Plenary lecture: Michèle Artigue

Title: Didactical Design in Mathematics Education

Current context
Increasing interest in design issues. Reflection on the value of the outcomes of didactical research, and impact of research on educational practices.
Motivation: external and internal

• math education is a sensitive domain for our societies
• increasing pressure of international evaluations, tests, etc.
• increasing debates about curriculum reforms and the supposed influence of didactical research on these

External side (Burkhardt and Schoenfeld, 2003)

• Start from evidence that educational research does not often lead directly to practical advances
• Development of “engineering research”
• Design experiments – promising model of interaction

Internal side (Cobb, 2007)

• Multiplicity of theoretical frame
• Two criteria proposed
• Multi-level vision of design
• Experimental design has to be its unique methodology

Didactical design – mathematics education
Diversity of perspectives

• Didactical design as research tool
• Didactical design as development tool
• Math education as design experiment

Didactical engineering (emerge in the early eighties)
Initial distinction between phenomenotechnique and didactical engineering

Didactical engineering as a research tool, shaped by theoretical foundations
– Influence of the theory of didactical situations (Brousseau)
    Learning processes as adaptation processes (Piaget)
    Focus on situation and milieu
    Distinction between different functionalities of mathematics knowledge (acting, expressing and communicating, proving)
    The teacher role

Didactical engineering – the predominant research methodology in the French didactic culture (esp. in the eighties)

Relationships between research and practice

• Relationship that is not under theoretical control
• Products communicated in different arenas (publications, teacher formation, etc.)

Relationships between research and practice

• Relationship that is not under theoretical control
• Products communicated in different arenas (publications, teacher formation, etc.)
• Results reproduced, used in textbooks, etc.

Subsequent evolution

• Better understanding of teachers’ practices
• Development of less invasive research methodologies
• New theoretical constructions
• Substantial body of research that impacts the vision of didactical design

Didactical design today

• Still a tool widely used
• Same epistemological sensitivity
• Importance of interaction with the milieu, more sophisticated vision of the teacher role
• Same importance to the a priori analysis
• (Differences on the view of the teacher in France and Italy, for instance)
• Didactical engineering still a research tool

Praxeology

• Practical part – type of task (technique)
• Theoretical part – technicological discourse (theory)