The French Didactic Tradition in Mathematics

Abstract

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 11 12 M. Artigue et al.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.Keywords French didactics · Mathematics education · Anthropological theory of the didactic · Theory of didactical situations · Theory of conceptual fields · Didactic research on line symmetry · Didactic research on algebra · Didactic research on proof · Didactic interactions · Influence of French didactics This chapter is devoted to the French didactic tradition. Reflecting the structure and content of the presentation of this tradition during the Thematic Afternoon at ICME-13, it is structured into two main parts. The first part, the three first sections, describes the emergence and evolution of this tradition, according to the four key features selected to structure the presentation and comparison of the didactic traditions in France, Germany, Italy and The Netherlands at the congress, and illustrates these through two case studies. These focus on two mathematical themes continuously addressed by French researchers from the early eighties, geometrical transformations, more precisely line symmetry and reflection, and algebra. The second part is devoted to the influence of this tradition on other educational cultures, and the connections established, in Europe and beyond. It includes four sections authored by researchers from Germany, Italy, Mexico and Tunisia with first-hand experience of these interactions. Finally, the chapter ends with a short epilogue. Sections 2.

Un point de vue sur la notion de transposition didactique (TD) et la transposition professionnelle (TP)

“…Depuis son origine et sa répercussion internationale dans les années 1980, la didactique des mathématiques a revêtu un caractère multi-théorique qui consiste, de manière simplifiée, à adopter plusieurs théories explicatives pour des phénomènes précis issus de l'enseignement et de l'apprentissage (ARTIGUE et all, 2019). Au départ, on peut enregistrer des recherches fortement influencées par la théorie des situations didactiques, avec une plus grande attention portée au rôle de l'étudiant.…”

Understanding teachers’ professional development through their interaction with resources: a multilingual project

“…DAD is originally steeped in the French didactics tradition in mathematics education (Artigue et al, 2019), where concepts such as didactical situation, institutional constraint and scheme are central. At the same time it also leans on socio-cultural theory, including notions such as mediation (Vygotsky, 1978) as constitutive of each cognitive process.…”

“…In this project, we consider that our experiences of the world and reflection on those experiences are mediated and shaped by available language, and that the use of English as lingua franca for international communication substantially limits what can be expressed and shared. The goal of the project is thus to document and compare the naming systems employed in mathematics teacher communities in the nine countries to describe the objects and events in their classrooms, in order to expand on the variety of constructs available for the purpose of theorizing about classroom practice and for identifying the characteristics of accomplished practice"(Artigue et al, 2019). But while the Lexicon project looked at the naming systems used to describe classroom activities, the young researchers workshop looked at the naming systems used to describe teachers' interactions with resources, before, during, and after class.…”

El desarrollo de la didáctica de las matemáticas, una mirada internacional

“…Igualmente Belhoste, en su texto antes mencionado, utilizando varios ejemplos -Alemania, Francia, Italiamuestra que la constitución e institucionalización de una comunidad matemática en estos países ha estado estrechamente ligada al desarrollo de instituciones educativas para esta disciplina. En el capítulo dedicado a la tradición didáctica francesa del libro resultante del grupo temático del congreso ICME-13 (International Congress of Mathematics Education) (Artigue et al, 2019), también hemos destacado la participación histórica de algunos de los más eminentes matemáticos franceses en cuestiones de enseñanza, mencionando en particular el papel de Nicolás de Condorcet, quien presidió el Comité de Educación Pública en los primeros años de la Revolución francesa, Por lo tanto, no es sorprendente que fuera en matemáticas y con ocasión de un congreso internacional de matemáticos (el quinto, en 1908) que se creó la primera organización internacional, llamada entonces CIEM (Commission Internationale de l'Enseignement Mathématique) en francés, dedicada a la enseñanza de una disciplina. Actualmente, esta organización se conoce por su acrónimo en inglés ICMI (International Commission on Mathematical Instruction) modificado después de la Segunda Guerra Mundial.…”