National Reflections on the Netherlands Didactics of Mathematics : : Teaching and Learning in the Context of Realistic Mathematics Education.
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| Superior document: | ICME-13 Monographs |
|---|---|
| : | |
| Place / Publishing House: | Cham : : Springer International Publishing AG,, 2020. ©2020. |
| Year of Publication: | 2020 |
| Edition: | 1st ed. |
| Language: | English |
| Series: | ICME-13 Monographs
|
| Online Access: | |
| Physical Description: | 1 online resource (348 pages) |
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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 &
- 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.