Real Problem in the Classroom -- References.

5 Dutch Mathematicians and Mathematics Education-A Problematic Relationship -- 5.1 Start of a Tradition of Academic Involvement in Mathematics Teaching? -- 5.2 Aloofness of the Government -- 5.3 No Role for the Experts -- 5.4 A Stagnating World -- 5.5 The Times They Are A-Changin' -- 5.6 The Big Bang -- 5.7 Return of the Mathematicians -- 5.8 A New Start? -- References -- 6 Dutch Didactical Approaches in Primary School Mathematics as Reflected in Two Centuries of Textbooks -- 6.1 Introduction -- 6.1.1 Procedural Textbook Series -- 6.1.2 Conceptual Textbook Series -- 6.1.3 Dual Textbook Series -- 6.1.4 Textbooks Series in Use Over Five Time Periods -- 6.2 The Period 1800-1875: Procedural Didactics and Semi-textbook Use -- 6.2.1 Teaching Mathematics on the Blackboard and No Complete Textbook Series Available -- 6.2.2 The Textbook Series by Hemkes -- 6.2.3 Boeser's Mathematics Textbooks -- 6.3 The Period 1875-1900: Conceptual Textbook Series of a Heuristic Orientation -- 6.3.1 Influence from Germany -- 6.3.2 Versluys -- 6.3.3 Van Pelt -- 6.3.4 The Adage of the Conceptual Mathematics Textbook Series with a Heuristic Orientation -- 6.4 The Period 1900-1950: Dual Textbook Series -- 6.5 The Period 1950-1985: Procedural Textbook Series and Conceptual Textbook Series with a Functional Orientation -- 6.6 The Period 1985-1990: Towards a National Programme for Primary School Mathematics -- 6.7 The Period 1990-2010: Realistic Textbook Series -- 6.7.1 An Abundance of Textbook Series -- 6.7.2 The Results from the Cito PPON Studies -- 6.8 The Future Landscape of Textbook Series in the Netherlands -- References -- 7 Sixteenth Century Reckoners Versus Twenty-First Century Problem Solvers -- 7.1 Introduction -- 7.2 Arithmetic in the Sixteenth Century -- 7.2.1 Merchants, the New Rich of the Sixteenth Century -- 7.2.2 Traditional Arithmetic on the Counting Board.

7.2.3 A New Written Arithmetic Method with Hindu-Arabic Numbers -- 7.2.4 The Rise of the New Arithmetic Method in the Netherlands -- 7.2.5 The Content of the Dutch Arithmetic Books from the Sixteenth Century -- 7.2.6 Didactic Principles in Dutch Arithmetic Books from the Sixteenth Century -- 7.2.7 Interesting Exceptions -- 7.3 Arithmetic in the Twenty-First Century -- 7.3.1 Comparing Sixteenth and Twenty-First Century Education -- 7.3.2 Twenty-First Century Skills in General -- 7.3.3 Twenty-First Century Skills in Mathematics Education -- 7.3.4 The Content of the Mathematics Curriculum -- References -- 8 Integration of Mathematics and Didactics in Primary School Teacher Education in the Netherlands -- 8.1 Introduction -- 8.2 Mathematising and Didacticising -- 8.2.1 The Influence of Freudenthal on Mathematics Teacher Education -- 8.2.2 A Model for Learning to Teach Mathematics -- 8.3 New Developments in Primary School Mathematics Teacher Education -- 8.3.1 Mathematics &amp -- Didactics as a New Subject for Student Teachers -- 8.3.2 The Influence of Quality Monitoring -- 8.3.3 Growing Attention to Student Teachers' Mathematical Literacy -- 8.4 Standards for Primary School Mathematics Teacher Education: Adapting the View on Learning to Teach Mathematics -- 8.4.1 Towards Standards for Primary School Mathematics Teacher Education -- 8.4.2 Constructive, Reflective, Narrative -- 8.4.3 Mile -- 8.5 New Ideas About Learning to Teach Mathematics -- 8.6 A Mathematics Entrance Test for Student Teachers -- 8.7 The Knowledge Base for Primary Mathematics Teacher Education -- 8.7.1 Background -- 8.7.2 Defining Professional Mathematics Literacy -- 8.7.3 Content of the Knowledge Base -- 8.8 The Knowledge Base Test -- 8.8.1 Content of the Knowledge Base Test -- 8.8.2 Influence of the Knowledge Base Test on the Curriculum for Primary School Mathematics Teacher Education.

8.9 Recent Learning Materials for Student Teachers -- 8.10 Perspective: Searching for a Balance -- References -- 9 Secondary School Mathematics Teacher Education in the Netherlands -- 9.1 The Dutch Educational System -- 9.1.1 The School System -- 9.1.2 Secondary School Teacher Education -- 9.1.3 Continuous Professional Development -- 9.2 Aims of Teacher Education -- 9.2.1 Professional Competence a Teacher Must Have -- 9.2.2 A Broad Range of Teacher Competences is Required -- 9.2.3 The Approach to Mathematics Education -- 9.2.4 Mathematical Subject Knowledge for Secondary School Teachers -- 9.2.5 Research Skills for Secondary School Teachers -- 9.3 The Curricula for Secondary School Teacher Education -- 9.3.1 Quadrant 1: Reflective Practice -- 9.3.2 Quadrant 2: Theoretical Concepts and Exercises -- 9.3.3 Quadrant 3: Practice and Work in a Safe Environment -- 9.3.4 Quadrant 4: Learning on the Job -- 9.3.5 Merging All Activities: Exhibiting and Assessing Competence -- 9.4 Reflections on the Current Situation -- 9.4.1 Reflection on the Dutch Educational System -- 9.4.2 Reflection on the Aims of Dutch Secondary School Mathematics Teacher Education -- 9.4.3 Reflection on the Curricula for Secondary School Teacher Education -- References -- 10 Digital Tools in Dutch Mathematics Education: A Dialectic Relationship -- 10.1 Introduction -- 10.2 A Brief Flash-Back -- 10.3 The Case of Handheld Graphing Calculators -- 10.3.1 Initial Expectations -- 10.3.2 Developing Practices -- 10.3.3 Additional Symbolics -- 10.3.4 Conclusions on the Graphing Calculator Case -- 10.4 The Case of the Digital Mathematics Environment -- 10.4.1 Technological Development -- 10.4.2 Design Choices -- 10.4.3 Role for the Teacher -- 10.4.4 Conclusion on the Digital Mathematics Environment Case -- 10.5 Conclusion -- References.

11 Ensuring Usability-Reflections on a Dutch Mathematics Reform Project for Students Aged 12-16 -- 11.1 Vision -- 11.1.1 Radical Innovation -- 11.1.2 Pioneering -- 11.1.3 The Educational and Societal Context of the Change -- 11.1.4 The Dutch School System -- 11.2 The Content of the New Curriculum -- 11.2.1 RME-The Vision in a Nutshell -- 11.2.2 RME in Secondary Education -- 11.2.3 Examples from Final Examinations -- 11.2.4 The Change in Content -- 11.2.5 From Mathematics for a Few to Mathematics for All -- 11.3 Implementation -- 11.3.1 Implementation Theories -- 11.3.2 Initiation Phase -- 11.3.3 Implementation Phase -- 11.3.4 Continuation and Institutionalisation -- 11.4 Reflection -- 11.4.1 How Sustainable Is the New Situation? -- 11.4.2 The Way Forwards -- References -- 12 A Socio-Constructivist Elaboration of Realistic Mathematics Education -- 12.1 Introduction -- 12.2 Conceptual Compatibility of (Socio-)Constructivism and Realistic Mathematics Education -- 12.3 A Socio-Constructivist Perspective on Teaching and Learning -- 12.4 Symbolising and Modelling -- 12.4.1 Emergent Modelling -- 12.5 RME in Terms of Instructional Design Heuristics -- 12.5.1 Emergent Modelling Heuristic -- 12.5.2 Guided Reinvention Heuristic -- 12.5.3 Didactical Phenomenology Heuristic -- 12.6 Pedagogical Content Tools -- 12.7 RME and Classroom Practice -- 12.8 Recent Research on Instructional Practice in the Netherlands -- 12.9 Conclusion -- References -- 13 Eighteenth Century Land Surveying as a Context for Learning Similar Triangles and Measurement -- 13.1 Introduction -- 13.2 Surveying and the Teaching and Learning of Measurement by Using Similar Triangles -- 13.3 History of Mathematics as a Context for Mathematics Education -- 13.4 Research Questions -- 13.4.1 Role of History for Motivation -- 13.4.2 Influence on the Learning Process.

13.4.3 Students' View on the Role of Mathematics in Society.