European Traditions in Didactics of Mathematics.

• Superior document: ICME-13 Monographs
• Author: Blum, Werner.
• TeilnehmendeR: Artigue, Michèle.; Mariotti, Maria Alessandra.; Sträßer, Rudolf.; Van den Heuvel-Panhuizen, Marja.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2019.; ©2019.
• Year of Publication: 2019
• Edition: 1st ed.
• Language: English
• Series: ICME-13 Monographs
• Physical Description: 1 online resource (215 pages)

Table of Contents

Intro -- Contents -- 1 European Didactic Traditions in Mathematics: Introduction and Overview -- 1.1 Introduction -- 1.2 The Role of Mathematics and Mathematicians -- 1.3 The Role of Theory -- 1.4 The Role of Design Activities for Teaching and Learning Environments -- 1.5 The Role of Empirical Research -- 1.6 The Presented Cases -- References -- 2 The French Didactic Tradition in Mathematics -- 2.1 The Emergence and Development of the French Didactic Tradition -- 2.1.1 A Tradition with Close Relationship to Mathematics -- 2.1.2 A Tradition Based on Three Main Theoretical Pillars -- 2.1.3 Theoretical Evolutions -- 2.1.4 Relationship to Design -- 2.1.5 The Role of Empirical Research -- 2.2 Research on Line Symmetry and Reflection in the French Didactic Tradition -- 2.2.1 Students' Conceptions, Including Proof and Proving, and Classroom Design -- 2.2.2 The Study of Teachers' Practices and Their Effects on Students' Learning -- 2.2.3 Current Research -- 2.3 Research on School Algebra in the French Didactic Tradition. From Didactic Transposition to Instrumental Genesis -- 2.3.1 What Algebra Is to Be Taught: Didactic Transposition Constraints -- 2.3.2 Teaching Algebra at Secondary School Level -- 2.3.3 Algebra and ICT -- 2.4 View of the French Tradition Through the Lens of Validation and Proof -- 2.4.1 Cohesion -- 2.4.2 Interchange -- 2.4.3 Dissemination -- 2.5 Didactic Interactions Between France and Italy. A Personal Journey -- 2.5.1 Opportunities for Collaboration: SFIDA, Summer Schools and European Projects -- 2.5.2 A Personal Scientific Journey -- 2.6 Didactic Interactions Between France and Latin-America: The Case of Mexico -- 2.6.1 The DME at CINVESTAV and Its Relation to "the" French School -- 2.6.2 The DIE-CINVESTAV: A Strong Influence on Basic Education Supported by TDS.

2.6.3 The PROME at CICATA-IPN: A Professionalization Program for Teachers that Generates Relations Between France and Latin America -- 2.6.4 Theoretical Currents, Methodologies and Tools -- 2.6.5 Areas of Opportunity and Perspectives -- 2.7 Didactic Interactions Between France and African Countries. The Case of Tunisia -- 2.7.1 The Emergence of Didactic Interactions Between France and Tunisia -- 2.7.2 Development and Institutionalization -- 2.7.3 Some Outcomes of the French-Tunisian Didactic Collaboration -- 2.8 Epilogue -- References -- 3 Didactics of Mathematics in the Netherlands -- 3.1 Mathematics Education in the Netherlands Viewed from Four Perspectives -- 3.1.1 The Role of Mathematics and Mathematicians in Mathematics Education in the Netherlands -- 3.1.2 The Role of Theory in Mathematics Education in the Netherlands -- 3.1.3 The Role of Design in Mathematics Education in the Netherlands -- 3.1.4 The Role of Empirical Research in Mathematics Education in the Netherlands -- 3.2 Students' Own Productions and Own Constructions-Adri Treffers' Contributions to Realistic Mathematics Education -- 3.2.1 Introduction -- 3.2.2 Treffers' Theoretical Framework for Realistic Mathematics Education -- 3.2.3 Students' Own Productions -- 3.2.4 Students' Own Constructions -- 3.2.5 Challenging Students with Classical Puzzles -- 3.2.6 Students' Input Is the Basis of Everything -- 3.3 Contexts to Make Mathematics Accessible and Relevant for Students-Jan de Lange's Contributions to Realistic Mathematics Education -- 3.3.1 Introduction -- 3.3.2 Using a Central Context for Designing Education -- 3.3.3 Contexts for Introducing and Developing Concepts -- 3.3.4 Relevant Mathematics Education -- 3.3.5 Conclusion -- 3.4 Travelling to Hamburg -- 3.4.1 Introduction -- 3.4.2 Task Design -- 3.4.3 Field Tests -- 3.4.4 Possible Task Extensions -- 3.4.5 Conclusion.

3.5 Voices from Abroad -- 3.5.1 Realistic Mathematics Education in the United States -- 3.5.2 Two Decades of Realistic Mathematics Education in Indonesia -- 3.5.3 Implementing Realistic Mathematics Education in England and the Cayman Islands -- 3.5.4 Reflections on Realistic Mathematics Education in South Africa -- 3.5.5 Influences of Realistic Mathematics Education on Mathematics Education in Belgium -- References -- 4 The Italian Didactic Tradition -- 4.1 Introduction -- 4.2 Mathematicians and Educational Issues: A Historical Overview -- 4.3 The Development of an Italian Research Paradigm -- 4.3.1 The Early International Presentations of the Italian Didactics of Mathematics -- 4.3.2 A Retrospective Analysis 30 Years Later: Some Examples from Classroom Innovation to Theoretical Elaborations -- 4.3.3 The Impact of Italian Research at the International Level -- 4.3.4 Mathematics Teacher Education and Professional Development in Italy -- 4.4 Collective and Personal Experiences of Collaboration Between French and Italian Researchers -- 4.4.1 The Séminaire Franco Italien de Didactique de l'Algèbre -- 4.4.2 Encounter with Various Intellectual Traditions and Methods in French-Italian Ph.D. Projects -- 4.5 The Italian Tradition From a Chinese Cultural Perspective -- 4.5.1 On the Historical Aspects of the Italian Tradition -- 4.5.2 On the Characteristic Aspects of the Italian Tradition -- 4.5.3 On the Institutional Aspects of the Italian Tradition -- References -- 5 The German Speaking Didactic Tradition -- 5.1 Introductory Remark -- 5.2 Historical Sketch on German Speaking Didactics of Mathematics -- 5.2.1 Starting Point in the 1960s -- 5.2.2 Institutionalisation -- 5.2.3 The 1970s/1980s: The "Realistic Turn" -- 5.2.4 Didactics in the German Democratic Republic (GDR) -- 5.2.5 1990s: The PISA Shock -- 5.3 The 21st Century-At Present.

5.3.1 Stoffdidaktik Enlarged-The Design of Learning Environments -- 5.3.2 Ongoing Diversification of Classroom Studies -- 5.3.3 Large Scale Comparative Studies -- 5.4 About the Future of German-Speaking Didactics of Mathematics -- 5.5 Comments from Critical Friends -- 5.5.1 Doing Empirical Research Differently: The Nordic and German Cases. A View from the Nordic Countries -- 5.5.2 Perspectives on Collaborative Empirical Research in Germany and in Poland -- 5.5.3 Didaktik der Mathematik and Didaktika Matematiky -- Appendix -- References -- 6 Didactics of Mathematics as a Research Field in Scandinavia -- 6.1 Introduction -- 6.2 Historical Background -- 6.3 Didactics of Mathematics Emerging as a Research Discipline in Scandinavia -- 6.4 The Development in Denmark -- 6.4.1 Mathematical Modelling -- 6.4.2 Mathematical Competencies -- 6.4.3 Political Aspects of Mathematics -- 6.4.4 The French Tradition in Denmark -- 6.5 The Development in Norway -- 6.5.1 The Constructivist Tradition -- 6.5.2 The Socio-cultural Tradition -- 6.5.3 Further Work Within the Socio-cultural Paradigm -- 6.5.4 Research on University Didactics -- 6.5.5 Classroom Research and Research on Aspects of Teacher Education -- 6.5.6 Large-Scale Studies -- 6.6 The Development in Sweden -- 6.6.1 Low Achievement -- 6.6.2 Phenomenography and Variation Theory -- 6.6.3 Learning by Imitative and Creative Reasoning -- 6.6.4 Assessment -- 6.6.5 Mathematics and Language -- 6.6.6 Early Learning of Mathematics -- 6.6.7 Inclusive Mathematics Education -- 6.6.8 Research on Particular Mathematical Topics -- 6.6.9 Research on Teacher Education -- 6.7 Important Initiatives Across the Countries -- 6.7.1 Nordic Studies in Mathematics Education (NOMAD) -- 6.7.2 The NORMA Conferences -- 6.7.3 The Nordic Graduate School for Mathematics Education (NoGSME) -- References.

7 Czech and Slovak Research in Didactics of Mathematics -- 7.1 Introduction -- 7.1.1 Aim of the Chapter -- 7.1.2 Brief History of Schooling and Teacher Education in the Region -- 7.2 Emergence of Didactics of Mathematics as a Science -- 7.2.1 International Perspective -- 7.2.2 National Perspective -- 7.2.3 Czechoslovak Research in Mathematics Education Before 1989 -- 7.3 Mathematics Education Research in the Czech Republic and in Slovakia After 1989 -- 7.3.1 Methodology -- 7.3.2 Development of Theories -- 7.3.3 Knowledge and Education of Future Elementary and Mathematics Teachers -- 7.3.4 Classroom Research -- 7.3.5 Pupils' Reasoning in Mathematics -- 7.4 Current Situation, Perspectives and Challenges -- References.