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Technology, Knowledge and Learning

, Volume 16, Issue 3, pp 247–265 | Cite as

A Mathematics Teacher’s Practice in a Technological Environment: A Case Study Analysis Using Two Complementary Theories

  • Michal Tabach
Article
  • 638 Downloads

Integrating technology in school mathematics has become more and more common. The teacher is a key person in integrating technology into everyday practice. To understand teacher practice in a technological environment, this study proposes using two theoretical perspectives: the theory of technological pedagogical content knowledge to analyze teachers’ knowledge, and instrumental orchestration to analyze teachers’ actions. Applying this dual perspective to one teacher’s practice can shed light on the complexities faced by a teacher who integrates technology in her practice.

Keywords

Technological pedagogical content knowledge Instrumental orchestration Mathematics teacher 

References

  1. 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, 245–274.CrossRefGoogle Scholar
  2. Artigue, M., Cerulli, M., Haspekian, M., & Maracci, M. (2009). Connecting and integrating theoretical frames: The TELMA contribution. International Journal of Computers for Mathematical Learning, 14(3), 217–240.CrossRefGoogle Scholar
  3. Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport, CT: Ablex.Google Scholar
  4. Ben-Zvi, D. (1999). Constructing an understanding of data graphs. In O. Zaslavaky (Ed.), Proceedings of the 23rd annual conference of the international group for the psychology of mathematics education, (Vol. 2, pp. 97–104). Haifa, Israel: Technion.Google Scholar
  5. Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics, 45(1–3), 35–65.CrossRefGoogle Scholar
  6. Brown, M. C., I. I., & Cato, B. (2008). Preface. In AACTE Committee on Innovation, Technology (Ed.), Handbook of technological pedagogical content knowledge (TPCK) for educators (pp. vii–x). NY, USA: Routledge.Google Scholar
  7. Bruce, B. C., & Hogan, M. C. (1998). The disappearance of technology: Toward an ecological model of literacy. In D. Reinking, M. McKenna, L. Labbo, & R. Kieffer (Eds.), Handbook of literacy and technology: Transforming in a post-typographic word (pp. 269–281). Hillsdale, NJ: Erlbaum.Google Scholar
  8. Drijvers, P. (2011). Teachers transforming resources into orchestrations. Paper presented at the CERME 7Seventh conference of European research in mathematics education.Google Scholar
  9. 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
  10. Ely, D. P. (1996). Trends in educational technology 1995. Eric Digest [Online]. Available: http://ericir.syr.edu/ithome/digests/trendsdig.html.
  11. German, T., & Barrett, C. (2005). Functional fixedness in a technologically sparse culture. Psychological Science, 16(1), 1–5.CrossRefGoogle Scholar
  12. Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.Google Scholar
  13. Graeber, A., & Tirosh, D. (2008). Pedagogical content knowledge: A useful or an elusive notion? In P. Sullivan (Ed.), Knowledge and beliefs in mathematics teaching and teaching development (pp. 117–132). Amsterdam, The Netherlands: Sense.Google Scholar
  14. Guin, D., Ruthven, K., & Trouche, L. (Eds.). (2005). The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument. New York: Springer.Google Scholar
  15. Hoyles, C., Noss, R., & Kent, P. (2004). On the integration of digital technologies into mathematics classrooms. International Journal of Computers for Mathematical Learning, 9(3), 309–326.CrossRefGoogle Scholar
  16. Koehler, M. J., & Mishra, P. (2008). Introducing TPCK. In AACTE Committee on Innovation, Technology (Ed.), Handbook of technological pedagogical content knowledge (TPCK) for educators (pp. 3–30). NY, USA: Routledge.Google Scholar
  17. Laborde, C. (2003). Technology used as a tool for mediating knowledge in the teaching of mathematics: The case of Cabri-geometry. In W. -C. Yang, S. C. Chu, T. de Alwis, & M. G. Lee (Eds.), Proceedings of the 8th Asian technology conference in mathematics (Vol. 1, pp. 23–38) Hsinchu Taiwan ROC: Chung Hua University.Google Scholar
  18. Lagrange, J. B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: Multidimensional overview of recent research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (Vol. 1, pp. 237–270). Dordrecht: Kluwer.CrossRefGoogle Scholar
  19. Lagrange, J. B., & Monaghan, J. (2009). On the adoption of a model to interpret teachers’ use of technology in mathematics lessens. In V. Durand- Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the sixth congress of the European society for research in mathematics education (pp. 1605–1614). Lyon: INRP. Retrieved on 4 April 2011, from http://www.inrp.fr/editions/editions-electroniques/cerme6/working-group-9.
  20. Mariotti, M. A. (2002). Influence of technologies advances in students’ math learning. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 757–786). Mahwah: Erlbaum.Google Scholar
  21. Mioduser, D. (1998). Framework for the study of the cognitive nature and architecture of technological problem solving. Journal of Technology Education and Design, 8(2), 167–184.CrossRefGoogle Scholar
  22. Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for integrating technology in teacher knowledge. Teacher College Records, 108(6), 1017–1054.CrossRefGoogle Scholar
  23. Norman, D. A. (1988). The psychology of everyday things. New York: Basic Books.Google Scholar
  24. Pierce, R., & Ball, L. (2009). Perceptions that may affect teachers’ intention to use technology in secondary mathematics classes. Educational Studies in Mathematics, 71(3), 299–317.CrossRefGoogle Scholar
  25. Prediger, S., Arzarello, F., Bosch, M., & Lenfant, A. (Eds.) (2008). Comparing, combining, coordinating—networking strategies for connecting theoretical approaches. Thematic Issue of ZDM, The International Journal on Mathematics Education, 40(2), 163–327.Google Scholar
  26. Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008b). Networking strategies and methods for connecting theoretical approaches: First steps towards a conceptual framework. ZDM The International Journal on Mathematics Education, 40(2), 165–178.CrossRefGoogle Scholar
  27. Robert, A., & Rogalski, J. (2005). A cross-analysis of the mathematics teacher’s activity. An example in a French 10th-grade class. Educational Studies in Mathematics, 59(1–3), 269–298.CrossRefGoogle Scholar
  28. Shulman, L. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.Google Scholar
  29. Tabach, M., Hershkowitz, R., Arcavi, A., & Dreyfus, T. (2008). Computerized environments in mathematics classrooms: A research—design view. In L. D. English, M. B. Bussi, G. A. Jones, R. A. Lesh, B. Sriraman, & D. Tirosh (Eds.), Handbook for international research in mathematics education (2nd ed., pp. 784–805). NY, USA: Routledge.Google Scholar
  30. 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(3), 281–307.CrossRefGoogle Scholar
  31. Trouche, L., & Drijvers, P. (2002). Handheld technology for mathematics education: Flashback into the future. ZDM The International Journal on Mathematics Education, 42(7), 667–681.CrossRefGoogle Scholar
  32. Vérillon, P., & Rabardel, P. (1995). Cognition and artifact: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology in Education, 9(3), 1–33.Google Scholar
  33. Yerushalmy, M. (2005). Challenging known transitions: Learning and teaching algebra with technology. For the Learning of Mathematics, 25(3), 37–42.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Tel-Aviv UniversityTel AvivIsrael

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