Skip to main content
Log in

Examining the didactic contract when handheld technology is permitted in the mathematics classroom

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

The use of mathematics analysis software (MAS) including handheld scientific and graphics calculators offers a range of pedagogical opportunities. Its use can support change in the didactic contract. MAS may become an alternative source of authority in the classroom empowering students to explore variation and regularity, manipulate simulations and link representations. Strategic use may support students to direct their own learning and explore mathematics, equipping them to share their findings with the teacher and the class with more confidence. This paper offers a framework for examining the impact of the use of MAS on the didactic contract. Lessons were observed in 12 grade 10 classes, with 12 different teachers new to MAS. MAS technology was used with a variety of didactic contracts, mostly traditional. The framework drew attention to many ways in which the teaching differed. Analysis of the didactic contract must consider both the teaching of mathematics and of technology skills, because these have different characteristics. In all classes, both teachers and students saw the teacher as having a responsibility to teach technology skills. Students saw technology skills as the main point of the lesson, but the teachers saw the lesson as primarily teaching mathematics—one of the mismatches which may need negotiation to adapt didactic contracts to teaching with MAS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Aldon, G. (Ed.). (2009). La fonction de l’enseigne. Mathématiques dynamiques (pp. 46–68). Paris, France: Hachette Livre.

    Google Scholar 

  • Artigue, M. (2001). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. Paper presented at CAME 2001 symposium on communicating mathematics through computer algebra systems. Utrecht, The Netherlands. http://Itsn.mathstore.ac.uk/came/events/freudenthal, Accessed 13 March 2008.

  • Ball, L., & Stacey, K. (2003). What should students record when solving problems with CAS? Reasons, information, the plan and some answers. In J. T. Fey, A. Cuoco, C. Kieran, L. Mullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 289–303). Reston, VA: The National Council of Teachers of Mathematics.

    Google Scholar 

  • Ball, L., & Stacey, K. (2006). Coming to appreciate the pedagogical uses of CAS. In Proceedings of the 30th conference of the international group for psychology in mathematics education (Vol. 2, pp. 105–112). Prague: PME.

  • Bennett, S., Maton, K., & Kervin, L. (2008). The ‘digital natives’ debate: A critical review of the evidence. British Journal of Educational Technology, 39(5), 775–786.

    Article  Google Scholar 

  • Berry, J. (1999). CAS as a mentor for the apprentice mathematician. Computer Algebra in Mathematics Education. Weizmann Institiute Israel. http://www.lkl.ac.uk/research/came/events/weizmann/CAME-Keynotes.pdf.

  • Brousseau, G. (1997). In N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds. & Trans.), Theory of didactical situations in mathematics : didactique des mathématiques (pp. 1970–1990). Dordrecht: Kluwer Academic Publishers.

  • Drijvers, P. (2005). Learning algebra in a computer algebra environment. International Journal for Technology in Mathematics Education, 11(3), 77–89.

    Google Scholar 

  • Drouhard, J.-P. (1997). Communication in the classroom with a CAS: The double didactic pyramid. In J. Berry, J. Monaghan, M. Kronfeller, & B. Kutzler (Eds.), The state of computer algebra in mathematics education (pp. 165–170). Lund, Sweden: Chartwell-Bratt.

    Google Scholar 

  • Etlinger, L. (1974). The electronic calculator: A new trend in school mathematics. Educational Technology, XIV(12), 43–45.

    Google Scholar 

  • Geiger, V. (2009). The master, servant, partner, extension-of-self framework in individual, small group and whole class contexts. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides. Proceedings of the 32nd conference of the mathematics education research group of australasia (pp. 201–208). Palmerston North, NZ: MERGA.

  • Guin, D & Trouche, L. (2002). Mastery by the teacher of the instrumental genesis in CAS environments: Necessity of instrumental orchestrations. In E. Schneider (Ed.), Zentralblatt für Didaktik der Mathematic, 34(5), 204-211.

  • Heid, M. K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19(1), 3–25.

    Article  Google Scholar 

  • Hersant, M., & Perrin-Glorian, M.-J. (2005). Characterization of an ordinary teaching practice with the help of the theory of didactic situations. Educational Studies in Mathematics, 59, 113–151.

    Article  Google Scholar 

  • Hoyles, C., Noss, R., & Kent, P. (2004). On the integration of digital technologies into mathematical classrooms. International Journal of Computers for Mathematical Learning, 9, 309–326.

    Article  Google Scholar 

  • Isoda, M., Stephens, M., Ohara, Y., & Miyakawa, T. (Eds.). (2007). Japanese lesson study in mathematics. Its impact, diversity and potential for educational improvements. Hackensack, NJ: World Scientific.

    Google Scholar 

  • Kieran, C., & Damboise, C. (2007). “How can we describe the relation between the factored form and the expanded form of these trinomials? We don’t even know if our paper and pencil factorizations are right”: The case for computer algebra systems (CAS) with weaker algebra students. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st conference of the international group for the psychology of mathematics education (Vol. 3, pp. 105–112). Seoul: PME.

  • Laborde, C., & Perrin-Glorian, M.-J. (2005). Teaching situations as object of research: Empirical studies within theoretical perspectives. Educational Studies in Mathematics, 59, 1–12.

    Article  Google Scholar 

  • Monaghan, J. (2004). Teachers’ activities in technology-based mathematics lessons. International Journal of Computers for Mathematical Learning, 9, 327–357.

    Article  Google Scholar 

  • Norton, S., McRobbie, C., & Cooper, T. (2000). Exploring secondary mathematics teachers reasons for not using computers in their teaching: Five case studies. Journal of Research on Computing in Education, 33(1), 87–109.

    Google Scholar 

  • Pierce, R., & Stacey, K. (2001a). Observations on students’ responses to learning in a CAS environment. Mathematical Education Research Journal, 3(1), 28–46.

    Google Scholar 

  • Pierce, R., & Stacey, K. (2001b). Reflections on the changing pedagogical use of computer algebra systems: Assistance for doing or learning mathematics. Journal of Computers in Mathematics and Science Teaching, 20(1), 141–163.

    Google Scholar 

  • Pierce, R., & Stacey, K. (2004). A framework for monitoring progress and planning teaching towards effective use of computer algebra systems. International Journal of Computers for Mathematical Learning, 9(1), 59–93.

    Article  Google Scholar 

  • Pierce, R., & Stacey, K. (2010). Mapping pedagogical opportunities provided by mathematics analysis software. International Journal of Computers for Mathematical Learning. doi:10.1007/s10758-010-9158-6.

  • Prenksy, M. (2001). Digital natives, digital immigrants. On the Horizon, 9(5), 1–6.

    Article  Google Scholar 

  • Ruthven, K., & Hennesey, 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.

    Article  Google Scholar 

  • Stacey, K. (1997). Mathematics–What should we tell the children? The International Journal of Computer Algebra in Mathematics Education, 4(4), 387–390.

    Google Scholar 

  • Stacey, P., & Stacey, K. (1983). Upper school mathematics in the 21st century. In D. Blane (Ed.), The essentials of mathematics education (pp. 384–388). Melbourne, Australia: Mathematical Association of Victoria.

    Google Scholar 

  • Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9, 281–307.

    Article  Google Scholar 

  • Trouche, L. (2005). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators (pp. 197–230). New York: Springer.

    Chapter  Google Scholar 

  • Vincent, J. (2003). Year 8 students’ reasoning in a Cabri environment. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics education researching: Innovation, networking, opportunity. Proceedings of the 26th annual conference of the Mathematics Education Research Group of Australasia (pp. 696–703). Sydney: MERGA.

  • Wander, R., & Pierce, R. (2009). Marina’s fish shop: A mathematically- and technologically-rich lesson. Australian Mathematics Teacher, 65(2), 6–12.

    Google Scholar 

  • Warfield, V. (2006). Invitation to didactique. http://www.math.washington.edu/~warfield/Didactique.html, Accessed 15 September 2009.

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 22, 390–408.

    Article  Google Scholar 

Download references

Acknowledgments

We wish to thank the project teachers and their students for their participation and feedback. We also thank Lynda Ball and to other visiting researchers who have joined in on classroom observation. We acknowledge the financial support of Texas Instruments and helpful comments from the anonymous reviewers.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Robyn Pierce.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pierce, R., Stacey, K. & Wander, R. Examining the didactic contract when handheld technology is permitted in the mathematics classroom. ZDM Mathematics Education 42, 683–695 (2010). https://doi.org/10.1007/s11858-010-0271-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-010-0271-8

Keywords

Navigation