Advertisement

Mathematics Education Research Journal

, Volume 30, Issue 4, pp 445–473 | Cite as

Making sense out of the emerging complexity inherent in professional development

  • Theodosia ProdromouEmail author
  • Ornella Robutti
  • Monica Panero
Article

Abstract

This paper reports on a study of the process of professional development for mathematics teachers. The analysis connects two theoretical frameworks: the Meta-Didactical Transposition model developed by Arzarello et al. (2014), which describes the macro level, and, at the micro level, the idea of emergence, which has been around since at least the time of Aristotle and has been defined by Mill (1843), Lewes (1875), Blitz (1992), Huxley and Huxley (1947) and many others. The meta-didactical transposition model considers the evolution of teachers’ practices as part of a community process, while the notion of emergence helps us to gain better insights into the details of the practices of individual teachers. This paper focuses on secondary school teachers’ learning of new digital technologies to illuminate this theoretical framework.

Keywords

Teachers’ professional development Technology GeoGebra Emergence Meta-didactical transposition Praxeology Agent 

References

  1. Aldon, G., Arzarello, F., Cusi, A., Garuti, R., Martignone, F., Robutti, O., Sabena, C., & Soury-Lavergne, S. (2013). The meta-didactical transposition: a model for analysing teachers’ education programmes. In A. M. Lindmeier & A. Heinze (Eds.), Proc. 37 th Conf. of the Int. Group for the Psychology of Mathematics Education (Vol. 1, pp. 97–124). Kiel, Germany: PME.Google Scholar
  2. 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(3), 245–274.  https://doi.org/10.1032/A:1022103903080. CrossRefGoogle Scholar
  3. Artigue, M., Drijvers, P., Lagrange, J.-B., Mariotti, M. A., & Ruthven, K. (2009). Technologies numériques dans l’enseignement des mathématiques, où en est-on dans les recherches et dans leur intégration? [Technology in mathematics education: How about research and its integration?]. In C. Ouvrier-Buffet & M.-J. Perrin-Glorian (Eds.), Approches plurielles en didactique des mathématiques; Apprendre à faire des mathématiques du primaire au supérieur: quoi de neuf? [Multiple approaches to the didactics of mathematics; learning mathematics from primary to tertiary level: What’s new?] (pp. 185–207). Paris: Université Paris Diderot Paris 7.Google Scholar
  4. Arzarello, F., Cusi, A., Garuti, R., Malara, N., Martignone, F., Robutti, O., & Sabena, C. (2014). Meta-didactical transposition: a theoretical model for teacher education programmes. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: an international perspective on technology focused professional development (pp. 347–372). Dordrecht: Springer.CrossRefGoogle Scholar
  5. Blitz, D. (1992). Emergent evolution: qualitative novelty and the levels of reality. Dordrecht: Kluwer Academic.CrossRefGoogle Scholar
  6. Chevallard, Y. (1985). La transposition didactique. Grenoble: La Pensée Sauvage.Google Scholar
  7. Chevallard, Y. (1992). Concepts fondamentaux de la didactique: perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques, 12(1), 73–112.Google Scholar
  8. Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221–266.Google Scholar
  9. Clark-Wilson, A. (2014). A methodological approach to researching the development of teachers’ knowledge in a multi-representational technological setting. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: an international perspective on technology focused professional development (pp. 277–296). Dordrecht: Springer.CrossRefGoogle Scholar
  10. Clark-Wilson, A., Aldon, G., Cusi, A., Goos, M., Haspekian, M., Robutti, O., & Thomas, M. (2014). The challenges of teaching mathematics with digital technologies—the evolving role of the teacher. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proc. 38 th Conf. of the Int. Group for the Psychology of Mathematics Education and 36 th Conf. of the North American Chapter of the Psychology of Mathematics Education (Vol. 1, pp. 87–116). Vancouver, Canada: PME.Google Scholar
  11. Davis, B., & Simmt, E. (2003). Understanding learning systems: mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.CrossRefGoogle Scholar
  12. De Freitas, E., & Sinclair, N. (2014). Mathematics and the body: material entanglements in the classroom. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  13. Drijvers, P. (2012). Teachers transforming resources into orchestrations. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources: mathematics curriculum materials and teacher development (pp. 265–281). New York/Berlin: Springer.Google Scholar
  14. 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: Information Age.Google Scholar
  15. 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
  16. Drijvers, P., Tacoma, S., Besamusca, A., van den Heuvel, C., Doorman, M., & Boon, B. (2014). Digital technology and mid-adopting teachers’ professional development: a case study. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: an international perspective on technology focused professional development (pp. 189–212). Dordrecht: Springer.CrossRefGoogle Scholar
  17. Goldstein, J. (1999). Emergence as a construct: history and issues. Emergence, 11, 49–72.CrossRefGoogle Scholar
  18. Goos, M. (2014). Researcher-teacher relationships and models for teaching development in mathematics education. ZDM, 46(2), 189–200.  https://doi.org/10.1007/s11858-013-0556-9.CrossRefGoogle Scholar
  19. Hohenwarter, J., Kocadere, S. A., & Hohenwarter, M. (2017). Math teachers’ adventure of ICT Integration: from an open online course towards an online teacher community. Proceedings of CERME10, Dublin, Feb. 2017.Google Scholar
  20. Hong, Y. Y., & Thomas, M. O. J. (2006). Factors influencing teacher integration of graphic calculators in teaching. Proceedings of the 11th Asian technology conference in mathematics (pp. 234–243). Hong Kong.Google Scholar
  21. Huxley, J. S., & Huxley, T. H. (1947). Evolution and ethics: 1893–1943. London: The Pilot Press.Google Scholar
  22. Jaworski, B. (2008). Mathematics teacher educator learning and development: an introduction. In B. Jaworski & T. Wood (Eds.), International handbook of mathematics teacher education (Vol. 4, pp. 1–13). Rotterdam: Sense.Google Scholar
  23. Johnson, S. (2001). Emergence: the connected lives of ants, brains, cities, and software. New York: Scribner.Google Scholar
  24. Kasti, H., & Jurdak, M. (2017). Analyzing MOOCs in terms of teacher collaboration potential and issues: the Italian experience. Proceedings of CERME10, Dublin, Feb. 2017.Google Scholar
  25. Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher Education, 9(1), 60–70.Google Scholar
  26. Lewes, G. H. (1875). Problems of life and mind (pp. 1874–1879). London: Truebner.Google Scholar
  27. 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, 45(7), 959–971.CrossRefGoogle Scholar
  28. Mason, J. (2014). Interactions between teacher, student, software and mathematics: getting a purchase on learning with technology. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: an international perspective on technology focused professional development (pp. 11–42). Dordrecht: Springer.CrossRefGoogle Scholar
  29. Mill, J. S. (1843). A system of logic ratiocinative and inductive (p. 1872). London: John W. Parker and Son.Google Scholar
  30. Opfer, V. D., & Pedder. (2011). Conceptualising teacher professional learning. Review of Educational Research, 81(3), 376–407.CrossRefGoogle Scholar
  31. Prodromou, T., & Lavicza, Z. (2017). Integrating technology into mathematics education in an entire educational system—reaching a critical mass of teachers and schools. International Journal for Technology in Mathematics Education, 24(4).Google Scholar
  32. Prodromou, T., Lavicza, Z., & Koren, B. (2015). Increasing students’ involvement in technology-supported mathematics lesson sequences. International Journal of Technology in Mathematics Education, 22(4), 169–177.  https://doi.org/10.1564/tme_v22.4.05.CrossRefGoogle Scholar
  33. Robutti, O. (2006). Motion, technology, gestures in interpreting graphs. International Journal for Technology in Mathematics Education, 13(3), 117–125.Google Scholar
  34. Robutti, O., Cusi, A., Clark-Wilson, A., Jaworski, B., Chapman, O., Esteley, C., Goos, M., Isoda, M., & Joubert, M. (2016). ICME international survey on teachers working and learning through collaboration: June 2016. ZDM Mathematics Education, 48(1), 651-690.Google Scholar
  35. Ruthven, K. (2009). Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics. Education & Didactique, 3(1), 131–149.CrossRefGoogle Scholar
  36. Schoenfeld, A. (2015). Thoughts on scale. ZDM - the International Journal of Mathematics Education, 47(1), 161–169.CrossRefGoogle Scholar
  37. Taranto, E., Arzarello, F., Robutti, O., Alberti, V., Labasin, S., & Gaido, S. (2017). Analyzing MOOCs in terms of teacher collaboration potential and issues: the Italian experience. Proceedings of CERME10, Dublin, Feb. 2017.Google Scholar
  38. 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.CrossRefGoogle Scholar
  39. Trouche, L. (2005). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument (pp. 197–230). New York: Springer.CrossRefGoogle Scholar
  40. Wenger, E. (1998). Communities of practice: learning, meaning, and identity. New York: Cambridge University Press.CrossRefGoogle Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2017

Authors and Affiliations

  1. 1.University of New EnglandArmidaleAustralia
  2. 2.Department of MathematicsUniversity of TurinTurinItaly

Personalised recommendations