ICME-13 Monographs Marja Van den Heuvel-Panhuizen Editor National Reflections on the Netherlands Didactics of Mathematics Teaching and Learning in the Context of Realistic Mathematics Education ICME-13 Monographs Series Editor Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität Hamburg, Hamburg, Germany Each volume in the series presents state-of-the art research on a particular topic in mathematics education and reflects the international debate as broadly as possible, while also incorporating insights into lesser-known areas of the discussion. Each volume is based on the discussions and presentations during the ICME-13 congress and includes the best papers from one of the ICME-13 Topical Study Groups, Discussion Groups or presentations from the thematic afternoon. More information about this series at http://www.springer.com/series/15585 Marja Van den Heuvel-Panhuizen Editor National Reflections on the Netherlands Didactics of Mathematics Teaching and Learning in the Context of Realistic Mathematics Education Editor Marja Van den Heuvel-Panhuizen Freudenthal Group & Freudenthal Institute Utrecht University Utrecht, The Netherlands Faculty of Education, Art and Culture Nord University Bodø, Norway The Open Access publication of this book was made possible in part by generous support from the Utrecht University Open Access Fund, the Nord University Open Access Fund, the Freudenthal Institute of Utrecht University, and the NVORWO (Netherlands Association for the Development of Mathematics Education). ISSN 2520-8322 ISSN 2520-8330 (electronic) ICME-13 Monographs ISBN 978-3-030-33823-7 ISBN 978-3-030-33824-4 (eBook) https://doi.org/10.1007/978-3-030-33824-4 © The Editor(s) (if applicable) and The Author(s) 2020. 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This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface This volume is part of the ICME-13 Monographs and is a spin-off of the Netherlands strand of the ICME-13 Thematic Afternoon on “European Didactic Traditions” held in Hamburg in 2016. In this session, four European countries—France, Italy, Germany, and the Netherlands—presented their approach to teaching and learning mathematics in school and in research and development. The session inspired mathematics didacticians familiar with Dutch mathematics education to reflect on the approach to teaching and learning mathematics education in the Netherlands and the role of the Dutch domain-specific instruction theory of Realistic Mathematics Education. This resulted in two volumes: International Reflections on the Netherlands Didactics of Mathematics—Visions on and Experiences with Realistic Mathematics Education and National Reflections on the Netherlands Didactics of Mathematics—Teaching and Learning in the Context of Realistic Mathematics Education. The current volume is the National Reflections book. The volume describes the Dutch approach to teaching and learning mathematics and is written by Dutch people. The authors of these “reflections from inside” have in various ways built up a hoard of expertise on this, either as a mathematics teacher, a mathematics teacher educator, a school advisor, or as a developer and researcher of instructional material, textbooks, teaching–learning trajectories, curricula, and examinations and tests. In 17 chapters, 28 authors reflect on mathematics education in the Netherlands and when doing this they have a broad scope. Several chapters discuss aspects of the theoretical underpinnings of the Dutch approach that, starting some 50 years ago, became rather dominant in the Netherlands, and that is known as Realistic Mathematics Education. Other chapters go back further in history or use history in their teaching of mathematics, or zoom in on changes in particular subject matter domains and in use of technology. One chapter shines a light on the relationship between Dutch mathematicians and mathematics education. Other chapters give a glimpse into the process of innovation and how the Dutch and in particular one Dutch institute have worked on the reform. To place these reflections from inside in the context of the Dutch educational system, the volume also contains chapters that v vi Preface explain how teacher education and testing in mathematics education are organised in the Netherlands. Of course, all the chapters in this volume together are not enough to give a full picture of the Netherlands didactic tradition. Other people might have told other experiences and might have other views, but the authors of this volume shared their knowledge about mathematics education in the Netherlands by writing a chapter about it. Thanks to their inspiring pieces of work, the volume could come into existence. However, especially instrumental for making this happening was Nathalie Kuijpers, who together with me checked and double-checked all the texts. Many, many thanks for this. Utrecht, The Netherlands Marja Van den Heuvel-Panhuizen May 2019 Contents 1 A Spotlight on Mathematics Education in the Netherlands and the Central Role of Realistic Mathematics Education ....... 1 Marja Van den Heuvel-Panhuizen 2 Mathematics in Teams—Developing Thinking Skills in Mathematics Education................................ 15 Monica Wijers and Dédé de Haan 3 Task Contexts in Dutch Mathematics Education............... 31 Pauline Vos 4 Mathematics and Common Sense—The Dutch School .......... 55 Rijkje Dekker 5 Dutch Mathematicians and Mathematics Education—A Problematic Relationship ..................... 63 Harm Jan Smid 6 Dutch Didactical Approaches in Primary School Mathematics as Reflected in Two Centuries of Textbooks .................... 77 Adri Treffers and Marja Van den Heuvel-Panhuizen 7 Sixteenth Century Reckoners Versus Twenty-First Century Problem Solvers ....................................... 105 Marjolein Kool 8 Integration of Mathematics and Didactics in Primary School Teacher Education in the Netherlands ...................... 121 Wil Oonk, Ronald Keijzer and Marc van Zanten 9 Secondary School Mathematics Teacher Education in the Netherlands ...................................... 147 Joke Daemen, Ton Konings and Theo van den Bogaart vii viii Contents 10 Digital Tools in Dutch Mathematics Education: A Dialectic Relationship ................................. 177 Paul Drijvers 11 Ensuring Usability—Reflections on a Dutch Mathematics Reform Project for Students Aged 12–16 .................... 197 Kees Hoogland 12 A Socio-Constructivist Elaboration of Realistic Mathematics Education ............................................ 217 Koeno Gravemeijer 13 Eighteenth Century Land Surveying as a Context for Learning Similar Triangles and Measurement ........................ 235 Iris van Gulik-Gulikers, Jenneke Krüger and Jan van Maanen 14 The Development of Calculus in Dutch Secondary Education—Balancing Conceptual Understanding and Algebraic Techniques ................................ 263 Martin Kindt 15 The Emergence of Meaningful Geometry .................... 281 Michiel Doorman, Marja Van den Heuvel-Panhuizen and Aad Goddijn 16 Testing in Mathematics Education in the Netherlands .......... 303 Floor Scheltens, Judith Hollenberg-Vos, Ger Limpens and Ruud Stolwijk 17 There Is, Probably, No Need for Such an Institution—The Freudenthal Institute in the Last Two Decades of the Twentieth Century ................................ 331 Jan de Lange Chapter 1 A Spotlight on Mathematics Education in the Netherlands and the Central Role of Realistic Mathematics Education Marja Van den Heuvel-Panhuizen Abstract In this introductory chapter I give a preview of the landscape of issues concerning mathematics education in the Netherlands and the role of Realistic Math- ematics Education (RME) that one can come across in this volume, which contains the reflections of twenty-eight Dutch mathematics didacticians on teaching and learn- ing mathematics in