Credits : All modules are presented by Michèle Artigue (University Paris Diderot), except Module 0 by Jean-Luc Dorier (University of Geneva). All videos are filmed by Alexandre Bourquin (University of Geneva).
In this module, I describe the emergence of the instrumental approach, in the context of the study of the potential of CAS (Computer Algebra System) technology for mathematics learning in France, in the early nineties. I do it answering questions from Jorge Gaona, a Chilean Ph.D student of my research team. I think that knowing this story should help you better understand the ‘raisons d’être’ of this approach. I find also important to tell this story, answering questions of a young researcher who discovered the French didactic culture quite recently.
These two modules are devoted to the key concepts of the instrumental approach, making clear why and how, respectively cognitive ergonomics and ATD, the anthropological theory of the didactics, have provided the theoretical basis for this approach.
Retrospectively, I see this approach as resulting from a double process of deconstruction and reconstruction: the deconstruction of the dominant discourse regarding the potential and use of digital technologies in mathematics education, and the reconstruction of an alternative discourse thanks to cognitive ergonomics and ATD.
Module 2 is devoted to the ergonomic pillar of the instrumental qpproach, precisely the ergonomic perspective that Pierre Rabardel developed in collaboration with Pierre Vérillon. I introduce this perspective, focusing on the main elements that have been incorporated in the instrumental approach: the distinction between artefacts and instruments, and the concept of instrumental genesis with the dual processes of instrumentalization and instrumentation.
Module 3 is devoted to ATD, the second theoretical pillar of the instrumental approach. I first explain why ATD entered the scene, and then introduce the main elements of this theory incorporated in the instrumental approach: the concept of praxeology and the hierarchy of levels of didactic codetermination. I end this module by showing an interesting phenomenon of hybridization that resulted from this theoretical combination: the distinction between the epistemic and pragmatic values of techniques.
This fourth module is devoted to the first research works engaging the instrumental approach: the research carried out in the frame of a national project mentioned in Module 1, the doctoral theses by Badr Defouad in Paris and Luc Trouche in Montpellier. These made clear the complexity of instrumental geneses of CAS technology and the necessity of their institutional management. I synthesize the main empirical and theoretical outcomes of these research works, using selected examples. I end the module by evoking the rapid international dissemination of this approach, which induced new and fruitful theoretical combinations.
In this fifth module, I present and discuss the first test of the pertinence of the instrumental approach outside the CAS context where it emerged. This occurred with the doctoral thesis of a student of mine, Mariam Haspekian, with whom I have prepared this module. The thesis, defended in 2005, used the instrumental approach to study the integration of spreadsheet technology in middle school mathematics, with a particular focus on the use of spreadsheet for the introduction of algebra. I describe how this test showed the pertinence of the instrumental approach in this new context, led to question the educational discourse regarding spreadsheet and algebra, and also produced theoretical outcomes with the notion of instrumental distance.
This sixth module is devoted to the extension of the Instrumental Approach to dynamic geometry. I prepared it with Colette Laborde, a well-known researcher in the field of dynamic geometry who has been directly involved in this extension, through her investment in the MAGI project, “Learning better geometry with computers”. Relying on the research carried out in this project and the associated doctoral thesis by Angela Restrepo focusing on the development of dragging schemes by 6 graders, I show how this research made clear the complexity of the instrumental genesis of dragging, and proved the pertinence of the instrumental approach also for technologies designed with educational purposes.
This seventh module is devoted to the extension of the Instrumental Approach to the teacher. It has been prepared jointly with Maha Abboud, Mariam Haspekian and Luc Trouche, whose research has substantially contributed to this extension. I begin by the first step towards this extension: the introduction of the idea of instrumental orchestration by Luc Trouche in 2003. I move then to a complementary dimension of this extension with the idea of double instrumental genesis I introduced jointly with Mariam Haspekian, to account for the fact that, for a teacher, two distinct but intertwined instrumental geneses are at stake: a personal and a professional genesis, transforming the artefact respectively into a mathematical and a didactic instrument. I describe then how the combination with the Double Approach of teaching practices in the GUPTEN project led to a more global vision in terms of geneses of use, especially developed by Maha Abboud, Jean-Baptiste Lagrange and Fabrice Vzandebrouck.
In the previous modules, I have introduced the instrumental approach, explaining its “raison d’être”, tracing its progressive development since the mid-nineties, and showing some of its main outcomes. In the eighth and ninth modules, I reflect on the whole story. Since this approach has benefited from the contributions of many researchers from different countries and cultures, with different theoretical backgrounds and research interests, I find interesting to rely for this reflection on the concept of research praxeology I introduced jointly with Marianna Bosch and Josep Gascón in 2011. Doing so, I connect this reflection with a more recent dimension of my research activity, today known as the networking of theories. In this module, thus, I present the concept of research praxeology, as I envisage it now, using examples from previous modules to help make sense of this construction.
In this ninth module I continue the reflection undertaken in Module 8, drawing some lessons from the whole story. I do this by reviewing the different components of research praxeologies relying on the instrumental approach: the questions addressed, the techniques used to answer them, the theoretical discourse. This reflection makes clear substantial and convergent outcomes in terms of the understanding of instrumental geneses processes and their complexity; the production of many engineering designs; and also theoretical outcomes. There is no doubt that the praxeological dynamics of the instrumental approach has benefitted from the diversity of theoretical combinations it has generated. However, theoretical combinations and diversity are also source of questions. For instance, I show how the combination of cognitive ergonomics and ATD has been the source of vivid discussions regarding the relationships between schemes and techniques. And, concluding this series of modules, I insist on the fact that what has been shown is the collective work of a community, the empirical and theoretical advances that this community has made possible.