Michèle Artigue

• Doctor in math education
• Professor Emeritus at Paris Diderot University

In this epilogue, I reflect on the 16 contributions from mathematics educators that make up this book. What do I take away from them? What thoughts do they provoke? Before attempting to answer these questions, however, I will briefly explain my own relationship to mathematics and the role it has played and continues to play in my research activitie...

Este artigo examina a relação entre epistemologia e didática, e mais especificamente a função da análise epistemológica na didática. Os dois primeiros parágrafos centram-se na função de vigilância desta análise. O terceiro parágrafo é consagrado à noção de obstáculo epistemológico, sobre o qual a visibilidade da epistemologia em didática tende a co...

This article aims to contribute to the body of knowledge developed by mathematics education research on the implementation of innovative TPD devices, i.e. organized systems of arrangements for professional development of mathematics teachers, that emphasize their collaborative work and have a strong bottom-up dimension, as well as to the developmen...

The study of the development and use of digital resources in mathematics education involves a growing number of theoretical constructs, some widely used in mathematics education, others developed to meet the specific needs of this area of research. This characteristic is not peculiar to educational research on digital resources but is broadly share...

The study of the development and use of digital resources in mathematics education involves a growing number of theoretical constructs, some widely used in mathematics education, others developed to meet the specific needs of this area of research. This characteristic is not peculiar to educational research on digital resources but is broadly share...

This chapter is divided into five sections. In the first, Mogens Niss addresses the case of a partially successful curriculum reform in Denmark. It is the KOM Project (that began in 2000) which developed a theoretical proposal that sought to respond to specific difficulties in the transition between various cycles of education including higher educ...

Describing mathematics classroom teaching and learning is part of a professional expertise. Comparing ‘our distinct stories’ and ‘our professional languages’ about teaching and learning in mathematics classes around the world, reveals cultural and linguistic underpinnings of our ‘stories’ and ‘languages’. Analysing and understanding these ‘stories’...

The purpose of this article is to study the role of facilitators in professional development activities adapted from Lesson Studies, known as LSa. This requires a systemic approach, which takes into account the multiple actors of this device who work in various groups and institutions. After briefly describing the LSa device and specifying the theo...

This chapter contains the biographical portraits of the 54 members of the Central/Executive Committee of ICMI who passed away in the first 100 years of ICMI.Each of these portraits consists of a section of general biographical information and a section containing contributions to education and dissemination of mathematical culture. In the same vein...

The challenges raised by the teaching of mathematics for non-specialists in tertiary mathematics education were pointed out by mathematicians long ago. Since the beginning of the twentieth century, innovations and reflections have developed around the world, but research in mathematics education in this area is still underdeveloped. Where are we an...

Commentary to the ÉpiDEMES Special Issue aims to offer accessible accounts of University MathematicsEducation (UME) research to the Mathematics community

The pandemic has demonstrated more than ever that citizens around the world need to understand how mathematics contributes to understanding global challenges and ways of overcoming them. People need to understand that predictions are based on models that make use of assumptions and the best inputs available. They also need to learn to critically ev...

A significant distinguishing characteristic of the International Classroom Lexicon Project was the documentation of classroom pedagogical practices of mathematics teachers in the original languages of ten communities. These lexicons provide us with an opportunity to compare identified teacher practices within these communities. In this paper, we ex...

In this chapter synthesizing the main elements of my contribution to the advanced course on dialogues between theories offered at CRM in June 2019, I first introduce the notions of research praxeology and of scale of networking strategies, two conceptual tools developed and productively used for establishing connections between theories in the last...

Institutional transitions in education are inherently problematic, and this is by no means a recent phenomenon. Already, at the beginning of the twentieth century, the mathematician Felix Klein denounced a double discontinuity directly linked to such institutional transitions. However, research in this area has developed considerably in the last de...

This article is devoted to the theoretical resources likely to support implementation studies. After the introductory section, we focus on the potential offered by resources internal to the field of mathematics education, especially those offered by design-based research, by the systemic and ecological perspective underlying the anthropological the...

There is, in France, a long-term tradition of research in the didactics of mathematics. In this paper, we revisit this tradition using, as a specific lens, the research carried out on the educational use of digital tools and resources for teaching and learning mathematics. We first briefly introduce this tradition and the three main theories at the...

RésuméDans cet article s’interrogeant sur les méthodologies de recherche en didactique, après une introduction resituant ce questionnement dans l’histoire de ce champ de recherche, et les méthodologies au sein des praxéologies de recherche, je m’intéresse dans un premier temps à l’ingénierie didactique, une méthodologie emblématique de la volonté d...

The book presents developmental outcomes from an EU Erasmus+ project involving eight partner universities in seven countries in Europe. Its focus is the development of mathematics teaching and learning at university level to enhance the learning of mathematics by university students. Its theoretical focus is inquiry-based teaching and learning. It...

Este artículo trata del desarrollo internacional de la investigación didáctica en matemáticas. Después de recordar la relación especial que existe entre las matemáticas y su enseñanza, evoca en primer lugar la emergencia de la didáctica de las matemáticas como un campo de investigación específico, en un contexto marcado por la reforma de las matemá...

On the occasion of the 100th anniversary of the birth of the Hungarian mathematics educator, didactician and reform leader Tamás Varga, a conference on mathematics education has been organized in November 2019 and held at the Hungarian Academy of Science.

This article is based on the panel on inquiry based mathematics education and the development of learning trajectories held at the VARGA 100 Conference. After an introduction presenting the theme and organization of the panel, this article focuses on the diversity of conceptualizations of inquiry based education existing today in mathematics educat...

This chapter analyses the emergence and development of the documentational approach to didactics (DAD), paying specific attention to the theoretical sources and connections having inspired its progressive elaboration. After introducing the two main conceptual tools used for this analysis, the scale of networking strategies between theories (Bikner-...

In this chapter, we investigate the notion of “teachers as curriculum designers” from the literature and from six international perspectives. This is done in order to (1) develop a deeper understanding of the concept, and (2) provide an international perspective and illustrations of the different facets of teacher design. Based on this investigatio...

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 respectiv...

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...

This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states. It shows that while they all share common features both in the practice of learning and teaching at school and in research...

En este artículo, nos preguntamos acerca de las relaciones entre epistemología y didáctica, más precisamente acerca del papel que juega el análisis epistemológico en didáctica. En los dos primeros parágrafos, acentuamos la función de vigilancia de este análisis. En el tercero parágrafo, estudiamos la noción de obstáculo epistemológico, parte más vi...

The issues of reproducibility are at the heart of debates about the status of several fields of research and the didactics of mathematics, in its ambition to become a scientific field, cannot hide these issues. In this article, I address these issues by revisiting a research study on the reproducibility of didactical situations that was developed t...

The Proceedings of the Second Meeting of GeoGebra Clubs, a book that exhibits the papers presented at the event referenced during on 22 and 23 June this year. This proceedings present seventeen (17) papers made by high school students who participated in six (06) GeoGebra Clubs in Venezuela during the 2015-2016; eight (08) work done by teachers and...

This issue of ZDM collects research works sharing a common reference to the theoretical framework of Mathematical Working Spaces (MWS), a construction which emerged about one decade ago, and has progressively found its way in the mathematics education community, thanks to the collaborative work of an international group of researchers. In this reac...

In this text based on my closing lecture at the conference from which this book originated and on the reading of its different chapters, I come back to some main themes of this conference, intertwining my comments with a more general reflection on the didactic adventure. After evoking my first steps in didactics and the mixture of audacity and inge...

This chapter provides commentary and reflection on the goals and aims of this specific ICMI study, with comments situated within a personal background based on the theory of didactical situations. Detailed comments are made about Chaps. 2, 5, and 6, with some references made to various plenary chapters. Throughout, questions raised and/or answered...

In what is often called the “French didactical culture,” design has always played an essential role in research. This is attested by the introduction and institutionalization of a specific concept, that of didactical engineering, already in the early 1980s and by the way didactical engineering has accompanied the development of didactical research,...

The chapter briefly introduces the Theory of Didactical Situations (TDS) by referring to the data from Chap. 2. TDS provides a systemic framework for investigating teaching and learning processes in mathematics, and for supporting didactical design. The theory is structured around the notions of a-didactical and didactical situations and includes a...

The case study of Topaze effect shows a networking practice of connecting two theoretical approaches, TSD and IDS. It investigates empirically two phenomena, Topaze effect and funnel pattern, of the two theories and networks the theories by comparing and contrasting these phenomena including also the semiotic game phenomenon. This process leads to...

This chapter presents the main ideas and constructs of the book and uses the triplet (system of principles, methodologies, set of paradigmatic questions) for describing the theories involved. In Part II (Chaps. 3, 4, 5, 6, and 7), the diversity of five theoretical approaches is presented; these approaches are compared and systematically put into a...

In this chapter, the Anthropological Theory of the Didactic (ATD) is given a different status, its lenses and constructs being used for reflecting on the networking enterprise itself. For this purpose, the notion of praxeology first introduced for modeling mathematical and didactic activities is extended to research practices. This extension leads...

The case study of context, milieu, and media-milieu dialectic is a networking case that links TDS, AiC, and ATD. It compares and contrasts three concepts and their status within each theory, in order to learn how concepts which at a first glance seem to have a similar role in the understanding of teaching and learning in each theory differ.

In this article of the special issue devoted to the European project ReMath, we present and discuss the affordances of this project in terms of networking between theoretical frameworks. After clarifying the vision of theories and networking adopted in this project, we introduce the methodological constructs that have been developed and used in ReM...

Our chapter is in four sections. Michèle Artigue tells the story of her transition from mathematical logic to mathematics education and of collaborations at a wide variety of institutional levels. Günter Törner gives a history of collaboration between mathematics and mathematics education in Germany along with a list of recommendations to foster co...

Cet article présente un des temps forts du stage de formation continue, animé et organisé par le groupe Modélisation de l’IREM Paris 7 durant l’année 2012, sur le thème du nouvel enseignement MPS (Méthodes et Pratiques Scientifiques) en seconde. Il s’agit du déroulement d’un scénario MPS sur le thème « Science et vision du monde » que les formateur...

This synthesis is designed to provide insight into the most important issues involved in a large-scale implementation of inquiry-based learning (IBL). We will first turn to IBL itself by reflecting on (1) the definition of IBL and (2) examining the current state of the art of its implementation. Afterwards, we will move on to the implementation of...

The terms inquiry-based learning and inquiry-based education have appeared with increasing frequency in educational policy and curriculum documents related to mathematics and science education over the past decade, indicating a major educational trend. We go back to the origin of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 193...

A case of networking two didactic phenomena - the Topaze effect and the Funnel communications pattern - through analyses of the same episode from two theoretical perspectives is presented. It shows how this networked analysis deepens insight into the kind of learning of the same episode through complementary views, how it strengthens the theoretica...

Interdisciplinarity issues are not new in the field of education but they are given now an increasing importance, which reflects both in research interests and curricular decisions. In this text, I would like to use my personal experience of interdisciplinarity for approaching some of its dimensions and affordances in mathematics education, from it...

In this text, directly inspired by my closing lecture at the ICMI Study Conference in Hanoi, I use first my personal experience for analyzing the evolution of relationship with digital technologies in mathematics education along the last two decades, and for situating the reflection about the future into an historical dynamics. Then, I focus on som...

Résumé – Les études comparatives internationales visent à identifier et expliquer les différences entre phénomènes homologues dans plusieurs contextes. Elles sont menées avec une variété d'objectifs et de méthodes, et leurs résultats ainsi que les interprétations de ces derniers font l'objet de débats parfois vifs, surtout pour ce qui concerne les...

The networking of theories is a promising research practice for connecting theories systematically while valuing their identities. Strategies for the networking of theories and four case studies with different profiles are presented. Theoretical reflections on the cases show that the networking of theories can be regarded as a process that begins w...

This paper presents the methodology developed within TELMA for connecting and integrating the theoretical frames used by the different teams for studying the design and use of interactive learning environments in mathematics education. Two case studies are then analysed and compared in order to illustrate the methodology and the results it can lead...

Relying on the collective work carried out in the e-CoLab project concerning the experimentation of the new calculator TI-nspire, we address the issue of the relationships between the development of mathematical knowledge and instrumental genesis. By analyzing the design of some resources, we first show the importance given to these relationships b...

Paper available on Sense Publishers' website.

This chapter is concerned with the work that Kaleidoscope Network of Excellence made possible on technology-enhanced learning in mathematics. It presents some findings from two complementary initiatives that were carried out in this field: TELMA European Research Team and the Special Interest Group on Learning and Technology at Work. TELMA initiati...

We rely on discussions initiated at CERME4 and continued at CERME5 to compare, contrast and combine in a coherent way different theoretical frameworks currently used in mathematics education, with the eventual aim of networking between theoretical approaches. Specifically, we chose for this purpose the theory of didactic situations (TDS), the neste...

In this text, we report on a research project developed within the European research team TELMA (Technology Enhanced Learning in MAthematics) of the Kaleidoscope network of excellence created in 2004. We describe the conceptual and methodological tools we have progressively built for allowing productive research collaboration and overcoming the dif...