, Volume 51, Issue 1, pp 199–212 | Cite as

Cultural transposition: Italian didactic experiences inspired by Chinese and Russian perspectives on whole number arithmetic

  • Maria MelloneEmail author
  • Alessandro Ramploud
  • Benedetto Di Paola
  • Francesca Martignone
Original Article


The paper presents some reflections and activities developed by researchers and teachers involved in teacher education programs on cultural transposition. The construct of cultural transposition is presented as a condition for decentralizing the didactic practice of a specific cultural context through contact with other didactic practices of different cultural contexts. We discuss the background theoretical issues of this approach and also give an analysis of two examples of cultural transposition experiences carried out in Italy. In particular, by means of qualitative analysis of some excerpts, discussions, and interviews, we show that the contact with different perspectives coming from China and Russia fostered educational practices and reflections on whole number arithmetic education.


Cultural transposition Whole number arithmetic Early algebra 


  1. Bussi, M. G. B. (1996). Mathematical discussion and perspective drawing in primary school. Educational studies in mathematics, 31(1–2), 11–41.CrossRefGoogle Scholar
  2. Bussi, M. G. B., Bertolini, C., Ramploud, A., & Sun, X. (2017). Cultural transposition of Chinese lesson study to Italy. An exploratory study on fractions in a fourth-grade classroom. International Journal for Lesson and Learning Studies, 6(4), 1–17.Google Scholar
  3. Bussi, M. G. B., & Martignone, F. (2013). Cultural issues in the communication of research on mathematics education. For the Learning of Mathematics, 33, 2–8.Google Scholar
  4. Bartolini Bussi, M. G., Sun, X., & Ramploud, A. (2014). A dialogue between cultures about task design for primary school. In C. Margolinas (Ed.), Proceedings of the ICMI Study 22 (pp. 549–558). Oxford.Google Scholar
  5. Bussi, M. G. B., & Sun, X. H. (Eds.). (2018). Building the foundation: Whole Numbers in the Primary Grades. Cham: Springer International Publishing AG.Google Scholar
  6. Barton, B. (2008). The language of mathematics: Telling mathematical tales (Vol. 44). New York: Springer.CrossRefGoogle Scholar
  7. Beijing Education Science Research Institute and Beijing Instruction Research Center for Basic Education (1996). Shu Xue, vol. 24. Beijing.Google Scholar
  8. Bishop, A. J. (1988). Mathematical enculturation. A cultural perspective on mathematics education. Dordrecht: Kluwer Academic Publishers.Google Scholar
  9. Cai, J., & Knuth, E. (Eds.). (2011). Early algebraization: A global dialogue from multiple perspectives. New York: Springer.Google Scholar
  10. D’Ambrosio, U. (2006). Ethnomathematics—Link between traditions and modernity. Rotterdam: Sense Publishers.Google Scholar
  11. Davydov, V. V. (1982). The psychological characteristics of the formation of elementary mathematical operations in children. In T. P. Carpenter et al. (Eds.), Addition and subtraction: A cognitive perspective (pp. 224–238). Hillsdale: Lawrence Erlbaum.Google Scholar
  12. Derrida, J. (1967). De la grammatologie. Paris: De Minuit.Google Scholar
  13. Di Paola, B. (2016). Why Asian children outperform students from other countries? Linguistic and parental influences comparing Chinese and Italian children in Preschool Education. International Electronic Journal of Mathematics Education, 11(9), 3351–3359.Google Scholar
  14. Di Paola, B., Battaglia, O. R., & Fazio, C. (2016). Non-hierarchical clustering to analyse an open- ended questionnaire on algebraic thinking. South African Journal of Education, 36, 1–13.CrossRefGoogle Scholar
  15. Di Paola, B., Mellone, M., Martignone, F., & Ramploud, A. (2015). Un’esperienza educativa di trasposizione culturale nella scuola primaria. L’insegnamento della matematica e delle scienze integrate, 38(3), 363–387.Google Scholar
  16. Ernest, P., Sriraman, B., & Ernest, N. (Eds.). (2016). Critical mathematics education: Theory, praxis, and reality. Charlotte: Information Age Publishing.Google Scholar
  17. Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37–68.CrossRefGoogle Scholar
  18. Ivashova, O. (2011). The history and the present state of elementary mathematical education in Russia. In A. Karp & B. R. Vogel (Eds.), Russian mathematics education. Programs and practices (pp. 37–80). Singapore: World Scientific Publishing.CrossRefGoogle Scholar
  19. Jullien, F. (1993). Figures de l’immanence. Pour une lecture philosophique du Yi king. Le Classique du changement. Paris: Edition Grasset & Fasquelle.Google Scholar
  20. Jullien, F. (2005). La decostruzione da fuori. Dalla Grecia alla Cina e ritorno. Aut aut, 328, 71–87.Google Scholar
  21. Jullien, F. (2006). Si parler va sans dire. Du logos et d’autres ressources. Editions du Seuil.Google Scholar
  22. Leung, A., Baccaglini-Frank, A., & Mariotti, M. A. (2013). Discernment of invariants in dynamic geometry environments. Educational Studies in Mathematics, 84(3), 439–460.CrossRefGoogle Scholar
  23. Ling Lo, M. (2012). Variation theory and the improvement of teaching and learning. Acta Universitatis: Gothoburgensis.Google Scholar
  24. Lotman, J. M., & Uspenskij, B. A. (1975). Tipologia della Cultura. Milan: Bompiani.Google Scholar
  25. Mellone, M. (2011). “Looking for tricks”: a natural strategy, early forerunner of algebraic thinking… In M. Pytlak, T. Rowland, E. Swoboda (Eds.), Proceedings of the 7th Conference of the European Society for Research in Mathematics Education (pp. 1882–1890). Rzeszow: CERME.Google Scholar
  26. Mellone, M., Carotenuto, G., Di Bernardo, R., & Punzo, C. (2018). Algebraic thinking among graphical representations and algebraci symbols. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.). Proceedings of PME42, Vol. 1 (pp. 247–254). Umeå, Sweden: PME.Google Scholar
  27. Mellone, M., & Ramploud, A. (2015). Additive structure: An educational experience of cultural transposition. In Sun X., Kaur B. and Novotná N. (Eds.), Proceedings of the ICMI Study 23 (pp. 567–574). China, Macau: University of Macau.Google Scholar
  28. Mellone, M., Ramploud, A., Di Paola, B., & Martignone, F. (2017). Cultural transposition as a theoretical framework to foster teaching innovations. Proceedings of PME41, Vol.1 (p. 244). Singapore: PME.Google Scholar
  29. Mellone, M., & Tortora, R. (2017). A design study for an Italian fifth-grade class following Davydov. International Journal for Mathematics Teaching and Learning, 18(2), 240–256.Google Scholar
  30. Nuñes, T., Dorneles, B. V., Lin, P. J., & Rathgeb-Schnierer, E. (2016). Teaching and learning about whole numbers in primary school. In Teaching and learning about whole numbers in primary school (pp. 1–50). Cham: Springer International Publishing.CrossRefGoogle Scholar
  31. Ramploud, A. (2015). 数学 [shùxué] matematica, sguardi (d)alla Cina, Ph.D. Thesis, University of Modena e Reggio Emilia (Italy). Accessed 20 Dec 2017.
  32. Ramploud, A., & Di Paola, B. (2013). The Chinese perspective of variation to rethink the Italian approach to word-problems from a pre-algebraic point of view. In Fazio, C. (Ed.), Proceedings of CIEAEM 65 (pp. 525–535). Turin, Italy.Google Scholar
  33. Shao, G., Fan, Y., Huang, R., Ding, E., & Li, Y. (2012). Mathematics classroom instruction in China viewed from a historical perspective. In Y. Li & R. Huang (Eds.), How Chinese teach mathematics and improve teaching (pp. 11–28). New York: Routledge.Google Scholar
  34. Skovsmose, O. (1994). Towards a critical mathematics education. Educational Studies in Mathematics, 27(1), 35–57.CrossRefGoogle Scholar
  35. Spagnolo, F., & Di Paola, B. (2010). European and Chinese cognitive styles and their impact on teaching mathematics. Springer,. Studies in Computational Intelligence, 277, 1–267.Google Scholar
  36. Sun, X. (2011). An insider’s perspective: “Variation roblems” and their cultural grounds in Chinese curriculum practice. Journal of Mathematics Education, 4(1), 101–114.Google Scholar
  37. Sun, X., Kaur, B., & Novotná, J. (Eds.). (2015). Conference proceedings of the ICMI study 23: primary mathematics study on whole numbers. Accessed Dec 2017.
  38. Vygotskiĭ, L. S. (1962). Thought and language. Massachusetts Institute of Technology. Cambridge: MIT Press.Google Scholar
  39. Wood, T. (Ed.). (2008). The international handbook of mathematics teacher education. Rotterdam: Sense Publishers.Google Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  • Maria Mellone
    • 1
    Email author
  • Alessandro Ramploud
    • 2
  • Benedetto Di Paola
    • 3
  • Francesca Martignone
    • 4
  1. 1.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Università di Napoli Federico IINaplesItaly
  2. 2.Istituto Comprensivo J.F. KennedyReggio EmiliaItaly
  3. 3.Dipartimento di Matematica e InformaticaUniversità di PalermoPalermoItaly
  4. 4.Dipartimento di Scienze e Innovazione TecnologiaUniversità del Piemonte OrientaleAlessandriaItaly

Personalised recommendations