National reflections on the Netherlands didactics of mathematics : teaching and learning in the context of realistic mathematics education

• Main Author: Heuvel-Panhuizen, Marja van den
• Format: eBook Book
• Language: English
• Published: Cham Springer Nature Switzerland AG 2020; Springer Nature; Springer International Publishing AG; Springer Open
• Edition: 1
• Series: ICME-13 Monographs
• Subjects: Assessment; Assessment in the Netherlands; Cognition & cognitive psychology; Didactics of mathematics; Education; Education: examinations & assessment; Education: examinations and assessment; Educational system in the Netherlands; Educational systems and structures; Higher education, tertiary education; ICME 13 Thematic Afternoon; Learning & Instruction; Mathematics; Mathematics > Study and teaching > Netherlands; Mathematics Education; Mathematics in the Dutch educational system; Nonfiction; Open Access; Realistic Mathematics Education; Reform in mathematics education; RME; Society and Social Sciences; Tasks for teaching and assessing mathematics; Teacher education in the Netherlands; Teacher training; Teaching and Teacher Education; Teaching of a specific subject; Teaching skills & techniques; Teaching skills and techniques; Testing and Evaluation; Textbook

This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, consists of 17 chapters, in which educators from the Netherlands reflect on the teaching and learning of mathematics in their country and the role of the Dutch domain-specific instruction theory of R...

Table of Contents:

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