From artifact to instrument: mathematics teaching mediated by symbolic calculators

The evolution of calculation tools available for the learning of mathematics has been quick and profound. After the first illusions on a naturally positive integration of these tools, new theoretical approaches have emerged. They take into account individual and social processes of the mathematical instrument construction from a given artifact. In this article we show how analyzing constraints of the tool allows the understanding of its influence on the knowledge construction. We propose the concept of instrumental orchestration to design different devices which may be built in class and thus strengthen the socialized part of the instrumental genesis: instrumental orchestration is defined by objectives, configuration and exploitation modes. It acts at the same time on the artifact, on the subject, on the relationship the subject has with the artifact and on the way the subject considers this relation.

[1]  Luc Trouche,et al.  The Complex Process of Converting Tools into Mathematical Instruments: The Case of Calculators , 1998, Int. J. Comput. Math. Learn..

[2]  Jean-Pierre Archambault.  L'ordinateur pour enseigner les mathématiques , 1992 .

[3]  Marina Penglase,et al.  The graphics calculator in mathematics education: A critical review of recent research , 1996 .

[4]  Michèle Artigue,et al.  Learning Mathematics in a CAS Environment: The Genesis of a Reflection about Instrumentation and the Dialectics between Technical and Conceptual Work , 2002, Int. J. Comput. Math. Learn..

[5]  N. Balacheff,et al.  Didactique et intelligence artificielle , 1994 .

[6]  R. Sutherland,et al.  Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education , 2001 .

[7]  Paul Drijvers,et al.  Students encountering obstacles using a CAS , 2000, Int. J. Comput. Math. Learn..

[8]  Celia Hoyles,et al.  Windows on Mathematical Meanings , 1996 .

[9]  Dominique Guin,et al.  Conception et réalisation de ressources pédagogiques vivantes : des ressources intégrant les TICE en mathématiques , 2003 .

[10]  Gaëtan Bourmaud,et al.  From computer to instrument system: a developmental perspective , 2003, Interact. Comput..

[11]  P. Rabardel.  Les hommes et les technologies; approche cognitive des instruments contemporains , 1995 .

[12]  Celia Hoyles.  Steering between Skills and Creativity: A Role for the Computer?. , 2001 .

[13]  Luc Trouche,et al.  La parabole du gaucher et de la casserole à bec verseur: ètude des processus d'apprentissage dans un environnement de calculatrices symboliques , 2000 .

[14]  Lynn S. Liben,et al.  Piaget and the foundations of knowledge , 1983 .

[15]  S. Engel.  Thought and Language , 1964 .

[16]  Dominique Guin,et al.  Calculatrices symboliques. Transformer un outil en un instrument du travail mathématique : un problème didactique , 2002 .

[17]  Luc Trouche.  Regards croisés sur un environnement TI-92 , 1998 .

[18]  Luc Trouche.  E pur, si muove! , 1994 .