Extended Abstracts Spring 2019: Advances in the Anthropological Theory of the Didactic (Research Perspectives CRM Barcelona)

The book presents research works developed within the Anthropological Theory of the Didactic (ATD) by senior and young researchers that participated in the Intensive Research Program “Advances in the anthropological theory of the didactic and their consequences in curricula and teacher education” held at the Centre de Recerca Matematica (CRM) in Barcelona. It is organized in three axes of current research on the ATD: teacher education and the professionalization of teaching; the curriculum problem in the historical transition from the classical paradigm of visiting works to the emerging didactic paradigm of questioning the world; and research in didactics at the university level. Introduction to the Book with the “Extended Abstracts” Contents Acknowledgements Mathematics Teacher Education and the Professionalization of Teaching Modifying Teachers’ Didactic Praxeologies in the Perspective of the Paradigm of Questioning the World: The Case of the Technological-Theoretical Moment The Inquiry Implemented Preliminary Analysis Determining the Box of Maximum Volume The Dialectic of Media and Milieus The Dialectic of the Collective and the Individual The Problem with the Logos Block Preliminary Hypothesis and Conclusions The Dialectic of Media and Milieus Revisited The Teacher’s Praxeological Equipment References Pre-Service Teachers’ MPCK Enhancements Using the Framework of Anthropological Theory of the Didactic Introduction The DMC Prototype Materials and Method Results and Discussion References Evolution of a Teacher-Researcher While Developing a Co-disciplinary Study and Research Path Through Five Implementation Introduction Methodology The Study and Research Path Evolution of TR Throughout Implementations Discussion and Conclusions References Building Reference Paradidactic Praxeological Model for Investigating Teachers’ Reflection Introduction Theoretical Tools Context and Method Reference Paradidactic Praxeological Model Result of the Exploratory Analysis Description of the Paradidactic Practices Analysis of the Paradidactic Practices and Discussion Lack of Interplay Between MO and DO Existence of Unexpressed Theoretical Block of Paradidactic Praxeologies References Reflections on Teacher Professionalisation–A German Perspective Introduction: Characteristics of the Institutional Context Our Course in Didactics of Mathematics Improvement of the Fraction Task and Conclusion References A Co-Disciplinary Study and Research Path Within Two Groups of Pre-Service Mathematics Teacher Education Introduction Modelling and Study and Research Paths in the ATD Methodology The Epistemological Model of Reference, the SRP and the Mathematical and Physical Models Data Analysis Conclusions References The Ecology of the Didactic Divide in Teacher Education Introduction: The Didactic Divide as a Teacher-Educational Problem Revisiting the Phenomenon of Didactic Divide from an ATD Perspective Paradidactic Ecology of the Didactic Divide Teacher-Educational Didactic System as a Genre of the Paradidactic System The Scale of Levels of Paradidactic Determinacy Conditions for the Didactic Divide Epistemological Reflection: How to Confirm Identified Conditions? Final Remarks: On the Possibility of Overcoming the Didactic Divide References The Gap Between Studying a Generating Question and Planning Lessons Based on It Introduction ATD, Monumentalism and in-Service Teachers Training The SRP and an Epistemological Model of Reference Method Research Questions Results Discussion and Conclusions References Prospective Teachers Solving a Percentage Problem: An Analysis of the Construction of a Praxeology From the Outside Inwards: A Centripetal Depiction The Institutional Setting The Class and the Curriculum The Teaching Unit The Practical Working Conditions The Observed Didactic System The Question Q Under Study Conditions and Constraints Which Mathematical Praxeology? A Reference Model Which Didactic Milieu? Some Preliminary Remarks Didactic Moments Discussion References The Curriculum Problem and the Paradigm of Questioning the World The Cooperative Works, a Teacher Training System Open to the Local Social Network Introduction Theoretical Framework Description of the Cooperative Works Training System Methodological Framework Results Conclusion and Perspectives References Didactic Praxeologies Taking into Consideration the Collective Dimension of the Question’s Study Through Investigation When Implementing Mathematics’ Study and Research Paths in French Secondary Schools Mesogenetic Effects of Activated Didactic Praxeologies Chronogenetic Effects of Activated Didactic Praxeologies Conclusion References How Long Would It Take to Open a Padlock? A Study and Research Path with Grade 10 Students Introduction Research Questions and Methodology Institutional Context and Conditions for the Implementation Conditions and Methodology of the Implementation In Vivo Analysis of the SRP Presentation of the Generating Question and First Answers of the Students Padlock Combinations Padlocks with New Restrictions Classification of Padlocks and the Elaboration of the Question-Answer Map Institutionalisation Moment and the Evaluation Experimental Validation and Elaboration of the Final Answer Some Feedback from the Students Conclusions and Perspective References A Praxeological Analysis of the Proposal for Teaching Probability in Brazilian Textbooks of the Compulsory Education Introduction The Proposal of Probability Teaching in the Analyzed Textbooks Implications of Those Collections in Brazilian Education References Study and Research in Graph Theory: A Case of a Japanese Upper Secondary School Introduction Main Theoretical Constructs and Analysing Methods The Setting of Our Didactic Engineering The Economy of the Graph-Theoretic SRP The Ecology of the Graph-Theoretic SRP Final Remarks: A Constraint on the Teaching of Graph Theory References Overview of Research on Textbooks in Brazilian Compulsory Education Why Analyse Textbooks National Program of Textbooks Research Carried Out in the DDMat A Design for the Analysis of Textbooks Choosing the Corpus for Analysis Praxeological Analysis of the Course Part Praxeological Analysis of the Proposed Activities Part Cross-Checking the Data In Conclusion References Kernels of Mathematical Thinking as Task- and Curriculum Design Tool in the Pósa Method The Teaching of Lajos Pósa and the Hungarian Guided Discovery Approach for IBME Theorizing and Reconstructing the Pósa Method with Reverse Didactic Engineering and Didactic Re-engineering Methodology Web of Problem Threads (WPT) A Sample of a Problem Thread from the Pósa WPT — Object of Study Question 1 (Task A) — Table Tennis Tournament Question 2 (Task C) — 100 Whole Numbers on Board Question 3 (Task D) — 64 Points with Straight Lines Question 4 (Task E) — Magical Numbers Kernels of Threads Fostering the Development of “Mathematical Thinking” The Kernel Invariant (Quantities) Kernels of Mathematical Thinking (KoMT) & Curricula Based on KoMTs References The Constitution of the « Milieu » During an Inquiry Process: An Analysis in Terms of Question-Answer and Media-Milieu Dialectics The Institutional Context The Didactic Co-determinacy Scale: The Level of Discipline The Herbartian Scheme as Model for Inquiry-Based Activities Media-Milieu Dialectic Question-Answer Dialectic The Mathematical Exploration as an Individual Study and Research Path (SRP) Square-Wheeled Bike Exploration Analysis The Choice of Topic Identifying the Ingredients of the Milieu Conclusion and Perspectives References Pre-service Teachers’ Designing of an Inquiry Task Through the Course of Study and Research Paths for Teacher Education Purpose and Rationales of the Research Brief Description of the Course Theoretical Background and Research Questions Methodology Results Q-A Map by the Pre-service Teachers Milieu-Analysis: Extracted Discussion and Conclusion References Research in Didactics at University Level Deployment of Study and Research Paths in Mechanical Engineering Introduction Methodology Results Q-A Maps: Influence of the Q0 Media-Milieu Dialectics Students’ Adaptation to the SRP Inquiry Device Conclusions References Didactic Potentials of a Task Sequence: Teaching the Notion of a Space Curve Introduction Mathematical Context Theoretical Framework and Research Questions Context and Methodology Data and Findings Conclusion and Perspectives References A Reference Epistemological Model for the Case of Conics Introduction A Reference Epistemological Model on Conics Geometries An Analysis of the Dominant Model Under the Lens of the REM Final Considerations References Two Tasks to Teach Randomness and Probability Reasoning Introduction Rolling Dice as a Milieu Tossing Coins Final Remarks References The Problem-Based Learning Through the E-portfolio as a Methodological Basis for the Acquisition of the Transversal Competence of Solidarity and Social Commitment in Mathematics Subjects Introduction Acquisition of Sustainability Competence Through the Mathematics Subject Case Study Example of Project Proposal Conclusions References On a Vector Calculus Task that Led to Formation of a Praxeology: A Lucky Accident or an Implicit Fine Design? Introduction Theoretical Tools The First Two Phases of Analysis Conclusion References On the Didactic Transposition of the Concept of Ideal at the Bachelor Level Introduction Theoretical Framework Mathematical Organizations Ecology Methodology Presentation of the Institutions Ecological Analysis Institution CPGE Institution L2 Conclusion References