Teaching mathematics in complex environments
the necessity of instrumental orchestrations
DOI:
https://doi.org/10.23925/2358-4122.73678Keywords:
Artifact, Mathematical instrument, Instrumentation, Instrumentalization, Instrumental orchestrationAbstract
After an introduction which addresses some basic questions, this article is organized around three points: (1) The theoretical framework of the so-called ‘‘instrumental approach’’ which has been a theme in the last two CAME symposia; (2) A consideration of two processes (instrumentalization and instrumentation) which interact in the instrumental genesis; and (3) The introduction of the idea of instrumental orchestration as a way of allowing the teacher to assist the student’s instrumental genesis.
References
Allen, R., Wallace, M. and Cederberg, J. (1995). Preparing Teachers to Use Geometric Software. Proceedings of the Seventh International Congress on Mathematics Education.
Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning 7(3), 245–274.
Balacheff, N. (1994). Didactique et intelligence artificielle. Recherches en Didactique des Mathématiques, 14(1/2), 9–42.
Billeter, J.-F. (2002). Leçons sur Tchouang-Tseu, Editions Allia.
Bosch, M. and Chevallard, Y. (1999). La sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématique. Recherches en Didactique des Mathématiques, 19(1), 77–124.
Bourdieu, P. (2003). Images d’Algérie, une affinite´ élective. Actes Sud.
Changeux, J.-P. (2002). L’homme de vérité. Éditions Odile Jacob.
Chevallard, Y. (1992). Integration et viabilité des objets informatiques, le probléme de l’ingénierie didactique. in (Cornu ed.), L’ordinateur pour enseigner les mathematiques, PUF.
Debray, R. (2001). Dieu, un itinéraire. Editions Odile Jacob.
Dehaene, S. (1997). La bosse des maths. Editions Odile Jacob.
Guin, D. and Trouche, L. (1999). The Complex Process of Converting Tools into Mathematical Instruments. The Case of Calculators. International Journal of Computers for Mathematical Learning 3(3), 195–227.
Guin, D. and Trouche, L. (2002). Mastering by the teacher of the instrumental genesis in CAS environments: necessity of instrumental orchestrations. In, E. Schneider (Ed.), Zentralblatt für Didaktik der Mathematik, Vol. 34(5), pp. 204–211.
Guin, D., Ruthven, K. and Trouche, L. (Eds.) (2004). The Didactical Challenge of Symbolic Calculators: Turning a Computational Device into a Mathematical Instrument, Kluwer Academic Publishers, 400p.
Healy, L. (2002). Iterative design and Comparison of Learning Systems for Reflection in Two Dimensions, Unpublished PhD thesis, University of London.
Hoyles, C. (2001). Steering between Skills and Creativity: a Role for the Computer? For the Learning of Mathematics 21, Vol. 1, pp. 33–39.
Hoyles, C. and Noss, R. (1987). Children working in a structured Logo environment: from doing to understanding. Recherches en Didactique des Mathe´matiques 8(1/2), 131–174.
Houdé, O., Kayser, D., Koenig, O., Proust, J. and Rastier, F. (Eds.) (1998). Vocabulaire de sciences cognitives, PUF.
Houdé, O., Mazoyer, B. and Tzourio-Mazoyer, N. (Eds.) (2002). Cerveau et psychologie, PUF.
Joab, M., Guin, D. and Trouche, L. (2003). Conception et réalisation de ressources pédagogiques vivantes, des ressources intégrant les TICE en mathématiques. In C. Desmoulins, P. Marquet and D. Bouhineau (Eds.), Actes de la conférence EIAH 2003, ATIEF et INRP, pp. 259–270.
Lagrange, J.-B. and Py, D. (2002). De´velopper un environnement d’apprentissage utilisant le calcul formel. Hypothèses, méthode, première réalization. In, J.-F. Nicaud, E. Delozanne and B. Grugeon (Eds.), Logiciels pour l’apprentissage de l’algèbre, Sciences et Techniques Educatives, Vol. 9(1–2), pp. 91–120.
Lagrange, J.-B., Artigue, M., Laborde, C. and Trouche, L. (2003). Technology and mathematics education: a multidimensional study of the evolution of research and innovation, In, A.J. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick and F.K.S. Leung (Eds.), Second International Handbook of Mathematics Education, Kluwer Academic Publishers, pp. 239–271.
Lavoie, P. (1994). Contribution à une histoire des mathématiques scolaires au Québec: l’arithmétique dans les écoles primaires (1800–1920), Thèse de doctorat, Faculté des sciences de l’éducation, Université de Laval, Québec.
Noss, R. and Hoyles, C. (Eds.) (1996). Windows on Mathematical Meanings- Learning Cultures and Computers, Kluwer Academic Publishers.
Piaget, J. (1936). La naissance de l’intelligence chez l’enfant. Delachaux et Niestle´.
Rabardel, P. (1995). Les hommes et les technologies, approche cognitive des instruments contemporains, Armand Colin.
Rabardel, P. (2000). Elements pour une approche instrumentale en didactique des mathe´matiques, in M. Bailleul (Ed.), Actes de l’Ecole d’été de didactique des mathématiques, IUFM de Caen, pp. 203–213.
Rabardel, P. and Samurcay, R. (2001). From artifact to instrumented-mediated learning, New challenges to research on learning. International Symposium organized by the Center for Activity Theory and Developmental Work Research, University of Helsinki, March 21–23.
Ruthven, K. (2002). Instrumenting mathematical activity: reflections on key studies of the educational use of computer algebra systems, International Journal of Computers for Mathematical Learning, 7(3), 275–291.
Trouche, L. (1998). Faire des mathe´matiques avec des calculatrices symboliques, 38 variations sur un thème imposé, IREM, Université Montpellier, II.
Trouche, L. (2003). From Artifact to Instrument: Mathematics Teaching Mediated by Symbolic Calculators. In P. Rabardel and Y. Waern (Eds.), special issue of Interacting with Computers, Vol. 15(6) (in press).
Vergnaud, G. (1996). Au fond de l’apprentissage, la conceptualisation, Actes de l’école d’été de didactique des mathématiques, IREM, Clermont-Ferrand, 174–185.
Vergnaud, G. (1990). La théorie des champs conceptuels, Recherches en Didactique des Mathématiques, 10(2–3), 133–170.
Verillon, P. and Rabardel, P. (1995). Cognition and artifact: A contribution to the study of thought in relation to instrument activity, European Journal of Psychology in Education 9(3), 77–101.
Vygotski, L.S. (1934). Pense´e et langage, Flammarion (1978).
Wallon, H. (1949). Rôle d’autrui et conscience de soi, Enfance (n. special), 279–286.
Wartofsky, M. (1983). From genetic epistemology to historical epistemology: Kant, Marx and Piaget. in Liben, L.S. (Ed.), Piaget and the Foundations of Knowledges, Hillsdale, N.J., Lawrence Erlbaum.
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