ZDM

, Volume 45, Issue 7, pp 959–971 | Cite as

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

Original Article

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.

References

  1. Arzarello, F., & Robutti, O. (2010). Multimodality in multi-representational environments. ZDM—The International Journal on Mathematics Education, 42, 715–731.CrossRefGoogle Scholar
  2. 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
  3. Bétrancourt, M. (2005). The animation and interactivity principles. In R. E. Mayer (Ed.), Handbook of multimedia (pp. 287–296). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  4. 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
  5. 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
  6. 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.Google Scholar
  7. 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.Google Scholar
  8. 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
  9. 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).Google Scholar
  10. Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71, 199–218.CrossRefGoogle Scholar
  11. Hoyles, C., & Lagrange, J.-B. (2010). Mathematics education and technology—Rethinking the terrain: The 17th ICMI Study. New York: Springer.CrossRefGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. 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.
  14. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
  15. 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.Google Scholar
  16. 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.CrossRefGoogle Scholar
  17. 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.Google Scholar
  18. 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.CrossRefGoogle Scholar
  19. Maschietto, M. (2005). The Laboratory of Mathematical Machines of Modena. Newsletter of the European Mathematical Society, 57, 34–37.Google Scholar
  20. 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.Google Scholar
  21. 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.Google Scholar
  22. 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
  23. Pepin, B., Gueudet, G., & Trouche, L. (2013) Re-sourcing teachers’ work and interactions: a collective perspective on resources, their use and transformation. ZDMThe International Journal on Mathematics Education, 45(7) (this issue).Google Scholar
  24. 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
  25. Rabardel, P., & Bourmaud, G. (2003). From computer to instrument system: A developmental perspective. Interacting with Computers, 15(5), 665–691.CrossRefGoogle Scholar
  26. 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
  27. Sáenz-Ludlow, A., & Presmeg, N. (2006). Semiotic perspectives on learning mathematics and communicating mathematically. Guest editorial. Educational Studies in Mathematics, 61, 1–10.CrossRefGoogle Scholar
  28. Schnotz, W., & Lowe, R. (2003). External and internal representations in multimedia learning. Learning and Instruction, 13(2), 117–123.CrossRefGoogle Scholar
  29. 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
  30. 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.CrossRefGoogle Scholar
  31. 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.CrossRefGoogle Scholar
  32. Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52, 83–94.CrossRefGoogle Scholar
  33. 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.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2013

Authors and Affiliations

  1. 1.Dipartimento di Educazione e Scienze UmaneUniversità di Modena e Reggio EmiliaReggio EmiliaItaly
  2. 2.S2HEP, Institut Français de l’ÉducationEcole Normale Supérieure de LyonLyon Cedex 07France

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