Educational Studies in Mathematics

, Volume 71, Issue 3, pp 279–297 | Cite as

Using graphing software to teach about algebraic forms: a study of technology-supported practice in secondary-school mathematics



From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater depth through case study of two teachers each teaching two lessons of this type. The practitioner model developed in earlier research (Ruthven & Hennessy, Educational Studies in Mathematics 49(1):47–88, 2002; Micromath 19(2):20–24, 2003) provided a framework for synthesising teacher thinking about the contribution of graphing software. Further analysis highlighted the crucial part played by teacher prestructuring and shaping of technology-and-task-mediated student activity in realising the ideals of the practitioner model. Although teachers consider graphing software very accessible, successful classroom use still depends on their inducting students into using it for mathematical purposes, providing suitably prestructured lesson tasks, prompting strategic use of the software by students and supporting mathematical interpretation of the results. Accordingly, this study has illustrated how, in the course of appropriating the technology, teachers adapt their classroom practice and develop their craft knowledge: particularly by establishing a coherent resource system that effectively incorporates the software; by adapting activity formats to exploit new interactive possibilities; by extending curriculum scripts to provide for proactive structuring and responsive shaping of activity; and by reworking lesson agendas to take advantage of the new time economy.


Classroom teaching practice Computer graphing software Secondary-school mathematics Teacher knowledge and thinking Technology use and integration 



Particular thanks are due to the teacher colleagues featured in the case studies; to Theresa Daly our project secretary; and to the UK Economic and Social Research Council which funded the Eliciting Situated Expertise in ICT-integrated Mathematics and Science Teaching project (R000239823). An earlier report of this study was presented at the November 2008 day-conference of the British Society for Research in Learning Mathematics: we are grateful to the BSRLM audience as well as to the ESM editor and reviewers for their helpful comments and suggestions.


  1. Amarel, M. (1983). Classrooms and computers as instructional settings. Theory into Practice, 22, 260–266.CrossRefGoogle Scholar
  2. 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(3), 245–274. doi: 10.1023/A:1022103903080.CrossRefGoogle Scholar
  3. Assude, T. (2005). Time management in the work economy of a class. A case study: integration of Cabri in primary school mathematics teaching. Educational Studies in Mathematics, 59(1–3), 183–203. doi: 10.1007/s10649-005-5888-0.CrossRefGoogle Scholar
  4. Brown, S., & McIntyre, D. (1993). Making sense of teaching. Buckingham: Open University Press.Google Scholar
  5. Burns, R. B., & Anderson, L. W. (1987). The activity structure of lesson segments. Curriculum Inquiry, 17(1), 31–53. doi: 10.2307/1179376.CrossRefGoogle Scholar
  6. Burns, R. B., & Lash, A. A. (1986). A comparison of activity structures during basic skills and problem-solving instruction in seventh-grade mathematics. American Educational Research Journal, 23(3), 393–414.Google Scholar
  7. Caliskan-Dedeoglu, N. (2006). Usages de la géométrie dynamique par des enseignants de collège. Des potentialités à la mise en oeuvre: quelles motivations, quelles pratiques. Unpublished doctoral thesis, University of Paris 7.Google Scholar
  8. Department for Education and Employment [DfEE] (2001). Key stage 3 national strategy: framework for teaching mathematics. London: DfEE.Google Scholar
  9. Department for Education and Skills [DfES] (2003). Integrating ICT into mathematics at key stage 3. London: DfES.Google Scholar
  10. Doerr, H., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41(2), 143–163. doi: 10.1023/A:1003905929557.CrossRefGoogle Scholar
  11. Farrell, A. M. (1996). Roles and behaviors in technology-integrated precalculus classrooms. The Journal of Mathematical Behavior, 15(1), 33–53. doi: 10.1016/S0732-3123(96)90038-3.CrossRefGoogle Scholar
  12. Fey, J. (1989). Technology and mathematics education: a survey of recent developments and important problems. Educational Studies in Mathematics, 20(3), 237–272. doi: 10.1007/BF00310873.CrossRefGoogle Scholar
  13. Godwin, S., & Sutherland, R. (2004). Whole-class technology for learning mathematics: the case of functions and graphs. Education Communication and Information, 4(1), 131–152. doi: 10.1080/1463631042000210953.CrossRefGoogle 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. Jenson, J., & Rose, C. B. (2006). Finding space for technology: pedagogical observations on the organization of computers in school environments. Canadian Journal of Learning and Technology, 32(1). Accessed at
  16. Lagrange, J.-B., & Caliskan-Dedeoglu, N. (2009). Usages de la technologie dans des conditions ordinaires: le cas de la géométrie dynamique au collège: Potentialités, attentes, pratiques. Recherches en Didactique des Mathématiques, in press.Google Scholar
  17. Leinhardt, G. (1988). Situated knowledge and expertise in teaching. In J. Calderhead (Ed.), Teachers’ professional learning (pp. 146–168). London: Falmer.Google Scholar
  18. Leinhardt, G., Putnam, T., Stein, M. K., & Baxter, J. (1991). Where subject knowledge matters. Advances in Research in Teaching, 2, 87–113.Google Scholar
  19. Leinhardt, G., Weidman, C., & Hammond, K. M. (1987). Introduction and integration of classroom routines by expert teachers. Curriculum Inquiry, 17(2), 135–176. doi: 10.2307/1179622.CrossRefGoogle Scholar
  20. Monaghan, J. (2004). Teachers’ activities in technology-based mathematics lessons. International Journal of Computers for Mathematical Learning, 9(3), 327–357. doi: 10.1007/s10758-004-3467-6.CrossRefGoogle Scholar
  21. Office for Standards in Education [OfStEd] (2004). ICT in schools—the impact of government initiatives: secondary mathematics. London: OfStEd.Google Scholar
  22. 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(3), 275–291. doi: 10.1023/A:1022108003988.CrossRefGoogle Scholar
  23. Ruthven, K. (2007). Teachers, technologies and the structures of schooling. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, pp. 52–67.Google Scholar
  24. Ruthven, K. (2008). Towards a naturalistic conceptualisation of technology integration in classroom practice: the example of school mathematics. Education & Didactique.
  25. Ruthven, K., & Hennessy, S. (2002). A practitioner model of the use of computer-based tools and resources to support mathematics teaching and learning. Educational Studies in Mathematics, 49(1), 47–88. doi: 10.1023/A:1016052130572.CrossRefGoogle Scholar
  26. Ruthven, K., & Hennessy, S. (2003). Successful ICT use in secondary mathematics—a teacher perspective. Micromath, 19(2), 20–24.Google Scholar
  27. Ruthven, K., Hennessy, S., & Brindley, S. (2004). Teacher representations of the successful use of computer-based tools and resources in secondary-school English, Mathematics and Science. Teaching and Teacher Education, 20(3), 259–275. doi: 10.1016/j.tate.2004.02.002.CrossRefGoogle Scholar
  28. Ruthven, K., Hennessy, S., & Deaney, R. (2005). Incorporating dynamic geometry systems into secondary mathematics education: didactical perspectives and practices of teachers. In D. Wright (Ed.), Moving on with dynamic geometry (pp. 138–158). Association of Teachers of Mathematics: Derby.Google Scholar
  29. Ruthven, K., Hennessy, S., & Deaney, R. (2008). Constructions of dynamic geometry: a study of the interpretative flexibility of educational software in classroom practice. Computers & Education, 51(1), 297–317. doi: 10.1016/j.compedu.2007.05.013.CrossRefGoogle Scholar
  30. Simmt, E. (1997). Graphing calculators in high school mathematics. Journal of Computers in Mathematics and Science Teaching, 16(2/3), 269–289.Google Scholar
  31. Strauss, A., & Corbin, J. (1994). Grounded theory methodology: an overview. In N. K. Denzin, & Y. S. Lincoln (Eds.), Handbook of qualitative research. London: Sage.Google Scholar
  32. Wilson, S. M., Shulman, L. S., & Richert, A. E. (1987). ‘150 different ways’ of knowing: representations of knowledge in teaching. In J. Calderhead (Ed.),Exploring teachers’ thinking (pp. 104–124). London: Cassell.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Kenneth Ruthven
    • 1
  • Rosemary Deaney
    • 1
  • Sara Hennessy
    • 1
  1. 1.Faculty of EducationUniversity of CambridgeCambridgeUK

Personalised recommendations