Advertisement

A Methodological Approach to Researching the Development of Teachers’ Knowledge in a Multi-Representational Technological Setting

  • Alison Clark-Wilson
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 2)

Abstract

This chapter details the methodological approach adopted within a doctoral study that sought to apply and expand Verillon and Rabardel’s (European Journal of Psychology of Education, 10, 77–102, 1995) triad of instrumented activity as a means to understand the longitudinal epistemological development of a group of secondary mathematics teachers as they began to integrate a complex new multi-representational technology (Clark-Wilson, How does a multi-representational mathematical ICT tool mediate teachers’ mathematical and pedagogical knowledge concerning variance and invariance? Ph.D. thesis, Institute of Education, University of London, 2010a). The research was carried out in two phases. The initial phase involved fifteen teachers who contributed a total of sixty-six technology-mediated classroom activities to the study. The second phase adopted a case study methodology during which the two selected teachers contributed a further fourteen activities. The chapter provides insight into the methodological tools and processes that were developed to support an objective, systematic and robust analysis of a complex set of qualitative classroom data. The subsequent analysis of this data, supported by questionnaires and interviews, led to a number of conclusions relating to the nature of the teachers’ individual technology-mediated learning.

Keywords

Hiccup Instrumented activity Instrument utilisation scheme Multi-representational technology Social utilisation scheme TI-Nspire Mathematical variance and invariance 

Notes

Acknowledgements

The data collection carried out during Phase One of the study (and part of the data collection in Phase Two) was funded by Texas Instruments within two evaluation research projects, which have been published in Clark-Wilson (2008a) and (2009).

References

  1. Ahmed, A., & Williams, H. (1997). Numeracy project: A catalyst for teacher development and teachers researching. Teacher Development, 1, 357–384.CrossRefGoogle Scholar
  2. Arzarello, F., & Robutti, O. (2010). Multimodality in multi-representational environments. ZDM – The International Journal on Mathematics Education, 42, 715–731.CrossRefGoogle Scholar
  3. Artigue, M. (2001). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. Computer Algebra in Mathematics Education Symposium. Netherlands: Utrecht UniversityGoogle Scholar
  4. Bednarz, N., Kieran, C., & Lee, L. (Eds.). (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht: Kluwer.Google Scholar
  5. Clark-Wilson, A. (2008a). Research Report. Evaluating TI-Nspire in secondary mathematics classrooms. Chichester: University of Chichester.Google Scholar
  6. Clark-Wilson, A. (2008b). Teachers researching their own practice: Evidencing student learning using TI-Nspire. Day conference of the British Society for the Learning of Mathematics, 28 (2). University of Southampton.Google Scholar
  7. Clark-Wilson, A. (2009). Research Report. Connecting mathematics in the connected classroom: TI-Nspire Navigator. Chichester: University of Chichester.Google Scholar
  8. Clark-Wilson, A. (2010). How does a multi-representational mathematical ICT tool mediate teachers’ mathematical and pedagogical knowledge concerning variance and invariance? Ph.D. thesis, Institute of Education, University of London.Google Scholar
  9. Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218.CrossRefGoogle Scholar
  10. Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3, 195–227.CrossRefGoogle Scholar
  11. Haspekian, M. (2005). Intégration d’outils informatiques dans l’enseignement des mathématiques, étude du cas des tableurs. Ph.D., Doctoral thesis, University Paris 7.Google Scholar
  12. Haspekian, M. (2006). Evolution des usages du tableur. Rapport intermédiaire de l’ACI-EF Genèses d’usages professionnels des technologies chez les enseignants [Online]. Available: http://gupten.free.fr/ftp/GUPTEn-RapportIntermediaire.pdf
  13. Jaworski, B. (1994). Investigating mathematics teaching. London: Falmer.Google Scholar
  14. Kaput, J. (1986). Information technology and mathematics: Opening new representational windows. Journal of Mathematical Behavior, 5, 187–207.Google Scholar
  15. Kaput, J. (1998). Transforming algebra from an engine of inequity to an engine of mathematical power by ‘algebrafying’ the K-12 curriculum. In National Council of Teachers of Mathematics & Mathematical Sciences Education Board (Eds.), Proceedings of a national symposium. Washington, DC: National Research Council, National Academy Press.Google Scholar
  16. Kieran, C., & Wagner, S. (Eds.). (1989). Research issues in the learning and teaching of Algebra. Reston: Lawrence Erlbaum/NCTM.Google Scholar
  17. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Cambridge University Press.CrossRefGoogle Scholar
  18. Mason, J. (2002). Researching your own practice: The discipline of noticing. London: Routledge-Falmer.Google Scholar
  19. Mason, J. (2010). Asking mathematical questions mathematically. International Journal of Mathematical Education in Science & Technology, 31, 97–111.CrossRefGoogle Scholar
  20. Moreno-Armella, L., Hegedus, S. J., & Kaput, J. J. (2008). From static to dynamic mathematics: Historical and representational perspectives. Educational Studies in Mathematics, 68, 99–111.CrossRefGoogle Scholar
  21. Pierce, R., & Stacey, K. (2008). Using pedagogical maps to show the opportunities afforded by CAS for improving the teaching of mathematics. Australian Senior Mathematics Journal, 22(1), 6–12.Google Scholar
  22. Polanyi, M. (1962). Personal knowledge: Towards a post-critical philosophy. Chicago: The University of Chicago Press.Google Scholar
  23. Polanyi, M. (1966). The tacit dimension. Chicago: The Universty of Chicago Press.Google Scholar
  24. QSR International. (2008). Nvivo8. Melbourne: QSR International.Google Scholar
  25. Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8, 255–281.CrossRefGoogle Scholar
  26. Ruthven, K. (2002). Instrumenting mathematical activity: Reflections on key studies of the educational use of computer algebra systems. International Journal of Computers for Mathematical Learning, 7, 275–291.Google Scholar
  27. Schön, D. (1984). The reflective practitioner: How professionals think in action. New York: Basic Books.Google Scholar
  28. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.CrossRefGoogle Scholar
  29. Stacey, K. (2008). Pedagogical maps for describing teaching with technology. Paper presented at Sharing Inspiration Conference, Berlin. 16–18 May 2008.Google Scholar
  30. Sutherland, R., & Mason, J. (1995). Exploiting mental imagery with computers in mathematics education. Berlin: Springer.CrossRefGoogle Scholar
  31. Thompson, A. (1992). Teachers’ beliefs and conceptions; a synthesis of the research. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. New York: Macmillan.Google Scholar
  32. Verillon, P., & Rabardel, P. (1995). Cognition and artefacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10, 77–102.CrossRefGoogle Scholar
  33. Zodik, I., & Zaslavsky, O. (2008). Characteristics of teachers’ choice of examples in and for the mathematics classroom. Educational Studies in Mathematics, 69, 165–182.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.London Knowledge Lab, Institute of EducationUniversity of LondonLondonUK

Personalised recommendations