Advertisement

An Instrumental Approach to Mathematics Learning in Symbolic Calculator Environments

  • Luc Trouche
Chapter
Part of the Mathematics Education Library book series (MELI, volume 36)

Abstract

A rapid technological evolution (Chapter 1), linked to profound changes within the professional field of mathematics (Chapter 3), brings into question the place of techniques in mathematics teaching (Chapter 5). These changes have created serious difficulties for teachers; obliged to question their professional practices, they make different choices regarding integration of new technologies and techniques (Chapter 4), choices that are linked to their mathematical conceptions and to their teaching styles.

In this chapter, we place ourselves on the side of the students. We have already seen (Chapter 1) that they seem to adopt the new computing tools faster than the institution. In this chapter, we study more precisely their learning processes related to their use of symbolic calculators.

First of all, we pinpoint the didactic phenomena taking place in the experiments; subsequently, we suggest a new theoretical approach aimed at giving a better description, for each student, of the transformation of a technical tool into an instrument for mathematical work.

Key words

Computational transposition Instrumentation and instrumentalization process Instrumented technique Operational invariants Schemes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Artigue M. (1997) Le logiciel DERIVE comme révélateur de phénomènes didactiques liés à l’utilisation d’environnements informatiques pour l’apprentissage, Educational Studies in Mathematics 33(2), 133–169.Google Scholar
  2. Balacheff N. (1994) Didactique et intelligence artificielle, Recherches en Didactique des Mathématiques 14(1/2), 9–42.Google Scholar
  3. Bernard R., Faure C., Noguès M., Nouazé Y. & Trouche L. (1998) Pour une prise en compte des calculatrices symboliques en lycée. Montpellier: IREM, Université Montpellier II.Google Scholar
  4. Billeter J.F. (2002) Leçons sur Tchouang-Tseu, Editions Allia.Google Scholar
  5. Bouveresse L. (1995) Langage, perception et réalité, Editions Jacqueline Chambon.Google Scholar
  6. Chacon P.R. & Soto-Johnson H. (1998) The Effect of CAI in College Algebra incorporating both Drill and Exploration, The International Journal of Computer Algebra in Mathematics Education, 201–216.Google Scholar
  7. Duval R. (2000) Basic Issues for Research in Mathematics Education, in T. Nakahara & M. Koyama (Eds.), Proceedings of PME 24 (Vol. 1, pp. 55–69). Hiroshima: Hiroshima University.Google Scholar
  8. Dagher A. (1996) Apprentissage dans un environnement informatique: possibilité, nature, transfert des acquis, Educational Studies in Mathematics 30, 367–398CrossRefGoogle Scholar
  9. Defouad B. (2000) Etude de genèses instrumentales liées à l’utilisation de calculatrices symboliques en classe de première S, Doctoral Thesis. Paris: Université Paris VII.Google Scholar
  10. Guin D. & Trouche L. (1999) The complex process of converting tools into mathematical instruments: the case of calculators, International Journal of Computers for Mathematical Learning 3, 195–227.Google Scholar
  11. Luengo V. & Balacheff N. (1998) Contraintes informatiques et environnements d’apprentissage de la démonstration en géométrie, Sciences et Techniques Educatives 5(1), 15–45.Google Scholar
  12. Noss R. & Hoyles C. (1996) Windows on Mathematical Meanings, Learning Cultures and Computers (pp. 153–166). Dordrecht: Kluwer Academic Publishers.Google Scholar
  13. Rabardel P. (1995) Les hommes et les technologies, approche cognitive des instruments contemporains. Paris: Armand Colin.Google Scholar
  14. Schwarz B.B. & Dreyfus T. (1995) New actions upon old objects: a new ontological perspective on functions, Educational Studies in Mathematics 29(3), 259–291.CrossRefGoogle Scholar
  15. Trouche L. (1995) E pur si muove, Repères-Irem 20, 16–28.Google Scholar
  16. Trouche L. (1996) Enseigner les mathématiques en terminale scientifique avec des calculatrices graphiques et formelles. Montpellier: IREM, Université Montpellier II.Google Scholar
  17. Trouche L. (1997) A propos de l’enseignement des limites de fonctions dans un “environnement calculatrice”, étude des rapports entre processus de conceptualisation et processus d’instrumentation, Doctoral Thesis. Montpellier: Université Montpellier II.Google Scholar
  18. Trouche L. (2000) La parabole du gaucher et de la casserole à bec verseur: étude des processus d’apprentissage dans un environnement de calculatrices symboliques, Educational Studies in Mathematics 41(2), 239–264.Google Scholar
  19. Trouche L. (2001) Description, prescription, à propos de limites de functions, in J.B. Lagrange & D. Lenne (Eds.), Calcul formel et apprentissage des mathématiques (pp. 9–26). Paris: INRP.Google Scholar
  20. Vergnaud G. (1996) Au fond de l’apprentissage, la conceptualization, in R. Noirfalise & M.J. Perrin (Eds.), Actes de l’Ecole d’Eté de Didactique des Mathématiques (pp. 16–28). Clermont-Ferrand: IREM, Université Clermont-Ferrand II.Google Scholar
  21. Verillon P. & Rabardel P. (1995) Cognition and artifacts: A contribution to the study of thought in relation to instrument activity, European Journal of Psychology of Education 9(3), 77–101.Google Scholar
  22. Vygotsky L.S. (1962) Thought and Language. Cambridge, MA: MIT Press.Google Scholar
  23. Yerushalmy M. (1997) Reaching the unreachable: technology and the semantics of asymptotes, International Journal of Computers for Mathematical Learning 2, 1–25.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Luc Trouche
    • 1
  1. 1.LIRDEF, LIRMM & IREMUniversité Montpellier IIFrance

Personalised recommendations