The Anthropological Theory of the Didactic

• In Event: Dealing With Diverse Discourses (3D): Can We Build on Each Other’s Research Contributions?

Abstract

Theory
The Anthropological Theory of the Didactic (ATD) (Chevallard, 1985). ATD emerged from the theory of didactic transposition and is a pillar of the French didactic tradition. I usually combine its constructs with those of the Theory of Didactical Situations (TDS) (Brousseau, 1986) and also the Instrumental Approach (IA).

Keywords
• Institution: Any kind of social organization. ATD is especially interested in didactic institutions devoted to the diffusion of knowledge, and more generally in the didactic activity of institutions.
• Praxeology: The way ATD models human practices. In its most elementary form (pointwise praxeology), a praxeology is conceived as a 4-uple made of a type of task and a technique to perform this task, a technological discourse describing, explaining and justifying the technique and a theory backing up the technology.
• Hierarchy of levels of didactic co-determination: This hierarchy aims at capturing the diversity conditions and constraints shaping praxeolologies, from the level of particular mathematical topics and themes up to the level of societies and civilizations, and the interaction between these.
• Research and Study Path: The model of combination between inquiry and study of existing institutional answers which is at the basis of didactic engineering within the paradigm of « Questioning the word » that ATD proposes to substitute to the traditional « Monumentalist » vision of mathematics teaching.
• Reference epistemological model: An epistemological model built by the researcher that transcends institutional positions and norms.
• Learning: a social process shaped by the institutional praxeologies one person is exposed to, and a combination of adaptation and acculturation processes, as is also the case in TDS.
• Mathematics: the diversity of human practices that are recognized as mathematics by some institution.

Basic Tenets
• ATD postulates that praxeology is, in some way, the basic unit into which one can analyse human action at large, and thus any activity related to the production, diffusion, or acquisition of knowledge.
• Any praxeology can be considered as an answer to a question arising in an institutional setting which becomes its raison d’être.
• Knowing something, for instance a mathematical topic, is always relative to a given institution, and a given position within an institution.

Typical Methods or Methodology
As a framework of comparison, ATD is compatible with a variety of methodologies, including textual analysis and the analysis of classroom discourse.

Findings
• Discontinuities between praxeologies are an important source of difficulties for students and of misunderstanding between teacher and students, in institutional transitions. Research has shown the strong under-estimation of such discontinuities in the teaching of algebra and functions, and the general teacher tendency to wrongly give a cognitive nature to the resulting students’ difficulties.
• Most often, students are exposed to unconnected and incomplete praxeological organisations in schools, which do not allow them to access the raisons d’être of algebra, and limits what they can learn.
• Mathematics techniques have pragmatic and epistemic values, and both values contribute to their educational legitimacy and learning potential.

Scholarly Significance
It is an important contribution of ATD to provide a detailed model of levels of didactic co-determination.

Author

• Michèle Artigue, Université Paris Diderot