# Didactical engineering

__Draft 1__

**Editor**: Michèle Artigue, DIDIREM, Université Paris 7.

**Contributors**: …/…

## Contents

#### Definition

Didactical engineering is the design and experimentation of teaching sequences, adopting an internal mode of validation based on the comparison between a priori and a posteriori analysis within the framework of the theory of didactical situations. It includes four steps:

- (i) preliminary analyses investigating the epistemological, cognitive and institutional conditions and constraints;
- (ii) design and a priori analysis with particular attention paid to the identification and choice of values for the didactic variables and anticipation of their potential effect on the “students-milieu” interaction;
- (iii) experimentation;
- (iv) a posteriori analysis and validation of the hypotheses underlying the design

#### Comments on the history

The term Didactical engineering was introduced in mathematics education by French researchers in the early eighties (e.g. Chevallard 1982) for denoting a specific form of didactical design inspired by the theory of didactical situations (Brousseau, 1997). Didactical engineering became then a privileged methodology of research within this community.

- “Compared with other types of research based on class experiments, the methodology of didactical engineering is also characterized by the register in which it is placed and the methods of validation used. [...] (It situates) in a case study mode where validation is essentially internal, founded on the confrontation between a priori and a posteriori analysis” (Artigue, 1992, p. 44)

The term was progressively used in different scientific cultures and beyond the sole mathematics, for denoting both research and development designs presenting these characteristics. The links of such constructions with the theory of didactical situations are more or less strong, even if globally these designs tend to optimize the mathematical responsibility of students through adidactical interaction with an appropriate “milieu” (Warfield, 2006). Didactical engineering also extended to designs aiming at teacher education.

#### Related terms

Design research, Didactical design, Instructional design, Learning design

#### Translation issues

French: ingénierie Didactique

Spanish: ingeniería didáctica

#### Disciplinary issues

In TEL research, didactical engineering has played an essential role for identifying the learning and teaching affordances of technology in school settings as these could not be inferred from naturalistic observations. In such research, the way digital artifacts, considered as elements of the “milieu”, impact learning processes by creating new possibilities of action and interaction with the “milieu” and by changing their economy has been emphasized.

#### Key references

[1] Artigue M. (1992) Didactic engineering. In: Douady R., Mercier A. (eds.) Research in Didactique of Mathematics. Selected Papers, pp. 41-66. Grenoble : La Pensée Sauvage. (translation of : Artigue M. (1990) Ingénierie didactique. Recherches en Didactique des Mathématiques, vol. 9/3, 281-308).

[2] Artigue M. (2009). Didactical design in mathematics education. In, C. Winslow (ed.), Nordic Research in Mathematics Education. Proceedings from NORMA08 in Copenhaguen, April 21-April 25, 2008. pp. 7-16. Sense Publishers.

[3] Brousseau, G. (1997). Theory of didactical situations in mathematics. Kluwer Academic Publishers.

[4] Chevallard Y. (1982), Sur l’ingénierie didactique. Contribution à la préparation de la IIe Ecole d’Eté de Didactique des Mathématiques, Note de travail, IREM d’Aix-Marseille.

[5] Margolinas, C., Abboud-Blanchard, M., Bueno-Ravel, L., Douek, N., Fluckiger, A., Gibel, P., et al. (Eds.). (2011). En amont et en aval des ingénieries didactiques. Grenoble: La pensée sauvage.

[6] (Ruthven K., Laborde C., Leach J., Tiberghien A. 2009). Design Tools in Didactical Research: Instrumenting the Epistemological and Cognitive Aspects of the Design of Teaching Sequences, Educational Researcher, Vol. 38, No. 5, pp. 329–342.

[7] Warfield, V. M. (2006). Invitation to Didactique.