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Handheld technology for mathematics education: flashback into the future

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Abstract

In the 1990s, handheld technology allowed overcoming infrastructural limitations that had hindered until then the integration of ICT in mathematics education. In this paper, we reflect on this integration of handheld technology from a personal perspective, as well as on the lessons to be learnt from it. The main lesson in our opinion concerns the growing awareness that students’ mathematical thinking is deeply affected by their work with technology in a complex and subtle way. Theories on instrumentation and orchestration make explicit this subtlety and help to design and realise technology-rich mathematics education. As a conclusion, extrapolation of these lessons to a future with mobile multi-functional handheld technology leads to the issues of connectivity and in- and out-of-school collaborative work as major issues for future research.

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Notes

  1. These are also now available on handheld devices.

  2. The wireless connection works between the students’ HHT and the teacher’s PC, not between the students’ HHT, which is certainly a result of institutional constraints: the students are not allowed to communicate during the examinations.

References

  • Aldon, G., Artigue, M., Bardini, C., Baroux-Raymond, D., Bonnafet, J.-L., Combes, M.-C., et al. (2008). Nouvel environnement technologique, nouvelles ressources, nouveaux modes de travail: Le projet e-CoLab (expérimentation Collaborative de Laboratoires mathématiques). Repères IREM, 72, 51–78.

    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, 245–274.

    Article  Google Scholar 

  • Brousseau, G. (1997). Theory of didactic situations. Dordrecht: Kluwer.

    Google Scholar 

  • Brown, R. G. (2010). Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested? Educational Studies in Mathematics, 73(2), 181–203.

    Article  Google Scholar 

  • Burril, G., Allison, J., Breaux, G., Kastberg, S., Leatham, K., & Sanchez, W. (Eds.). (2002). Handheld graphing technology in secondary mathematics: Research findings and implications for classroom practice. Dallas, USA: Texas Instruments.

  • Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41, 143–163.

    Article  Google Scholar 

  • Doorman, M., Drijvers, P., & Kindt, M. (1994). De grafische rekenmachine in het wiskundeonderwijs [The graphic calculators in mathematics education]. Utrecht: Freudenthal Instituut.

    Google Scholar 

  • Drijvers, P. (1995). Neem de grafiek over … [Copy the graph…]. Nieuwe Wiskrant, tijdschrift voor Nederlands wiskundeonderwijs, 14(4), 29–35.

    Google Scholar 

  • Drijvers, P. (1998). Assessment and new technologies: Different policies in different countries. The International Journal on Computer Algebra in Mathematics Education, 5(2), 81–93.

    Google Scholar 

  • Drijvers, P. (1999). Op hoeveel nullen eindigt 1998!? [With how many zeros ends 1998!?]. Euclides, 74, 275–277.

    Google Scholar 

  • Drijvers, P. (2009). Tools and tests: Technology in national final mathematics examinations. In C. Winslow (Ed.), Nordic research on mathematics education, proceedings from NORMA08 (pp. 225–236). Rotterdam: Sense.

    Google Scholar 

  • Drijvers, P., & Doorman, M. (1996). The graphics calculator in mathematics education. Journal of Mathematical Behaviour, 14(4), 425–440.

    Article  Google Scholar 

  • Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics (submitted).

  • Drijvers, P., Kieran, C., & Mariotti, M. A. (2009). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & J.-B. Lagrange (Eds.), Digital technologies and mathematics teaching and learning: Rethinking the terrain (pp. 89–132). New York: Springer.

    Chapter  Google Scholar 

  • Drijvers, P., & Trouche, L. (2008). From artefacts to instruments: A theoretical framework behind the orchestra metaphor. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics. Cases and perspectives (Vol. 2, pp. 363–392). Charlotte, NC: Information Age.

    Google Scholar 

  • Falcade, R., Laborde, C., & Mariotti, M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66, 317–333.

    Article  Google Scholar 

  • Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1, 155–177.

    Article  Google Scholar 

  • Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71, 199–218.

    Article  Google Scholar 

  • Guin, D., Ruthven, K., & Trouche, L. (Eds.). (2005). The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument. New York: Springer.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Habgood, M. P. J., Ainsworth, S. E., & Benford, S. (2005). Endogenous fantasy and learning in digital games. Simulation and Gaming, 36(4), 483–498.

    Article  Google Scholar 

  • Hoyles, C. (2003). From instrumenting and orchestrating convergence to designing and recognising diversity. In Lecture presented at the CAME3 conference, Reims, June 23–24. http://www.lkl.ac.uk/research/came/events/reims/. Accessed 4 Oct 2009.

  • Hoyles, C., Kalas, I., Trouche, L., Hivon, L., Noss, R., & Wilensky, U. (2009). Connectivity and virtual networks for learning. In C. Hoyles & J.-B. Lagrange (Eds.), Digital technologies and mathematics teaching and learning: Rethinking the terrain (pp. 439–462). New York: Springer.

    Chapter  Google Scholar 

  • Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 323–349). Dordrecht: Kluwer.

    Google Scholar 

  • Kieran, C., & Drijvers, P. (2006). The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11(2), 205–263.

    Article  Google Scholar 

  • Kindt, M. (1992a). Functie-onderzoek begint met de grafiek I [Function investigation starts with the graph I]. Euclides, 67, 200–204.

    Google Scholar 

  • Kindt, M. (1992b). Functie-onderzoek begint met de grafiek II [Function investigation starts with the graph II]. Euclides, 67, 227–230.

    Google Scholar 

  • Laborde, C., & Capponi, B. (1994). Cabri-géomètre Constituant d’un Milieu pour l’Apprentissage de la Notion de Figure Géométrique. Recherches en Didactique des Mathématiques, 14, 165–210.

    Google Scholar 

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

    Article  Google Scholar 

  • Maschietto, M., & Trouche, L. (2010). Mathematics learning and tools from theoretical, historical and practical points of view: The productive notion of mathematics laboratories. ZDM, 42, 33–47.

    Article  Google Scholar 

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

    Google Scholar 

  • Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.

    Google Scholar 

  • Parzysz, B. (1988). Knowing vs seeing, problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19(1), 79–92.

    Article  Google Scholar 

  • Patton, C. M., Tatar, D., & Dimitriadis, Y. (2008). Trace theory, coordination games and GroupScribbles. In J. Voogt & G. Knezek (Eds.), International handbook of information technology in primary and secondary education (pp. 921–994). New York: Springer.

    Chapter  Google Scholar 

  • Rabardel, P. (2002). People and technology—A cognitive approach to contemporary instruments. http://ergoserv.psy.univ-paris8.fr. Accessed 20 Dec 2005.

  • Roschelle, J. (2003). Unlocking the learning value of wireless mobile devices. Journal of Computer Assisted Learning, 19(3), 260–272.

    Article  Google Scholar 

  • Ruthven, K. (1990). The influence of graphic calculator use on translation from graphic to symbolic forms. Educational Studies in Mathematics, 21(5), 431–450.

    Article  Google Scholar 

  • Scardamalia, M. (2002). Collective cognitive responsibility for the advancement of knowledge. In B. Smith (Ed.), Liberal education in a knowledge society (pp. 67–98). Chicago: Open Court.

    Google Scholar 

  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.

    Article  Google Scholar 

  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169.

    Article  Google Scholar 

  • Thomas, M. O. J., Wilson, A. J., Corballis, M. C., & Lim, V. K. (2008). Neuropsychological evidence for the role of graphical and algebraic representations in understanding function. In M. Goos, K. Makar, & R. Brown (Eds.), Navigating currents and charting directions, proceedings of the 30th annual conference of the mathematics education research group of Australasia (Vol. 2, pp. 515–521). Brisbane: MERGA Inc.

    Google Scholar 

  • Trgalova, J., Jahn, A. P., & Soury-Lavergne, S. (2009). Quality process for dynamic geometry resources: the Intergeo project. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of CERME 6 (pp. 1161–1170). Lyon: INRP.

  • Trouche, L. (1994). Calculatrices graphiques, la grande illusion. Repères IREM, 20, 39–55.

    Google Scholar 

  • Trouche, L. (1998). Expérimenter et prouver, 38 variations sur un thème imposé [Experimentation and evidence, 38 variations to an imposed theme]. Montpellier: IREM, Université Montpellier 2.

    Google Scholar 

  • 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 [The parable of the left-handed and the skillet: Study on the learning process in a symbolic calculator environment]. Educational Studies in Mathematics, 41, 239–264.

    Article  Google Scholar 

  • Trouche, L. (2004). Managing complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9, 281–307.

    Article  Google Scholar 

  • Trouche, L. (2005). Construction et conduite des instruments dans les apprentissages mathématiques: Nécessité des orchestrations. Recherches en didactique des mathématiques, 25, 91–138.

    Google Scholar 

  • Vergnaud, G. (1996). Au fond de l’apprentissage, la conceptualisation. In R. Noirfalise & M.-J. Perrin (Eds.), Actes de l’école d’été de didactique des mathématiques (pp. 174–185). Clermont-Ferrand: IREM, Université Clermont-Ferrand 2.

    Google Scholar 

  • Weigand, H.-G. (1989). Über die Anzahl der Endnullen bei n!. Praxis der Mathematik, 31, 343–349.

    Google Scholar 

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Authors and Affiliations

  1. INRP (National Institute for Pedagogical Research), Lyon, France

    Luc Trouche

  2. Freudenthal Institute for Science and Mathematics Education, Utrecht University, Utrecht, The Netherlands

    Paul Drijvers

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  1. Luc Trouche
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  2. Paul Drijvers
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Correspondence to Luc Trouche.

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Trouche, L., Drijvers, P. Handheld technology for mathematics education: flashback into the future. ZDM Mathematics Education 42, 667–681 (2010). https://doi.org/10.1007/s11858-010-0269-2

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