Teaching with Digital Technology: Obstacles and Opportunities

  • Michael O. J. ThomasEmail author
  • Joann M. Palmer
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 2)


A key variable in the use of digital technology in the mathematics classroom is the teacher. In this chapter we examine research that identifies some of the obstacles to, and constraints on, secondary teachers’ implementation of digital technology. While a lack of physical resources is still a major extrinsic concern we introduce a framework for, and highlight the crucial role of, the intrinsic factor of teachers’ Pedagogical Technology Knowledge (PTK). Results from a research study relating confidence in using technology to PTK are then presented. This concludes that confidence may be a critical variable in teacher construction of PTK, leading to suggestions for some ways in which professional development of teachers could be structured to strengthen confidence in technology use.


Technology PTK Instrumental genesis TPACK 


  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. doi: 10.1023/A:1022103903080.CrossRefGoogle Scholar
  2. Ball, D. L., Hill, H. C., & Bass, H. (2005). Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, Fall, 14–22–43–46.Google Scholar
  3. Becker, H. J. (2000a). Findings from the teaching, learning and computing survey: Is Larry Cuban right? Paper presented at the 2000 school technology leadership conference of the council of chief state officers, Washington, DC.Google Scholar
  4. Becker, H. J. (2000b). How exemplary computer-using teachers differ from other teachers: Implications for realizing the potential of computers in schools. Contemporary Issues in Technology and Teacher Education, 1(2), 274–293.Google Scholar
  5. Brousseau, G. (1997). Theory of didactical situations in mathematics: Didactique des mathematiques, 1970–1990. (trans & Eds: Balacheff, N., Cooper, M.,Sutherland,R., & Warfield, V.). Dordrecht: Kluwer Academic Publishers.Google Scholar
  6. Carifio, J., & Perla, R. J. (2007). Ten common misunderstandings, misconceptions, persistent myths and urban legends about Likert scales and Likert response formats and their antidotes. Journal of Social Sciences, 3(3), 106–116.CrossRefGoogle Scholar
  7. Cuban, L. (2001). Oversold and underused: Computers in the classroom. Cambridge, MA: Harvard University Press.Google Scholar
  8. Forgasz, H. (2006a). Factors that encourage and inhibit computer use for secondary mathematics teaching. Journal of Computers in Mathematics and Science Teaching, 25(1), 77–93.Google Scholar
  9. Forgasz, H. J. (2006b). Teachers, equity, and computers for secondary mathematics learning. Journal of Mathematics Teacher Education, 9(5), 437–469.CrossRefGoogle Scholar
  10. Gibson, J. J. (1977). The theory of affordances. In R. Shaw & J. Bransford (Eds.), Perceiving, acting and knowing: Towards an ecological psychology (pp. 67–82). Hillsdale: Erlbaum.Google Scholar
  11. Goos, M. (2005). A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology. Journal of Mathematics Teacher Education, 8, 35–59.CrossRefGoogle Scholar
  12. 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.Google Scholar
  13. Heid, M. K., Thomas, M. O. J., & Zbiek, R. M. (2013). How might computer algebra systems change the role of algebra in the school curriculum? In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 597–642). Dordrecht: Springer.Google Scholar
  14. Hill, H., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330–351. doi: 10.2307/30034819.CrossRefGoogle Scholar
  15. 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
  16. Jamieson, S. (2004). Likert scales: How to (ab)use them. Medical Education, 38, 1212–1218.CrossRefGoogle Scholar
  17. Jaworski, B. (2001). Developing mathematics teaching: Teachers, teacher-educators and researchers as co-learners. In F.-L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education. Dordrecht: Kluwer.Google Scholar
  18. Jaworski, B. (2003). Research practice into/influencing mathematics teaching and learning development: Towards a theoretical framework based on co-learning partnerships. Educational Studies in Mathematics, 54, 249–282.CrossRefGoogle Scholar
  19. Jaworski, B. (2006). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9, 187–211.CrossRefGoogle Scholar
  20. 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
  21. Lagrange, J.-B. (2003). Learning techniques and concepts using CAS: A practical and theoretical reflection. In J. T. Fey (Ed.), Computer algebra systems in secondary school mathematics education (pp. 269–283). Reston: National Council of Teachers of Mathematics.Google Scholar
  22. Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054.CrossRefGoogle Scholar
  23. Palmer, J. M. (2011). Examining relationship of teacher confidence to other attributes in mathematics teaching with graphics calculators. Unpublished M.Sc. Thesis, The University of Auckland.Google Scholar
  24. Paterson, J., Thomas, M. O. J., & Taylor, S. (2011). Decisions, decisions, decisions: What determines the path taken in lectures? International Journal of Mathematical Education in Science and Technology, 42(7), 985–996.CrossRefGoogle Scholar
  25. Pierce, R., Stacey, K., & Wander, R. (2010). Examining the didactic contract when handheld technology is permitted in the mathematics classroom. ZDM International Journal of Mathematics Education, 42, 683–695. doi: 10.1007/s11858-010-0271-8.CrossRefGoogle Scholar
  26. Rabardel, P. (1995). Les hommes et les technologies, approche cognitive des instruments contemporains. Paris: Armand Colin.Google Scholar
  27. Ruthven, K., & Hennessy, S. (2002). A practitioner model of the use of computer-based tools and resources to support mathematics learning and teaching. Educational Studies in Mathematics, 49, 47–88.CrossRefGoogle Scholar
  28. Schoenfeld, A. H. (2002). A highly interactive discourse structure. In J. Brophy (Ed.), Social constructivist teaching: Its affordances and constraints (Volume 9 of the series advances in research on teaching, pp. 131–169). Amsterdam: JAI Press.CrossRefGoogle Scholar
  29. Schoenfeld, A. H. (2008). On modeling teachers’ in-the-moment decision-making. In A. H. Schoenfeld (Ed.), A study of teaching: Multiple lenses, multiple views (Journal for Research in Mathematics Education Monograph No. 14, pp. 45–96). Reston: National Council of Teachers of Mathematics.Google Scholar
  30. Schoenfeld, A. H. (2011). How we think. A theory of goal-oriented decision making and its educational applications. New York: Routledge.Google Scholar
  31. Shulman, L. C. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–41.CrossRefGoogle Scholar
  32. Stewart, S., Thomas, M. O. J., & Hannah, J. (2005). Towards student instrumentation of computer-based algebra systems in university courses. International Journal of Mathematical Education in Science and Technology, 36(7), 741–750. doi: 10.1080/00207390500271651.CrossRefGoogle Scholar
  33. Thomas, M. O. J. (1996). Computers in the mathematics classroom: A survey. In P. C. Clarkson (Ed.), Technology in mathematics education (Proceedings of the 19th mathematics education research group of Australasia conference, pp. 556–563). Melbourne: MERGA.Google Scholar
  34. Thomas, M. O. J. (2006). Teachers using computers in the mathematics classroom: A longitudinal study. Proceedings of the 30th conference of the international group for the psychology of mathematics education, Prague, 5, 265–272.Google Scholar
  35. Thomas, M. O. J., & Chinnappan, M. (2008). Teaching and learning with technology: Realising the potential. In H. Forgasz, A. Barkatsas, A. Bishop, B. Clarke, S. Keast, W.-T. Seah, P. Sullivan, & S. Willis (Eds.), Research in mathematics education in Australasia 2004–2007 (pp. 167–194). Sydney: Sense Publishers.Google Scholar
  36. Thomas, M. O. J., & Hong, Y. Y. (2004). Integrating CAS calculators into mathematics learning: Issues of partnership. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th annual conference for the Psychology of Mathematics Education (Vol. 4, pp. 297–304). Bergen, Norway: Bergen University College.Google Scholar
  37. Thomas, M. O. J., & Hong, Y. Y. (2005). Learning mathematics with CAS calculators: Integration and partnership issues. The Journal of Educational Research in Mathematics, 15(2), 215–232.Google Scholar
  38. Thomas, M. O. J., & Hong, Y. Y. (2005b). Teacher factors in integration of graphic calculators into mathematics learning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 257–264). Melbourne: University of Melbourne.Google Scholar
  39. Thomas, M. O. J., Hong, Y. Y., Bosley, J., & delos Santos, A. (2008). Use of calculators in the mathematics classroom. The Electronic Journal of Mathematics and Technology (eJMT), [On-line Serial] 2(2). Available at. and
  40. Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.Google Scholar
  41. Zbiek, R. M., & Heid, M. K. (2011). Using technology to make sense of symbols and graphs and to reason about general cases. In T. Dick & K. Hollebrands (Eds.), Focus on reasoning and sense making: Technology to support reasoning and sense making (pp. 19–31). Reston: National Council of Teachers of Mathematics.Google Scholar
  42. Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A perspective of constructs. In F. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169–1207). Charlotte, NC: Information Age Publishing.Google Scholar
  43. Zbiek, R. M., & Hollebrands, K. (2008). A research-informed view of the process of incorporating mathematics technology into classroom practice by inservice and prospective teachers. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Volume 1 (pp. 287–344). Charlotte: Information Age.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.The University of AucklandAucklandNew Zealand

Personalised recommendations