# Teaching with Digital Technology: Obstacles and Opportunities

## Abstract

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.

## Keywords

Technology PTK Instrumental genesis TPACK## References

- 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 - 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 - 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 - 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 - 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
- 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 - Cuban, L. (2001).
*Oversold and underused: Computers in the classroom*. Cambridge, MA: Harvard University Press.Google Scholar - 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 - Forgasz, H. J. (2006b). Teachers, equity, and computers for secondary mathematics learning.
*Journal of Mathematics Teacher Education, 9*(5), 437–469.Google Scholar - 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 - 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.Google Scholar - 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 - 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 - 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 - 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 - Jamieson, S. (2004). Likert scales: How to (ab)use them.
*Medical Education, 38*, 1212–1218.CrossRefGoogle Scholar - 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 - 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 - 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 - 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 - 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 - Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge.
*Teachers College Record, 108*(6), 1017–1054.CrossRefGoogle Scholar - 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 - 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 - 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 - Rabardel, P. (1995).
*Les hommes et les technologies, approche cognitive des instruments contemporains*. Paris: Armand Colin.Google Scholar - 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 - 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 - 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 - Schoenfeld, A. H. (2011).
*How we think. A theory of goal-oriented decision making and its educational applications*. New York: Routledge.Google Scholar - Shulman, L. C. (1986). Those who understand: Knowledge growth in teaching.
*Educational Researcher, 15*, 4–41.CrossRefGoogle Scholar - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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. https://php.radford.edu/~ejmt/ContentIndex.php and http://www.radford.edu/ejmt - 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 - 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 - 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 - 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