Technology, Knowledge and Learning

, Volume 16, Issue 1, pp 35–54

Teachers’ Initial Orchestration of Students’ Dynamic Geometry Software Use: Consequences for Students’ Opportunities to Learn Mathematics



This paper reports from a case study with teachers at two schools in Norway participating in developmental projects aiming for inquiry communities in mathematics teaching and learning. In the reported case study, the teachers participated in one of the developmental projects focusing on implementation and use of computer software in mathematics teaching. I study teachers’ initial orchestration of dynamic geometry software (DGS) in mathematics teaching at lower secondary school. By utilising the notion of ‘instrumental orchestration’ from the theoretical perspective known as the ‘instrumental approach’ (Drijvers et al., in Educ Stud Math 75:213–234, 2010; Trouche, in Int J Comput Math Learn 9:281–307, 2004), I examine how teachers in their initial teaching with DGS empower students’ mathematics learning with the DGS software. According to this perspective, it involves teachers’ orchestration of two interrelated processes instrumentation and instrumentalisation. Analytical findings indicate that a difference in teachers’ empowerment is evident and consequences for students’ opportunities to engage with mathematics represented by the DGS are presented.


Dynamic geometry software Instrumental orchestration Instrumentalisation Instrumentation New tool for teachers 


  1. Arcavi, A., & Hadas, N. (2000). Computer mediated learning: An example of an approach. International Journal of Computers for Mathematical Learning, 5, 25–45.CrossRefGoogle Scholar
  2. Artigue, M. (2007). Digital technologies: A window on theoretical issues in mathematics education. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the fifth conference of the European society for research in mathematics education (pp. 68–82). Larnaca, Cyprus: University of Cyprus.Google Scholar
  3. Berry, J. S., Graham, T., Honey, S., & Headlam, C. (2007). A case study of the issues arising when teachers adopt the use of a new form of technology in their teaching for the first time. The International Journal for Technology in Mathematics Education, 14, 150–160.Google Scholar
  4. Bjuland, R., & Jaworski, B. (2009). Teachers’ perspectives on collaboration with didacticians to create an inquiry community. Research in Mathematics Education, 11, 21–38.CrossRefGoogle Scholar
  5. Bretscher, N. (2010). Dynamic geometry software: The teacher’s role in facilitating instrumental genesis. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the sixth conference of the European society for research in mathematics education (pp. 1340–1348). Lyon: INRP.Google Scholar
  6. Bueie, H. (n.d.). Innføring i Cabri. In . Retrieved April 13, 2011, from
  7. Chevallard, Y. (2007). Readjusting didactics to a changing epistemology. European Educational Research Journal, 6, 131–134.CrossRefGoogle Scholar
  8. Crisan, C., Lerman, S., & Winbourne, P. (2007). Mathematics and ICT: A framework for conceptualising secondary school mathematics teachers’ classroom practices. Technology, Pedagogy and Education, 16, 21–39.CrossRefGoogle Scholar
  9. Dörfler, W. (1993). Computer use and views of the mind. In C. Keitel & K. Ruthven (Eds.), Learning from computers: Mathematics education and technology (pp. 159–186). Berlin: Springer-Verlag.Google Scholar
  10. 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, 213–234.CrossRefGoogle Scholar
  11. Erfjord, I. (2008). Teachers’ implementation and orchestration of Cabri-use in mathematics teaching. Doctoral thesis in mathematics didactics, University of Agder, Kristiansand, Norway.Google Scholar
  12. Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht: Kluwer Academic Publishers.Google Scholar
  13. Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. The Journal of Mathematical Behavior, 22, 73–89.CrossRefGoogle Scholar
  14. Goos, M., & Soury-Lavergne, S. (2009). Teachers and teaching: theoretical perspectives and issues concerning classroom implementation. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology—rethinking the Terrain. The 17th ICMI study (pp. 311–328). New York: Springer.CrossRefGoogle Scholar
  15. Hagness, R., & Veiteberg, J. (1999). The Curriculum for the 10-year compulsory school in Norway. Oslo, Norway: National Centre for Educational Resources.Google Scholar
  16. Hals, S. (2010). IKT i matematikkopplæringentidstjuv eller tryllemiddel? En studie av faktorer som kan påvirke bruken av IKT generelt og GeoGebra spesielt, hos lærere og elever på 10. og 11. årstrinn. Master thesis in mathematics didactics, University of Agder, Kristiansand, Norway.Google Scholar
  17. Haspekian, M. (2005). An instrumental approach to study the integration of a computer tool into mathematics teaching: The case of spreadsheets. International Journal of Computers for Mathematical Learning, 10, 109–141.CrossRefGoogle Scholar
  18. Hennessy, S., Ruthven, K., & Brindley, S. (2005). Teacher perspectives on integrating ICT into subject teaching: Commitment, constraints, caution, and change. Journal of Curriculum Studies, 37, 155–192.CrossRefGoogle Scholar
  19. Kasten, S. E., & Sinclair, N. (2009). Using dynamic geometry software in the mathematics classroom: A study of teachers’ choices and rationales. The International Journal for Technology in Mathematics Education, 16, 133–143.Google Scholar
  20. KD. (2006). Læreplanverket for Kunnskapsløftet (English version available and retrieved August 20, 2010 from ). Oslo, Norway: Utdanningsdirektoratet.
  21. Kieran, C., & Drijvers, P. (2006). The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11, 205–226.CrossRefGoogle Scholar
  22. Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-Geometry. International Journal of Computers for Mathematical Learning, 6, 283–318.CrossRefGoogle Scholar
  23. Laborde, C., Kynigos, C., Hollebrands, K., & Strässer, R. (2006). Teaching and learning geometry with technology. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 275–304). Rotterdam: Sense.Google Scholar
  24. Lagrange, J.-B. (2005). Curriculum, classroom practices, and tool design in the learning of functions through technology-aided experimental approaches. International Journal of Computers for Mathematical Learning, 10, 143–189.CrossRefGoogle Scholar
  25. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.Google Scholar
  26. Long, J. B. (1987). Cognitive ergonomics and human-computer interaction. In P. Warr (Ed.), Psychology at work (Third ed. ed., pp. 73–95). Harmondsworth: Penguin.Google Scholar
  27. Monaghan, J. (2001). Teachers’ classroom interaction in ICT-based mathematics lessons. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th international conference for the psychology of mathematics education (pp. 3-383–3-390). Utrecht: Freudenthal institute.Google Scholar
  28. Monaghan, J. (2004). Teachers’ activities in technology-based mathematics lessons. International Journal of Computers for Mathematical Learning, 9, 327–357.CrossRefGoogle Scholar
  29. Monaghan, J. (2007). Computer algebra, instrumentation and the anthropological approach. The International Journal for Technology in Mathematics Education, 14, 63–71.Google Scholar
  30. Rabardel, P. (2002). People and technology, a cognitive approach to contemporary instruments. Retrieved August 20, 2010 from
  31. Trouche, L. (2003). From artifact to instrument: Mathematics teaching mediated by symbolic calculators. Interacting with Computers: The Interdisciplinary Journal of Human-Computer Interaction, 15, 783–800.Google Scholar
  32. 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, 281–307.CrossRefGoogle Scholar
  33. Trouche, L., & Drijvers, P. (2010). Handheld technology for mathematics education: Flashback into the future. ZDM: The International Journal on Mathematics Education, 42, 667–681.CrossRefGoogle Scholar
  34. Vérillon, P., & Rabardel, P. (1995). Cognition and artefact: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10, 77–101.CrossRefGoogle Scholar
  35. Villarreal, M. E., Esteley, C. B., & Mina, M. V. (2010). Modeling empowered by information and communication technologies. ZDM: The International Journal on Mathematics Education, 42, 405–419.CrossRefGoogle Scholar
  36. Wagner, J. (1997). The unavoidable intervention of educational research: A framework for reconsidering research-practitioner cooperation. Educational Researcher, 26, 13–22.Google Scholar
  37. Wells, G. (1999). Dialogic inquiry: Towards a sociocultural practice and theory of education. Cambridge, MA: Cambridge University Press.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.University of Agder (UiA)KristiansandNorway

Personalised recommendations