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The Role and Uses of Technologies in Mathematics Classrooms: Between Challenge and Modus Vivendi

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Abstract

Drawing support from theoretical frameworks, this article analyses the role and uses of technology in the teaching of mathematics, with specific reference to the complexity of integrating technology into teaching. Four aspects are discussed here: the changes that technology brings about in classroom mathematical activity, the difficulties students encounter in solving problems in a technology-rich environment, the evaluation of potential assignments and the creation of conditions appropriate for learning, and the difficulties faced by teachers who use technology in deciding when and how to intervene. This analysis is illustrated by examples taken primarily from dynamic geometry, but similar analyses could be conducted for computerized environments of other kinds.

Résumé

Cet article porte sur le rôle et l’utilisation des technologies, plus spécifiquement sur la complexité de l’intégration des technologies en enseignement des mathématiques, en s’appuyant pour aborder cette question sur certains cadres théoriques. Quatre aspects y sont développés: les changements que provoquent ces technologies sur l’activité mathématique mobilisée à l’école, les difficultés que les élèves rencontrent dans la résolution de problèmes dans un tel environnement, l’analyse des tâches proposées et des conditions propices à un apprentissage, et la complexité de la gestion de l’intervention pour un enseignant qui intègre de telles technologies. Cette analyse est illustrée par des exemples provenant principalement d’un environnement de géométrie dynamique mais des analyses semblables peuvent être conduites dans d’autres types d’environnements informatiques.

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References

  • Ainley, J., Bills, L., & Wilson K. (2005). Designing spreadsheet-based tasks for purposeful algebra. International Journal of Computers for Mathematical Learning, 10(3), 191–215.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Arzarello, F. (2000). Inside and outside: Spaces, times and language in proof production. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24 th Psychology for Mathematics Education international conference (vol. 1; pp. 23–38). Hiroshima: Japan.

    Google Scholar 

  • Arzarello, F., Micheletti, C., Olivero, F., & Robutti, O. (1998). Dragging in Cabri and modalities of transition from conjectures to proofs in geometry. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Psychology for Mathematics Education international conference (vol. 2; pp. 32–39). Stellenbosch, South Africa: University of Stellenbosch.

    Google Scholar 

  • Arzarello, F., Olivero, F., Paola, D, & Robutti, O. (2002). A cognitive analysis of dragging practices in Cabri environments. Zentralblatt für Didaklik der Mathemulik, 34(3), 66–72.

    Article  Google Scholar 

  • Assude, T. (2005). Time management in the work economy of a class—A case study: Integration of Cabri in primary school mathematics teaching. Educational Studies in Mathematics, 59(1/2/3), 183–203.

    Article  Google Scholar 

  • Bellemain, F., & Capponi, B. (1992). Spécificité de l’organisation d’une séquence d’enseignement lors de l’utilisation de l’ordinateur. Educational Studies in Mathematics, 23(1), 59–97.

    Article  Google Scholar 

  • Birebent, A. (2001). Articulation entre la calculatrice et l’approximation décimale dans les calculs numériques de l’enseignement secondaire français. Doctoral thesis. Université de Grenoble I.

    Google Scholar 

  • Bosch, M., & Chevallard, Y. (1999). La sensibilité de l’activité mathématique aux ostensifs. Recherches en didactique des mathématiques, 19(2), 77–124.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Eds. & Trans.). Dordrecht, The Netherlands: Kluwer Academic.

  • Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en didactique des mathématiques, 19(2), 221–265.

    Google Scholar 

  • D’Amore, B. (2003). Le basi filosofische, pedagogiche, epistemologiche e concettuali della Didattica della Matematica. Bologna, Italy: Pitagora.

    Google Scholar 

  • Defouad, B. (2000). Elude de genèses instrumentales liées à l’utilisation d’une calculatrice symbolique en classe de première S. Doctoral thesis, Université Paris 7.

    Google Scholar 

  • Duval, R. (2000). Basic issues for research in mathematics education. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th conference of the international group for the Psychology of Mathematics Education. (Vol. 1; pp. 55–69). Hiroshima: Hiroshima University.

    Google Scholar 

  • Falcade, R. (2006). Théorie des situations, médiation sémiotique et discussions collectives dans des séquences d’enseignement avec Cabri-géomètre pour la construction des notions de fonction et de graphe de fonction. Thèse de doctorat, Université de Grenoble 1.

    Google Scholar 

  • Gallou-Dumiel, E. (1989). Logo et symétrie centrale. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th international conference for the Psychology of Mathematics Education (vol. 2; pp. 3–10). Paris, France: G.R. Didactique CNRS Paris V, Laboratoire PSYDEE.

    Google Scholar 

  • Grugeon, B. (2006, May). Effets d’une formation sur les pratiques d’intégration d’un logiciel de géométrie dynamique: quelles perspectives pour une nouvelle ingénierie? Paper presented to the Colloque EMF 2006, Université de Sherbrooke: Québec.

    Google Scholar 

  • Guin D., & Trouche L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. The International Journal of Computers for Mathematical Learning, 6(2), 143–165.

    Google Scholar 

  • Guin D., & Trouche L. (2002). Calculatrices symboliques—transformer un outil en un instrument du travail mathématique: un problème didactique. Grenoble, France: La Pensée Sauvage.

    Google Scholar 

  • Hadas, N., Hershkowitz, R., & Schwarz, B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44(1–3), 127–150.

    Article  Google Scholar 

  • Haspekian, M. (2005). An ‘instrumental approach’ to study the integration of a computer tool into mathematics teaching: The case of spreadsheets. International Journal of Computers for Mathematical Learning, 10(2), 109–141.

    Article  Google Scholar 

  • Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second International Handbook of Mathematics Education (Part 1; pp.323–349). Dordrecht, The Netherlands: Kluwer Academic.

    Chapter  Google Scholar 

  • Hoyles, C., & Sutherland, R. (1990). Pupil collaboration and teaching interventions in the logo environment. Journal für Malhematik-Didaktik, 4, 324–343.

    Google Scholar 

  • Jahn, A.P. (2002). ‘Locus’ and ‘trace’ in Cabri-géomètre: Relationships between geometric and functional aspects in a study of transformations. Zentralblall für Didaktik der Mathematik, 34(2), 78–84.

    Article  Google Scholar 

  • Jones, K. (2002). Research on the use of dynamic geometry software: Implications for the classroom. MicroMath, 18(3), 18–20.

    Google Scholar 

  • Kadunz, G. (2002). Macros and modules in geometry. Zentralblall für Didaktik der Mathematik, 34(3), 73–77.

    Article  Google Scholar 

  • Kaput, J. (2001, January). Changing representational infrastructures changes most everything: The case of SimCalc algebra, and calculus. Paper presented at the NAS symposium on improving learning with informational technology. Washington, DC. Available: https://doi.org/www.simcalc.umassd.edu/library/Iibrary_2001.php (accessed 26 November 2006).

    Google Scholar 

  • Korkmaz, O. (2003). La perspective cavalière en classe de Seconde: savoir géométrique ou technique de dessin. DEA ‘Environnements Informatiques d’Apprentissage humain.’ Masters thesis, Université de Grenoble 1.

    Google Scholar 

  • Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 99–154). Dordrecht, The Netherlands: Kluwer Academic.

    Google Scholar 

  • Laborde, C. (1995). Designing tasks for learning geometry in a computer-based environment. In L. Burton & B. Jaworski (Eds.), Technology in mathematics teaching: A bridge between teaching and learning (pp. 35–68). London: Chartwell-Bratt.

    Google Scholar 

  • Laborde C. (2001). Integration of technology in the design of geometry tasks with Cabri-geometry. International Journal of Computers for Mathematical Learning, 6, 283–317.

    Article  Google Scholar 

  • Lagrange, J.B. (1999). Complex calculators in the classroom: Theoretical and practical reflections on teaching precalculus. International Journal of Computers for Mathematical Learning, 4(1), 51–81.

    Article  Google Scholar 

  • Lagrange, J.B. (2001). L’intégration des instruments informatiques dans l’enseignement: une approche par les techniques. Educational Studies in Mathematics, 43(1), 1–30.

    Article  Google Scholar 

  • Lagrange, J.B., Artigue, M., Laborde C., & Trouche, L. (2003). Technology and math education: A multidimensional overview of recent research and innovation. In J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (Part 1; pp. 237–270). Dordrecht, The Netherlands: Kluwer Academic.

    Chapter  Google Scholar 

  • Leron, U., & Hazzan, O. (1998). Computers and applied constructivism. In D. Tinsley & D.C. Johnson (Eds.), Information and communications technologies in school mathematics (pp. 195–203). London: Chapman & Hall.

    Chapter  Google Scholar 

  • Leung, A., & Lopez-Real, F. (2004). Theorem justification and acquisition in dynamic geometry: A case of proof by contradiction. International Journal of Computers for Mathematical Learning, 7(2), 145–165.

    Article  Google Scholar 

  • Mariotti, M.A. (2001). Justifying and proving in the Cabri environment. International Journal of Computers for Mathematical Learning, 6(3), 257–281.

    Article  Google Scholar 

  • Mariotti, M.A., Laborde, C., & Falcade, R. (2003). Function and graph in a DGS environment. In N.A. Pateman, B.J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2003 joint meeting of International Group for the Psychology of Mathematics Education and North American chapter (Vol. 3; pp. 237–244). Honolulu, Hawaii: CRDG, College of Education, University of Hawaii.

    Google Scholar 

  • Monaghan, J. (2004). Teachers’ activities in technology-based lessons. International Journal of Computers for Mathematical Learning, 9(3), 327–357.

    Article  Google Scholar 

  • Moreno Armella, L. (1999). Epistemología ed educazione matemática. La Matemetica e la sua Didattica, 1, 43–59.

    Google Scholar 

  • Moreno, J. (2006). Articulation des registres graphique et symbolique pour l’étude des équations différentielles avec Cabri-géomètre: analyse des difficultés des étudiants et rôle du logiciel. Thesis, Université Joseph Fourier, Grenoble, France.

    Google Scholar 

  • Mousley, J., Lambdin, D., & Koc, Y. (2003). Mathematics teacher education and technology. In A. Bishop, M. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (Part 1; pp. 395–432). Dordrecht, The Netherlands: Kluwer Academic.

    Chapter  Google Scholar 

  • Netz, R. (1999). The shaping of deduction in Greek mathematics. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Noble, T., Nemirovsky, R., Dimattia, C., & Wright, T. (2004). Learning to make to see: Making sense of mathematics of change in middle school. International Journal of Computers for Mathematical Learning, 9(2), 109–167.

    Article  Google Scholar 

  • Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht, The Netherlands: Kluwer Academic.

    Book  Google Scholar 

  • Olivero, F. (2002). The proving process within a dynamic geometry environment. Doctoral thesis, Graduate School of Education, University of Bristol.

    Google Scholar 

  • Pierce, R., & Stacey, K. (2004). A framework for monitoring progress and planning teaching towards the effective use of computer algebra systems, international Journal of Computers for Mathematical Learning, 9(1), 59–93.

    Article  Google Scholar 

  • Plegat-Soutjis, F., Camps, J.-F., Alban, A., Lutz, G., Morcillo, A., & Tricot, A. (2003). Utilité, utilisabilité, acceptabilité: interpréter les relations entre trois dimensions de l’évaluation des EIAH. In C. Desmoulins, P. Marquet, & D. Bouhineau (Eds.), Environnements informatiques pour l’apprentissage humain (pp. 391–402). Paris: ATIEF/INRP.

    Google Scholar 

  • Rolet, C. (1996). Dessin et figure en géométrie: analyse et conceptions de futurs enseignants dans le contexte Cabri-géomètre. Thesis, Université Lyon 1.

    Google Scholar 

  • Ruthven K., Hennessy S., & Deaney R. (2005). Incorporating dynamic geometry systems into secondary mathematics education: Didactical perspectives and practices of teachers. In Moving on with dynamic geometry (pp. 138–158). Derby, UK: Association of Mathematics Teachers.

    Google Scholar 

  • Senach, B. (1993). L’évaluation ergonomique des interfaces homme-machine: une revue de la littérature. In J.C. Sperandino (Ed.), L’ergonomie dans la conception des projets informatiques. Toulouse: Octarès.

    Google Scholar 

  • Sinclair, M. (2003). Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52(3), 289–317.

    Article  Google Scholar 

  • Sträßer, R. (1992). Didaktische Perspektiven auf Werkzeug-Software im Geometrie-Unterricht der Sekundarstufe I. Zentralblatt für Didaktik der Mathematik. 24(5), 197–201.

    Google Scholar 

  • Talmon, V., & Yerushalmy, M. (2004). Understanding dynamic behavior: Parent-child relations in dynamic geometry environments. Educational Studies in Mathematics, 57(1), 91–119.

    Article  Google Scholar 

  • Tapan, S. (2003, February-March). Integration of ICT in the teaching of mathematics in situations for treatment of difficulties in proving. Paper presented to CERME3 (3rd conference of the European Society for Research in Mathematics Education), Bellaria, Italy.

    Google Scholar 

  • Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology in Education, 9(3), 77–101.

    Article  Google Scholar 

  • Wong, N.Y. (2003). The influence of technology on the mathematics curriculum. In A.J. Bishop, M.A. Clements, C. Keitel, & F.K.S. Leung (Eds.), Second international handbook on mathematics education (Part I; pp. 271–321). Dordrecht, The Netherlands: Kluwer Academic.

    Chapter  Google Scholar 

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Laborde, C. The Role and Uses of Technologies in Mathematics Classrooms: Between Challenge and Modus Vivendi. Can J Sci Math Techn 7, 68–92 (2007). https://doi.org/10.1080/14926150709556721

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