Abstract
This chapter will consider in more depth the possible contribution of technology -- especially CAS -- to the study of mathematical domains. Using a theoretical approach to treat examples of classroom activities, we will show how a didactical reflection can help to understand this contribution. A variety of new techniques will be presented and related to paper-and-pencil techniques. Examining the pragmatic and epistemic value of both types of technique will help to make sense of classroom situations. It will also help to clarify the situation of teachers wanting to integrate new tools. Consideration of other approaches will show that educators emphasize the use of computer algebra to promote ‘conceptual’ mathematics. Nevertheless, they cannot ignore instrumented techniques when considering the real potentialities of new tools and the conditions for their integration.
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References
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.
Artigue M. & Lagrange J.B. (1999) Instrumentation et écologie didactique de calculatrices complexes: éléments d’analyse à partir d’une expérimentation en classe de Première S, in D. Guin (Ed.), Actes du congrès Calculatrices symboliques et géométriques dans l’enseignement des mathématiques (pp. 15–38). Montpellier: IREM, Université Montpellier II.
BECTa (2002) ImpaCT2: The Impact of Information and Communication Technologies on Pupil Learning and Attainment. London: Department for Education and Skills. (http://www.becta.org.uk/research/index.cfm.).
Chevallard Y. (1999) L’analyse des pratiques enseignantes en théorie anthropologique du didactique, Recherches en Didactique des Mathématiques 19(2), 221–266.
Goldenberg P. (2003) Algebra and Computer Algebra, in Fey (Ed.), Computer Algebra Systems in Secondary School Mathematics Education, NCTM monograph.
Guin D. & Delgoulet J. (1997) Etude des modes d’appropriation de calculatrices graphiques et symboliques dans une classe de seconde. Montpellier: IREM, Université Montpellier II.
Guin D. & Trouche L. (2002) Calculatrices symboliques. Transformer un outil en un instrument du travail mathématique: un problème didactique. Grenoble: La Pensée Sauvage éditions.
Heid M.K. (1988) Resequencing skills and concepts in applied calculus, Journal for Research in Mathematics Education 19(1) 3–25.
Kieran C. & Wagner S. (1989) The research agenda conference on algebra: background and issues, In Kieran & Wagner (Eds.), Research Issues in the Learning and Teaching of Algebra (pp. 1–10). NCTM-LEA.
Lagrange J.B. (2000) L’intégration d’instruments informatiques dans l’enseignement: une approche par les techniques, Educational Studies in Mathematics 43(1), 1–30.
Mayes R. (1997) Current state of research into CAS in mathematics education, in J. Berry, J. Monaghan (Eds.), The state of computer algebra in mathematics education (pp. 171–189). Chartwell-Bratt.
Monaghan J., Sun S. & Tall D. (1994) Construction of the Limit Concept with a Computer Algebra System, in Proceedings of PME 8 (Vol. 3, pp. 279–189). Lisbon: University of Lisbon.
Mounier G. & Aldon G. (1996) A Problem Story: Factorisations of xn-1, International DERIVE Journal 3(3), 51–61.
Pérez Fernández J. (1998) Los systemas de cálculo simbólico en la enseñanza de las matemáticas, in Hodgson & al (Eds.), Selected lectures 8th International Congress on Mathematical Education (pp. 345–368). SAEM THALES.
Rachlin S. (1989) The research agenda in algebra: a curriculum development perspective, in Kieran and Wagner (Eds.), Research Issues in the Learning and Teaching of Algebra (pp. 257–265). NCTM-LEA.
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.
Schneider E. (1999) La TI-92 dans l’enseignement des mathématiques, des enseignant(e)s découvrent la didactique des mathématiques, in D. Guin (Ed.), Actes du congrès Calculatrices symboliques et géométriques dans l’enseignement des mathématiques, Mai 1998 (pp. 49–60). Montpellier: IREM, Université Montpellier II.
Sierpinska A. & Lerman S. (1996) Epistemologies of mathematics and mathematics education, in Bishop & al (Eds.), International Handbook of Mathematics Education (pp. 827–876). Dordrecht: Kluwer Academic Publishers.
Trouche L. & al (1998) Faire des Mathématiques au lycée avec des calculatrices symboliques. Montpellier: IREM, Université Montpellier II.
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Lagrange, JB. (2005). Using Symbolic Calculators to Study Mathematics. In: Guin, D., Ruthven, K., Trouche, L. (eds) The Didactical Challenge of Symbolic Calculators. Mathematics Education Library, vol 36. Springer, Boston, MA. https://doi.org/10.1007/0-387-23435-7_6
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DOI: https://doi.org/10.1007/0-387-23435-7_6
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