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The Duo “Pascaline and e-Pascaline”: An Example of Using Material and Digital Artefacts at Primary School

  • Michela MaschiettoEmail author
  • Sophie Soury-Lavergne
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 9)

Abstract

The paper presents the design and the analysis of teaching experiments at primary school concerning the introduction and use of a “duo of artefacts”, constituted by the pascaline i.e., the arithmetical machine Zero+1, and its digital version e-pascaline. The idea of ‘duo of artefacts’ represents the innovative component of this research work, because the e-pascaline is constructed in a complementary way with respect to the pascaline. The duo of artefacts is proposed to support student’s conceptualization processes of numbers as sign of a quantity, number sequences and recursive addition. Computation and manipulation of base ten notation are two processes that students often consider separately. This duo enables the design of situations that required those two processes to be connected and to consider their effect on each other. With duo of artefacts, technology allows the development of learning environments in which it is possible to study the articulation between material and digital manipulatives for mathematical conceptualization.

References

  1. Bartolini Bussi, M. G., & Inprasitha, M. (2015). Theme 3: Aspects that affect whole number learning. In X. Sun, B. Kaur, & J. Novotna (Eds.) (pp. 277–281). Presented at the The Twenty-third ICMI Study: Primary Mathematics Study on Whole Numbers, Macau, China.Google Scholar
  2. Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. Springer.Google Scholar
  3. 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, 75(2), 213–234.CrossRefGoogle Scholar
  4. Edwards, L., Radford, L., & Arzarello, F. (Eds.). (2009). Gestures and multimodality in the construction of mathematical meaning. Educational Studies in Mathematics, 70(2).Google Scholar
  5. Fyfe, E. F., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26(1), 9–25. doi: 10.1007/s10648-014-9249-3 CrossRefGoogle Scholar
  6. Gueudet, G., Bueno-Ravel, L., & Poisard, C. (2014). Teaching mathematics with technologies at Kindergarten: Resources and orchestrations. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era (Vol. 2, pp. 213–240). Springer.Google Scholar
  7. Kalenine, 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
  8. Laborde, C., & Laborde, J.-M. (2011). Interactivity in dynamic mathematics environments: What does that mean? In Integration of Technology into Mathematics Education: past, present and future Proceedings of the Sixteenth Asian Technology Conference in MathematicsTCM. Bolu, Turkey. Retrieved from http://atcm.mathandtech.org/EP2011/invited_papers/3272011_19113.pdf
  9. Ladel, S., & Kortenkamp, U. (2015). Development of conceptual understanding of place value. In The twenty-third ICMI study: Primary mathematics study on whole numbers (p. 323). Macau, China: ICMI.Google Scholar
  10. Lakoff, G., & Nunez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
  11. 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.), ICMI study 22 Task design in mathematics education (pp. 81–90). Royaume-Uni: Oxford.Google Scholar
  12. Maschietto, M. (2015). The arithmetical machine Zero +1 in mathematics laboratory: Instrumental genesis and semiotic mediation. International Journal of Science and Mathematics Education, 13(1), 121–144. doi: 10.1007/s10763-013-9493-x CrossRefGoogle Scholar
  13. Maschietto, M., & Savioli, K. (2014). Numeri in movimento. Attività per apprendere l’aritmetica con la pascalina. Collana Artefatti intelligenti. Trento: Erickson.Google Scholar
  14. Maschietto, M., & Soury-Lavergne, S. (2013). Designing a duo of material and digital artifacts: The pascaline and Cabri Elem e-books in primary school mathematics. ZDM—The International Journal on Mathematics Education, 45(7), 959–971. doi: 10.1007/s11858-013-0533-3
  15. Moyer, P., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? In NCTM (Ed.), Teaching children mathematics (pp. 372–377).Google Scholar
  16. Moyer-Packenham, P., & Bolyard, J. J. (2016). Revisiting the definition of a virtual manipulative. In P. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (Vol. 7, pp. 3–23). Cham: Springer International Publishing. Retrieved from http://link.springer.com/10.1007/978-3-319-32718-1_1
  17. Moyer-Packenham, P. S. (Ed.). (2016). International perspectives on teaching and learning mathematics with virtual manipulatives. Berlin, New York, NY: Springer.Google Scholar
  18. Moyer-Packenham, P., Slakind, G., & Bolyard, J. (2008). Virtual manipulatives used by K-8 teachers for mathematics instruction: Considering mathematical, cognitive, and pedagogical fidelity. Contemporary Issues in Technology and Teacher Education, 8(3). Retrieved from http://www.citejournal.org/vol8/iss3/mathematics/article1.cfm
  19. Olympiou, G., & Zacharia, Z. C. (2012). Blending physical and virtual manipulatives: An effort to improve students’ conceptual understanding through science laboratory experimentation. Science Education, 96(1), 21–47. doi: 10.1002/sce.20463 CrossRefGoogle Scholar
  20. Ravenstein, J., & Ladage, C. (2014). Ordinateurs et Internet à l’école élémentaire française. Education & Didactique, 8(3), 9–21.CrossRefGoogle Scholar
  21. Sarama, J., & Clements, D. H. (2016). Physical and virtual manipulatives: What is “Concrete”? In P. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (Vol. 7, pp. 71–93). Cham: Springer International Publishing. Retrieved from http://link.springer.com/10.1007/978-3-319-32718-1_4
  22. Soury-Lavergne, S., & Maschietto, M. (2013). A la découverte de la «pascaline» pour l’apprentissage de la numération décimale. In C. Ouvrier-Buffet (Ed.), XXXIXe colloque de la COPIRELEM Faire des mathématiques à l’école: de la formation des enseignants à l’activité de l’élève. France: Quimper.Google Scholar
  23. Soury-Lavergne, S., & Maschietto, M. (2015a). Articulation of spatial and geometrical knowledge in problem solving with technology at primary school. ZDM—The International Journal on Mathematics Education, 47(3), 435–449. doi: 10.1007/s11858-015-0694-3
  24. Soury-Lavergne, S., & Maschietto, M. (2015b). Number system and computation with a duo of artefacts: The pascaline and the e-pascaline. In X. Sun, B. Kaur, & J. Novotna (Eds.), The twenty-third ICMI study: Primary mathematics study on whole numbers (pp. 371–378). Macau, China: ICMI.Google Scholar
  25. Tricot, A., Plégat-Soutjis, F., Camps, J.-F., Amiel, A., Lutz, G., & Morcillo, A. (2003). Utilité, utilisabilité, acceptabilité. Interpréter les relations entre trois dimensions de l’évaluation des EIAH. In Proceedings of EIAH (pp. 391–402). Strasbourg, France.Google Scholar
  26. Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52, 83–94.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Università di Modena e Reggio EmiliaModenaItaly
  2. 2.S2HEP Institut Français de l’Education ENS de LyonLyonFrance

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