European Didactic Traditions in Mathematics: Aspects and Examples from Four Selected Cases (original) (raw)
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European Didactic Traditions in Mathematics: Introduction and Overview
ICME-13 monographs, 2019
European traditions in the didactics of mathematics share some common features such as a strong connection with mathematics and mathematicians, the key role of theory, the key role of design activities for learning and teaching environments, and a firm basis in empirical research. In this first chapter, these features are elaborated by referring to four cases: France, the Netherlands, Italy and Germany. In addition, this chapter gives an overview on the other chapters of the book. Keywords European didactic traditions • Overview 1.1 Introduction Across Europe, there have been a variety of traditions in mathematics education, both in the practice of learning and teaching at school and in research and development, which have resulted from different cultural, historical and political backgrounds. Despite these varying backgrounds, most of these traditions share some common
The French Didactic Tradition in Mathematics
European Traditions in Didactics of Mathematics, 2019
This chapter presents the French didactic tradition. It first describes the emergence and development of this tradition according to four key features (role of mathematics and mathematicians, role of theories, role of design of teaching and learning environments, and role of empirical research), and illustrates it through two case studies respectively devoted to research carried out within this tradition on algebra and on line symmetry-reflection. It then questions the influence of this tradition through the contributions of four researchers from Germany, Italy, Mexico and Tunisia, before ending with a short epilogue.
Didactics of mathematics: concepts, roots, interactions and dynamics from France
Tools and Mathematics: Instruments for Learning, 2016
This chapter analyses specificities of the French field of 'didactics of mathematics', questioning its reasons, tracing the geneses of concepts related to artefacts and following influences on, and interactions with, the international communities of research. This complex genesis is traced in four sections: a first section on the roots of the didactics of mathematics in France, a second section on two founding theoretical frameworks (the theory of didactical situations of Brousseau, and the theory of conceptual fields of Vergnaud), a third section on the anthropological approach of Chevallard, a fourth focusing on specific approaches dedicated to artefacts and resources in mathematics education. Beyond historical and cultural specificities, the chapter aims to evidence the potential of interactions between teachers and researchers, as well as interactions between researchers in mathematics and mathematics education for improving our understanding of learning and teaching issues in mathematics. In this chapter, I analyse specificities of the French field of " didactics of mathematics " , questioning its reasons, tracing the geneses of concepts related to artefacts, and following influences on and interactions with the international communities of research. Questioning the dynamics of the theoretical frameworks, that we bear and that leads us, is complex, as each theory is a result of individual and collective pathways (Trouche, 2009), which meet a set of sometimes critical facts and are subjects to multiple influences. I have organized this chapter in four sections, giving voice to some main actors 1 involved in these complex geneses: a first section on the roots of the didactics of mathematics in France, a second section on two founding theoretical frameworks (the theory of didactical situations of Brousseau, and the theory of conceptual fields of Vergnaud), a third section on the anthropological approach of Chevallard, a fourth focusing on specific approaches dedicated to artefacts and resources in mathematics education
Reflections from abroad on the Netherlands Didactic Tradition in Mathematics Education. Abstracts
2016
s ICME 13 Hamburg 2016 ICME 13 Hamburg 2016 Ha r Reflections from inside on the Netherlands Didactic Tradition in Mathematics Education Abstracts ICME 13 Hamburg 2016 ICME 13 Hamburg 2016 Har versie 2 201606029N.indd All Pages 11-7-2016 13:36:47 1 Reflections from abroad on the Netherlands didactic tradition in mathematics education abstract internationaal.indd 1 11-7-2016 13:39:10internationaal.indd 1 11-7-2016 13:39:10 2 The Netherlands contribution to the ICME 13 Thematic Afternoon on ‘European Didactic Traditions’ is prepared by a committee consisting of Marja van den Heuvel-Panhuizen Paul Drijvers Michiel Doorman Marc van Zanten
International Reflections on the Netherlands Didactics of Mathematics
ICME-13 Monographs, 2020
use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
2020
use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Didactics of Mathematics in the Netherlands
ICME-13 Monographs, 2019
This chapter highlights key aspects of the didactics of mathematics in the Netherlands. It is based on the Dutch contribution to the Thematic Afternoon session on European didactic traditions in mathematics, organised at ICME13 in Hamburg 2016. The chapter starts with a section in which mathematics education in the Netherlands is viewed from four perspectives in which subsequently attention is paid to the role of mathematics and mathematicians, the role of theory, the role of design, and the role of empirical research. In all these themes Hans Freudenthal has played a key role. Hereafter, the focus is on two Dutch mathematics educators (Adri Treffers for primary school and Jan de Lange for secondary school) who each left an important mark on how the didactics of mathematics has developed in the last half century and became known as Realistic Mathematics Education (RME). To illustrate the principles of this domain-specific instruction theory a concrete task is worked out in the section "Travelling to Hamburg". The chapter concludes with five sections featuring voices from abroad in which mathematics educators from other countries give a short reflection on their experiences with RME. Keywords Realistic mathematics education • IOWO • Freudenthal • Mathematisation • Mathematics as a human activity • Didactical phenomenology • Empirical didactical research • Treffers • Students' own productions and constructions • De Lange • Contexts for introducing and developing concepts • Design-based research • Task design • Parametric curve • Findings from field tests M. Van den Heuvel-Panhuizen (B)
National Reflections on the Netherlands Didactics of Mathematics
ICME-13 Monographs, 2020
use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.