The Didactics of Mathematics: Approaches and Issues : A Homage to Michèle Artigue

This book, the outcome of a conference organised in 2012 in Paris as a homage to Michèle Artigue, is based on the main component of this event. However, it offers more than a mere reflection of the conference in itself, as various well-known researchers from the field have been invited to summarize the main topics where the importance of Artigue’s contribution is unquestionable. Her multiple interest areas, as a researcher involved in a wider community, give to this volume its unique flavour of diversity. Michèle Artigue (ICMI 2013 Felix Klein Award, CIAEM 2015 Luis Santaló Award) is without doubt one of the most influential researchers nowadays in the field of didactics of mathematics. This influence rests both on the quality of her research and on her constant contribution, since the early 1970s, to the development of the teaching and learning of mathematics. Observing her exemplary professional history, one can witness the emergence, the development, and the main issues of didactics of mathematics as a specific research field. Front Matter....Pages i-x Introduction: Perspectives on Didactics of Mathematics through Michèle Artigue’s Contributions....Pages 1-13 Didactique Goes Travelling: Its Actual and Potential Articulations with Other Traditions of Research on the Learning and Teaching of Mathematics....Pages 15-41 Networking Different Theoretical Perspectives....Pages 43-55 Three Perspectives on the Issue of Theoretical Diversity....Pages 57-86 Conversion, Change, Transition... in Research About Analysis....Pages 87-121 Digital Technology and Mathematics Education: Core Ideas and Key Dimensions of Michèle Artigue’s Theoretical Work on Digital Tools and Its Impact on Mathematics Education Research....Pages 123-142 Digital Technology and Mathematics Education: The Teacher Perspective in Mathematics Education Research—A Long and Slow Journey Still Unfinished....Pages 143-153 History of Science, Epistemology and Mathematics Education Research....Pages 155-189 Inquiry-Based Education (IBE): Towards an Analysing Tool to Characterise and Analyse Inquiry Processes in Mathematics and Natural Sciences....Pages 191-217 The Researcher in the Wider Community....Pages 219-237 Preparing Young Researchers in Mathematics Education: Beyond Simple Supervising....Pages 239-252 Epilogue. A Didactic Adventure....Pages 253-269 This book, the outcome of a conference organised in 2012 in Paris as a homage to Michèle Artigue, is based on the main components of this event. However, it offers more than a mere reflection of the conference in itself, as various well-known researchers from the field have been invited to summarize the main topics where the importance of Artigue's contribution is unquestionable. Her multiple interest areas, as a researcher involved in a wider community, give to this volume its unique flavour of diversity. Michèle Artigue (ICMI 2013 Felix Klein Award, CIAEM 2015 Luis Santaló Award) is without doubt one of the most influential researchers nowadays in the field of didactics of mathematics. This influence rests both on the quality of her research and on her constant contribution, since the early 1970s, to the development of the teaching and learning of mathematics. Observing her exemplary professional history, one can witness the emergence, the development, and the main issues of didactics of mathematics as a specific research field Preface -- Acknowledgements -- Contents -- 1 Introduction: Perspectives on Didactics of Mathematics through Michèle Artigue's Contributions -- 1.1 Didactics of Mathematics as a Specific Research Domain -- 1.1.1 At the Very Beginning: The Year 1968 -- 1.1.2 Reproducibility of Didactical Situations: Towards a Normal Science -- 1.1.3 The French School of Didactics of Mathematics Within an International Community -- 1.2 The Multiplicity of Theoretical Frameworks: Networking Theories -- 1.3 Didactics of Mathematics and Related Research Fields -- 1.3.1 Mathematics -- 1.3.2 Epistemology and History 2.2.2 Reflections of a "Traveler" -- 2.3 First Entr'acte -- 2.4 Lost in Translation -- 2.4.1 Didactique as Traveller -- 2.4.1.1 Destinations: Places Travelled -- 2.4.1.2 Itineraries: Some Accomplishments -- 2.4.1.3 Baggage: The Burden of Terminology -- 2.4.2 Didactique in Translation -- 2.5 Second Entr'acte -- 2.6 Some Reflections on Ecology of Didactic Research and Theories: The Case of France and Italy -- 2.6.1 Introduction -- 2.6.2 Institutional and Economic Constraints -- 2.6.3 The Influence of the Cultural Context -- 2.6.4 A Healthy (or Unhealthy?) Eclecticism -- 2.7 Third Entr'acte 1.3.3 Psychology, Cognition, Semiotics and Sociology -- 1.4 Didactics of Mathematics and the Outside World of Mathematics Education -- 1.4.1 Inquiry-Based Education -- 1.4.2 The Researcher in the Wider Community -- 1.4.3 "L'École Artigue" -- 1.4.4 Artigue's Didactic Aventure -- References -- 2 Didactique Goes Travelling: Its Actual and Potential Articulations with Other Traditions of Research on the Learning and Teaching of Mathematics -- 2.1 Introduction -- 2.2 Towards a Dialogue Between Traditions and Approaches in Mathematics Education -- 2.2.1 Contrasting Traditions 2.8 Epistemology as a Research Category in Mathematics Teaching and Learning -- 2.8.1 Introduction -- 2.8.2 Epistemology and Teaching -- 2.9 Concluding Comments -- References -- 3 Networking Different Theoretical Perspectives -- 3.1 The "Problématique" -- 3.2 Methods and Methodologies of Networking -- 3.3 The Results of Networking -- 3.4 Concluding Remarks -- References -- 4 Three Perspectives on the Issue of Theoretical Diversity -- 4.1 Introduction -- 4.2 The Richness of Didactic Theories and Their Networking for a Multidimensional Approach of Didactic Phenomena 4.2.1 Main Theories: The Theory of Conceptual Fields, the Theory of Didactic Situations and the Anthropological Theory of Didactics -- 4.2.1.1 A Theory Centred on the Modeling of Knowledge Acquisition -- 4.2.1.2 A Theory Centred on the Conditions of the Operation of Situations in an Educational System -- 4.2.1.3 A Theory Focused on Institutions -- 4.2.2 Functionalities of Theories -- 4.2.2.1 Dynamics of a Multidimensional Approach: Complementarity Between Theories and Evolution of Research Questions -- 4.2.2.2 Scope and Adaptability of Theoretical Frameworks Her multiple interest areas, as a researcher involved in a wider community, give to this volume its unique flavour of diversity.Michele Artigue (ICMI 2013 Felix Klein Award, CIAEM 2015 Luis Santalo Award) is without doubt one of the most influential researchers nowadays in the field of didactics of mathematics. 4.2.2.3 Different Cultures and Common Sensitivities: Contributions of a Comparison Between Theories