National Reflections on the Netherlands Didactics of Mathematics: Teaching and Learning in the Context of Realistic Mathematics Education (ICME-13 Monographs)

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 & 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
		13.4.4 Two Questions in the Margin: Is History Essential, and What Is the Role of Old Language?
	13.5 Method
		13.5.1 Background
		13.5.2 Participants and Data Collection
		13.5.3 Teaching Material
	13.6 Findings
		13.6.1 An Observation: Two Students as Surveyor
		13.6.2 Findings from All Students Involved in the Data Set
		13.6.3 Judgements and Views of the Teachers
	13.7 Conclusions and Discussion
	References
14 The Development of Calculus in Dutch Secondary Education—Balancing Conceptual Understanding and Algebraic Techniques
	14.1 A Forwards Run of Fifty Years
	14.2 After 50 Years of Discussion, Calculus Entered the National Written Final Examination
	14.3 The Influence of New Math
	14.4 The HEWET Project: A Small Revolution in Pre-University Secondary Education
	14.5 Discrete Calculus in Secondary Pre-Higher-Vocational Education
	14.6 Calculus in Mathematics B for Secondary Pre-university Education
	14.7 Back to the Future?
	References
15 The Emergence of Meaningful Geometry
	15.1 A World-Wide Change in Geometry Education
	15.2 First Steps Towards a New Geometry Education in the Netherlands
	15.3 Precursors of Meaningful Geometry Education in the Netherlands
	15.4 The Early Experiments: The Focus on Spatial Insight
		15.4.1 Five Examples of Vision Geometry
		15.4.2 What These Tasks Have in Common
	15.5 A Change in Geometry Education: Geometry Problems in 1976 and in 2002
	15.6 An Example of Local Organisation: The Nearest Neighbour Principle
	15.7 Final Remarks
	References
16 Testing in Mathematics Education in the Netherlands
	16.1 Introduction
	16.2 Testing Mathematics in the Netherlands
		16.2.1 Dutch Education System
		16.2.2 Primary Education
		16.2.3 Secondary Education
	16.3 Function of Tests
		16.3.1 Tests to Evaluate and Adjust Instruction
		16.3.2 Tests to Evaluate Proficiency and Make Decisions About Students
		16.3.3 Tests to Evaluate Proficiency and Make Decisions About Classes and Schools
		16.3.4 Tests to Evaluate Proficiency and Make Decisions About the Quality of Education
	16.4 Use of Tests for Accountability
		16.4.1 Primary Education
		16.4.2 Secondary Education
	16.5 Discussion
		16.5.1 Content-Related Issues
		16.5.2 Use of Test Scores
		16.5.3 Use of Tests
	Appendix A
	Appendix B
	Appendix C
	Appendix D
	Appendix E
	References
17 There Is, Probably, No Need for Such an Institution—The Freudenthal Institute in the Last Two Decades of the Twentieth Century
	17.1 Introduction
	17.2 The Mission: Innovation in Mathematics Education
	17.3 By Means of Connecting Research and Practice (Developmental Research)
	17.4 In Teams of Talented People, ‘Organised’ in Ways that Let Them Shine
	17.5 Working in a Flat, Informal, Maybe Even Somewhat Chaotic, Organisational Structure
	17.6 Connecting All Players—Politicians, Scientists, Practitioners, Textbook Authors—Using a Variety of Dissemination Methods
	17.7 By Powerful and Relevant New Ideas
	17.8 Provocative and Innovative with Vision
	17.9 Reaching Out Internationally to Validate Theories
	17.10 Having Fun
	References