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Designing a duo of material and digital artifacts: the pascaline and Cabri Elem e-books in primary school mathematics

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Abstract

This paper focuses on a duo of artifacts, constituted by a physical artifact and its digital counterpart. It deals with the theoretically and empirically underpinned design process of the digital artifact, the e-pascaline developed with Cabri Elem technology, in reference to a physical artifact, the pascaline. The theoretical frameworks of the instrumental approach and the theory of semiotic mediation together with the analysis of teaching experiments with the pascaline support the design in terms of continuity and discontinuity between the two artifacts. The components of the digital artifact were chosen from among the components of the physical artifact that are the object of instrumental genesis by the students and that are analyzed as having a semiotic potential that contributes to didactical aims. Components instrumented by students which had inadequate semiotic potential were eliminated. With the resulting duo, each artifact adds value to the use of the other artifact for mathematical learning.

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Notes

  1. http://www.unige.ch/math/EnsMath/Rome2008/WG4/WG4.html. Accessed 30 July 2013.

  2. Its commercial name is Zero + 1, produced by Quercetti Company.

  3. Cabri Elem technology is produced by Cabrilog Company.

  4. http://www-m10.ma.tum.de/ix-quadrat. Accessed 30 July 2013.

  5. http://christophe.bascoul.free.fr/pascaline_dossier/web.html. Accessed 30 July 2013.

  6. http://www.macchinematematiche.org. Accessed 30 July 2013.

  7. A French project supported by the Ministry of Education, directed by the IFÉ; a part of the project concerns the use of the physical pascaline and the design of the associated e-books. http://educmath.ens-lyon.fr/Educmath/recherche/equipes-associees/mallette. Accessed 30 July 2013.

References

  • Arzarello, F., & Robutti, O. (2010). Multimodality in multi-representational environments. ZDM—The International Journal on Mathematics Education, 42, 715–731.

    Article  Google Scholar 

  • Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: artifacts and signs after a Vygotskian perspective. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 746–783). New York: Routledge.

    Google Scholar 

  • Bétrancourt, M. (2005). The animation and interactivity principles. In R. E. Mayer (Ed.), Handbook of multimedia (pp. 287–296). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Boucheix, J. M. (2008). Young learners’ control of technical animations. In R. K. Lowe & W. Schnotz (Eds.), Learning with animations (pp. 208–234). New York: Cambridge University Press.

    Google Scholar 

  • Canalini Corpacci, R., & Maschietto, M. (2011). Gli artefatti-strumenti e la comprensione della notazione posizionale nella scuola primaria. La ‘pascalina’ Zero + 1 nella classe: genesi strumentale. L’Insegnamento della Matematica e delle Scienze Integrate, 34A(2), 161–188.

    Google Scholar 

  • Canalini Corpacci, R., & Maschietto, M. (2012). Gli artefatti-strumenti e la comprensione della notazione posizionale nella scuola primaria. La ‘pascalina’ Zero + 1 e sistema di strumenti per la notazione posizionale. L’Insegnamento della Matematica e delle Scienze Integrate, 35A(1), 33–58.

  • Casarini, A., & Clementi, F. (2010). Numeri… in macchina: alla scoperta della pascalina. In USR E-R, ANSAS E-R, Regione Emilia-Romagna & F. Martignone (Eds.), Scienze e Tecnologie in Emilia-Romagna (Vol. 2, pp. 141–145). Napoli: Tecnodid Editrice.

  • Drijvers, P., Kieran, C., & Mariotti, M. A. (2010). Integrating technology into mathematics education: theoretical perspectives. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology—Rethinking the terrain: The 17th ICMI Study (pp. 89–132). New York: Springer.

    Google Scholar 

  • Edwards, L., Radford, L., & Arzarello, F. (Eds.) (2009). Gestures and multimodality in the construction of mathematical meaning. Educational Studies in Mathematics, Special issue, 70(2).

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

    Article  Google Scholar 

  • Hoyles, C., & Lagrange, J.-B. (2010). Mathematics education and technology—Rethinking the terrain: The 17th ICMI Study. New York: Springer.

    Book  Google Scholar 

  • Kalénine, S., Pinet, L., & Gentaz, E. (2011). The visuo-haptic and haptic exploration of geometrical shapes increases their recognition in preschoolers. International Journal of Behavioral Development, 35, 18–26.

    Article  Google Scholar 

  • Laborde, C., & Laborde, J.-M. (2011). Interactivity in dynamic mathematics environments: what does that mean? Proceedings of ATCM conference. http://atcm.mathandtech.org/EP2011/invited_papers/3272011_19113.pdf. Accessed 30 July 2013.

  • Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.

    Google Scholar 

  • Mackrell, K., Maschietto, M., & Soury-Lavergne, S. (2013). The interaction between task design and technology design in creating tasks with Cabri Elem. In C. Margolinas (Ed.), Proceedings of the ICMI Study 22 Conference: Task design in mathematics education (pp. 81–89). Oxford, UK, July 2013.

  • Manches, A., O’Malley, C., & Benford, S. (2010). The role of physical representations in solving number problems: a comparison of young children’s use of physical and virtual materials. Computer & Education, 54, 622–640.

    Article  Google Scholar 

  • Mariotti, M. A. (2012). ICT as opportunities for teaching-learning in a mathematics classroom: the semiotic potential of artifacts. In T. Y. Tso (Ed.), Proceedings of the 36th Conference of the Intern. Group for the Psychology of Mathematics Education (Vol. 1, pp. 25–40). Taipei: PME.

  • Martin, T., & Schwartz, D. (2005). Physically Distributed Learning: Adapting and reinterpreting physical environments in the development of fraction concepts. Cognitive Science, 29(4), 587–625.

    Article  Google Scholar 

  • Maschietto, M. (2005). The Laboratory of Mathematical Machines of Modena. Newsletter of the European Mathematical Society, 57, 34–37.

  • Maschietto, M. (2011). Instrumental geneses in mathematics laboratory. In B. Ubuz (Ed.), Proc. of the 35th Conference of the Intern. Group for the Psychology of Mathematics Education (Vol. 3, pp. 121–128). Ankara: PME.

  • Maschietto, M., Bartolini Bussi, M. G., Mariotti, M. A., & Ferri, F. (2004). Visual representations in the construction of mathematical meanings. Paper for ICME 10—TSG16: Visualisation in the teaching and learning of mathematics, Copenhagen, Denmark.

  • Maschietto, M., & Ferri, F. (2007). Artefacts, schèmes d’utilisation et significations arithmétiques. In J. Szendrei (Ed.), Proceedings of the CIEAEM 59 (pp. 179–183). Hungary: Dobogóko.

    Google Scholar 

  • Pepin, B., Gueudet, G., & Trouche, L. (2013) Re-sourcing teachers’ work and interactions: a collective perspective on resources, their use and transformation. ZDM – The International Journal on Mathematics Education, 45(7) (this issue).

  • Poisard, C., Bueno-Ravel, L., & Gueudet, G. (2011). Comprendre l’intégration de ressources technologiques en mathématiques par des professeurs des écoles. Recherches en didactique des mathématiques, 31(2), 151–189.

    Google Scholar 

  • Rabardel, P., & Bourmaud, G. (2003). From computer to instrument system: A developmental perspective. Interacting with Computers, 15(5), 665–691.

    Article  Google Scholar 

  • Restrepo, A. (2008). L’instrumentation du déplacement dans les environnements de géométrie dynamique : Le cas de Cabri-Géomètre. Doctoral dissertation. Grenoble: Université Joseph Fourier.

    Google Scholar 

  • Sáenz-Ludlow, A., & Presmeg, N. (2006). Semiotic perspectives on learning mathematics and communicating mathematically. Guest editorial. Educational Studies in Mathematics, 61, 1–10.

    Article  Google Scholar 

  • Schnotz, W., & Lowe, R. (2003). External and internal representations in multimedia learning. Learning and Instruction, 13(2), 117–123.

    Article  Google Scholar 

  • Soury-Lavergne, S. (2006). Instrumentation du déplacement dans l’initiation au raisonnement déductif avec Cabri-géomètre. In N. Bednarz & C. Mary (Eds.), L’enseignement des mathématiques face aux défis de l’école et des communautés, Actes du colloque EMF 2006. Sherbrooke: Université de Sherbrooke.

    Google Scholar 

  • Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307.

    Article  Google Scholar 

  • Trouche, L., & Drijvers, P. (2010). Handheld technology for mathematics education: Flashback into the future. ZDM–The International Journal on Mathematics Education, 42(7), 667–681.

    Article  Google Scholar 

  • Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52, 83–94.

    Article  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 of Education, 10(1), 77–101.

    Article  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Educazione e Scienze Umane, Università di Modena e Reggio Emilia, Via Allegri, 9, 42100, Reggio Emilia, Italy

    Michela Maschietto

  2. S2HEP, Institut Français de l’Éducation, Ecole Normale Supérieure de Lyon, 19 allée de Fontenay, BP 17424, 69347, Lyon Cedex 07, France

    Sophie Soury-Lavergne

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  1. Michela Maschietto
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  2. Sophie Soury-Lavergne
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Correspondence to Sophie Soury-Lavergne.

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Maschietto, M., Soury-Lavergne, S. Designing a duo of material and digital artifacts: the pascaline and Cabri Elem e-books in primary school mathematics. ZDM Mathematics Education 45, 959–971 (2013). https://doi.org/10.1007/s11858-013-0533-3

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