Mathematics Education Research Journal

, Volume 22, Issue 2, pp 48–68 | Cite as

Cas-enabled technologies as ‘agents provocateurs’ in teaching and learning mathematical modelling in secondary school classrooms

  • Vince Geiger
  • Rhonda Faragher
  • Merrilyn Goos


This paper draws on a one year study of three secondary school classrooms to examine the nature of student-student-technology interaction when working in partnership with computer algebra systems (CAS) on mathematical modelling tasks and the classroom affordances and constraints that influence such interaction. The analysis of these data indicates that CAS enabled technologies have a role to play as provocateurs of productive student-student-teacher interaction in both small group and whole class settings. Our research indicates that technologies that incorporate CAS capabilities have the potential to mediate collaborative approaches to mathematical enquiry within life-related mathematical tasks.


Mathematics Education Focus Group Interview Mathematics Classroom Computer Algebra System Mathematic Education Research Journal 
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  1. Beatty, R., & Geiger, V. (2010). Technology, communication and collaboration: Rethinking communities of inquiry, learning and practice. In C. Hoyles, & J-B. Lagrange (Eds.),Digital technologies and mathematics teaching and learning: Rethinking the terrain (pp. 251–284). New York:Springer.Google Scholar
  2. Blum, W., Galbraith, P., Henn, H. & Niss, M. (Eds.) (2007).Modelling and applications in mathematics education: The 14th ICMI study. New York:Springer.Google Scholar
  3. Burns, R. (2000).Introduction to research methods (4th ed.). Melbourne:Longman.Google Scholar
  4. Burrill, G. (1992). The graphing calculator: A tool for change. In J. F. C. Hirsch (Ed.),Calculators in mathematics education (pp. 14–22). Reston, VA:NCTMGoogle Scholar
  5. Confrey, J., & Maloney, A. (2007). In W. Blum, P. Galbraith, H. Henn & M. Niss (Eds.),Modelling and applications in mathematics education: The 14th ICMI study (pp. 57–68). New York:Springer.CrossRefGoogle Scholar
  6. Diezmann, C., Faragher, R., Lowrie, T., Bicknell, B., & Putt, I. (2004). Exceptional students in mathematics. In B. Perry, G. Anthony & C. Diezmann (Eds.),Research in Mathematics Education in Australasia 2000 – 2003. Flaxton, QLD:Post Pressed.Google Scholar
  7. Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator.Educational Studies in Mathematics, 41(2), 143–163.CrossRefGoogle Scholar
  8. Drijvers, P. (2000).Learning algebra in a computer algebra environment. Utrecht, The Netherlands:CD-B Press.Google Scholar
  9. Galbraith, P., Renshaw, P., Goos, M., & Geiger, V. (1999). Technology, mathematics, and people: Interactions in a community of practice. In J. Truran & K. Truran (Eds.),Making the difference (Proceedings of 22nd annual conference of the Mathematics Education Research Group of Australasia, Adelaide, pp. 223–230). Sydney:MERGA.Google Scholar
  10. Galbraith, P., Renshaw, P., Goos, M., & Geiger, V. (2003). Technology-enriched classrooms: Some implications for teaching applications and modelling. In Q. Ye, W. Blum, S. K. Houston, & Q. Jiang (Eds.),Mathematical modelling in education and culture (pp. 111–125). Chichester, UK:Horwood.Google Scholar
  11. Geiger, V. (1998). Students’ perspectives on using computers and graphing calculators during mathematical collaborative practice. In C. Kanes, M. Goos & E. Warren (Eds.),Teaching mathematics in new times (Proceedings of the 21st annual conference of the Mathematics Education Research Group of Australasia, pp. 217–224). Gold Coast, QLD:MERGA.Google Scholar
  12. Geiger, V., & Goos, M. (1996). Number plugging or problem solving? Using technology to support collaborative learning. In P. Clarkson (Ed.),Technology in mathematics education (Proceedings of the 19th annual conference of the Mathematics Education Research Group of Australasia, pp. 229–236). Melbourne:MERGA.Google Scholar
  13. Geiger, V., Faragher, R., Redmond, T., & Lowe, J. (2008). CAS enabled devices as provocative agents in the process of mathematical modelling. In M. Goos, R. Brown & K Maker (Eds.),Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Brisbane, Vol. 1, pp. 246–253). Adelaide:MERGA.Google Scholar
  14. Goos, M., & Cretchley, P. (2004). Computers, multimedia, and the internet in mathematics education. In B. Perry, C. Diezmann & G. Anthony (Eds.),Research in mathematics education in Australasia 2000–2003 (pp. 151–174). Flaxton, QLD:Post Pressed.Google Scholar
  15. Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2000a).Classroom voices: Technology enriched interactions in a community of mathematical practice. Paper presented at the Working Group for Action 11 (The Use of Technology in Mathematics Education) at the 9th International Congress on Mathematical Education, Tokyo/Makuhari, 31 July – 6 August 2000.Google Scholar
  16. Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2000b). Reshaping teacher and student roles in technology-enriched classrooms.Mathematics Education Research Journal, 12(3), 303–320.CrossRefGoogle Scholar
  17. Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms.Journal of Mathematical Behavior, 22(1), 73–89.CrossRefGoogle Scholar
  18. Huntley, M. A., Rasmussen, C. L., Villarubi, R. S., Santong, J., & Fey, J. T. (2000). Effects of standards-based mathematics education: A study of the Core-Plus Mathematics Project algebra and function strand.Journal for Research in Mathematics Education, 31(3), 328–361.CrossRefGoogle Scholar
  19. Kissane, B. (1999). The algebraic calculator and mathematics education. In W.-C. Yang, D. Wang, S.-C. Chu, & G. Fitz-Gerald (Eds.),Proceedings of the 4th Asian Technology Conference on Mathematics (pp. 123–132). Guangzhou, China:Program Committee.Google Scholar
  20. Kissane, B. (2001). The algebra curriculum and personal technology: Exploring the links. In A. Rogerson (Ed.),Proceedings of the International Conference: New Ideas in Mathematics Education (pp. 127–132). Palm Cove, QLD:Program Committee.Google Scholar
  21. Lincoln, Y. S., & Guba, E. G. (1985).Naturalistic inquiry. Beverly Hills, CA:Sage.Google Scholar
  22. Manouchehri, A. (2004). Using interactive algebra software to support a discourse community.Journal of Mathematical Behavior, 23(1), 37–62.CrossRefGoogle Scholar
  23. Niss, M., Blum, W., & Galbraith, P. (2007). In W. Blum, P. Galbraith, H. Henn & M. Niss (Eds.),Modelling and applications in mathematics education: The 14th ICMI study (pp. 3–32). New York:Springer.CrossRefGoogle Scholar
  24. Pea, R. (1985). Beyond amplification: Using the computer to reorganize mental functioning.Educational Psychologist, 20(4), 167–182.CrossRefGoogle Scholar
  25. Pea, R. (1987). Cognitive technologies for mathematics education. In A. H. Schoenfeld (Ed.),Cognitive science and mathematics education (pp. 89–122). Hillsdale, NJ:Lawrence Erlbaum Associates.Google Scholar
  26. Ramsden, P. (1997, June).Mathematica in education: Old wine in new bottles or a whole new vineyard? Paper presented at the Second International Mathematica Symposium, Rovamiemi, Finland.Google Scholar
  27. Simonsen, L., & Dick, T. (1997). Teachers’ perceptions of the impact of graphing calculators in the mathematics classroom.Journal of Computers in Mathematics and Science Teaching, 16, 239–268.Google Scholar
  28. Stake, R. (2005). Qualitative case studies. In N. Denzin & Y. Lincoln (Eds.), The Sage handbook of qualitative research (3rd ed.). Thousand Oaks, CA:Sage.Google Scholar
  29. Thomas, M. O. J. (2001). Building a conceptual algebra curriculum: The role of technological tools. In H. Chick, K. Stacey J. Vincent, & J. Vincent (Eds.),The future of teaching and learning of algebra (Proceedings of the 12th ICMI Study Conference) (pp. 582–589). Melbourne, Australia:Department of Science and Mathematics Education, The University of Melbourne.Google Scholar
  30. Trouche, L. (2005). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven & L. Trouche (Eds.),The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument (pp. 197–230). New York:Springer.CrossRefGoogle Scholar
  31. Victorian Curriculum and Assessment Authority (2006).Mathematics Victorian Certificate of Education study design. Melbourne: VCAA. Retrieved 20 November 2008 from Scholar
  32. Willis, S., & Kissane, B. (1989). Computer technology and teacher education in mathematics. In Department of Employment, Education and Training (Ed.),Discipline review of teacher education in mathematics and science (Vol. 3, pp. 57–92). Canberra:Australian Government Publishing Service.Google Scholar
  33. Yerushalmy, M. (2000). Problem solving strategies and mathematics resources: A longitudinal view on problem solving in a functional based approach to algebra.Educational Studies in Mathematics, 43(2), 125–147.CrossRefGoogle Scholar
  34. Zbiek, R. M. (2003). Using research to influence teaching and learning with Computer Algebra Systems. In J. Fey, A. Cuoco, C. Kieran, L. McMullin, & R. M. Zbieck (Eds.),Computer Algebra Systems in secondary school mathematics education (pp. 197–216). Reston, VA:NCTM.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia Inc. 2010

Authors and Affiliations

  • Vince Geiger
    • 1
  • Rhonda Faragher
    • 2
  • Merrilyn Goos
    • 3
  1. 1.School of EducationAustralian Catholic UniversityBanyoAustralia
  2. 2.School of EducationAustralian Catholic UniversityCanberra
  3. 3.Teaching and Educational Development InstituteThe University of QueenslandSt Lucia

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