Ways of acting when using technology in the primary school classroom: contingencies and possibilities for learning

Abstract

Digital technologies shape the processes of teaching and learning in the classroom. They create spaces for action, while at the same time they pose restrictions and can generate unexpected situations, both for teachers and students. In this paper, we show examples in which teachers respond to contingencies emerging from the use of interactive programs in the classrooms. By describing different ways in which teachers react to those contingencies, we show how the technology plays an important role, at times by creating unexpected situations, and at others in support of teachers’ explanations. In both cases it can promote modifications in students’ actions and shape teachers’ actions and responses in relation to a particular mathematical situation or problem. Understanding how teachers react when they are faced with an unexpected situation is important in order to gain knowledge about those particular responses that result in effective behaviors that are related to mathematics learning, and also in terms of the construction of rich learning environments that promote those kinds of behaviors. Results show that the kind of interaction that technology has the potential for promoting plays an important role in making students and teachers more aware of students’ doubts and misunderstandings, but that this potential needs to be accompanied by effective teachers’ strategies through which they use contingencies as opportunities to promote both their own and their students’ learning. This study contributes to deepening knowledge about teachers’ effective strategies in primary school classrooms as well as providing examples to promote reflection regarding teachers’ training programs.

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

Fig. 1
Fig. 2
Fig. 3

References

  1. Arafeh, S., Smerdon, B., & Snow, S. (2001). Learning from teachable moments: Methodological lessons from the secondary analysis of the TIMSS Video Study. In Annual meeting of the American Educational Research Association (pp. 1–10). Seattle, WA.

  2. Brown, L., Helliwell, T., & Coles, A. (2018). Working as mathematics teacher educators at the meta-level (to the focus of the teachers on developing their teaching). Avances de Investigación en Educación Matemática,13, 105–122.

    Article  Google Scholar 

  3. Clark-Wilson, A. (2014). A methodological approach to researching the development of teachers’ knowledge in a multi-representational technological setting. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: An international perspective on technology focused professional development (Vol. 2, pp. 277–297). Dordrecht: Springer.

    Google Scholar 

  4. Davis, B. (1996). Teaching mathematics: Toward a sound alternative. New York: Garland Publishing.

    Google Scholar 

  5. Davis, B., Sumara, D., & Luce-Kapler, R. (2000). Engaging minds: Learning and teaching in a complex world. London: Lawrence Erlbaum.

    Google Scholar 

  6. Drijvers, P., Kieran, C., & Mariotti, M. A. (2010). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology—rethinking the terrain (pp. 89–132). New York: Springer.

    Google Scholar 

  7. Foster, C. (2015). Exploiting unexpected situations in the mathematics classroom. International Journal of Science and Mathematics Education,13, 1065–1088.

    Article  Google Scholar 

  8. Lagrange, J, B., & Monahan J. (2009). On the adoption of a model to interpret teachers’ use of technology in mathematics lessons. In Proceedings of CERME 6 Lyon France © INRP 2010 (pp. 1605–1513). www.inrp.fr/editions/cerme6.

  9. Lozano, M. D. (2004). Characterising algebraic learning: an enactivist longitudinal study. Unpublished doctoral dissertation, University of Bristol.

  10. Lozano, M. D. (2015). Using enactivism as a methodology to characterise algebraic learning. ZDM Mathematics Education,47(2), 223–234.

    Article  Google Scholar 

  11. Lozano, M. D., & Trigueros, M. (2007). Mathematics learning with the use of the balance, a computer programme from Enciclomedia. In Proceedings of CERME 5, WG 9 Tools and technologies in mathematical didactics (pp. 1449–1459).

  12. Makar, K., Bakker, A., & Ben-Zvi, D. (2015). Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom. ZDM Mathematics Education,47, 1107–1120.

    Article  Google Scholar 

  13. Mason, J. (2002). Researching your own practice: The discipline of noticing. London: Routledge Falmer.

    Google Scholar 

  14. Maturana, H., & Varela, F. (1992). The tree of knowledge: The biological roots of human understanding (Revised ed.). Boston: Shambhala.

    Google Scholar 

  15. Rabardel, P. (1999). Eléments pour une approche instrumentale en didactique des mathématiques. In Actes de l'école d'été de didactique des mathématiques, Houlgate, 18–21 Août, IUFM de Caen (pp. 203–213).

  16. Reid, D. (1996). Enactivism as a methodology. In L. Puig & A. Gutierrez (Eds.), Proceedings 20th conf. of the international group for the psychology of mathematics education (Vol. 4, pp. 203–209). Valencia; PME.

  17. Roll, I., Holmes, N. G., Day, J., & Bonn, D. (2012). Evaluating metacognitive scaffolding in guided invention activities. Instructional Science,40(4), 691–710.

    Article  Google Scholar 

  18. Rowland, T., & Zazkis, R. (2013). Contingency in the mathematics classroom: Opportunities taken and opportunities missed. Canadian Journal of Science Mathematics and Technology Education,13, 137–153.

    Article  Google Scholar 

  19. Rowland, T., Thwaites, A., & Jared, L. (2015). Triggers of contingency in mathematics teaching. Research in Mathematics Education, 17(2), 74–91. https://doi.org/10.1080/14794802.2015.1018931.

    Article  Google Scholar 

  20. Simmt, E., & Kieren, T. (2015). Three “Moves” in enactivist research: a reflection. ZDM Mathematics Education, 47(2), 307-317.

    Article  Google Scholar 

  21. Sinclair, N., Bussi, M. G. B., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., et al. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM Mathematics Education,48(5), 691–719.

    Article  Google Scholar 

  22. Smit, J., & Van Eerde, H. A. (2011). A teacher’s learning process in dual design research: Learning to scaffold language in a multilingual mathematics classroom. ZDM—The International Journal on Mathematics Education,43(6–7), 889–900.

    Article  Google Scholar 

  23. Spiteri, M., & Chang Rundgren, S. (2020). Literature review on the factors affecting primary teachers’ use of digital technology. Technology, Knowledge and Learning,25, 115–128. https://doi.org/10.1007/s10758-018-9376-x.

    Article  Google Scholar 

  24. Stockero, S. L., & Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice. Journal of Mathematics Teacher Education,16(2), 125–147.

    Article  Google Scholar 

  25. Trigueros, M., Lozano, M. D., & Sandoval, I. (2014). Integrating technology in the primary school mathematics classroom: The role of the teacher. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: An international perspective on technology focused professional development, 2 (pp. 111–138). Dordrecht: Springer.

    Google Scholar 

  26. Varela, F. (1999). Ethical know-how: Action, wisdom and cognition. Stanford: University Press.

    Google Scholar 

  27. Zack, V., & Reid, D. A. (2003). Good-enough understanding: Theorising about the learning of complex ideas (part 1). For the Learning of Mathematics,23, 43–50.

    Google Scholar 

Download references

Acknowledgements

This project was funded by Conacyt’s Grant No. 145735. We would also like to thank Asociación Mexicana de Cultura A.C. and Instituto Tecnológico Autónomo de México for their support.

Author information

Affiliations

Authors

Corresponding author

Correspondence to María Trigueros.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Trigueros, M., Sandoval, I. & Lozano, M. Ways of acting when using technology in the primary school classroom: contingencies and possibilities for learning. ZDM Mathematics Education (2020). https://doi.org/10.1007/s11858-020-01171-9

Download citation

Keywords

  • Contingencies
  • Digital technology
  • Teachers’ role
  • Enactivism
  • Mathematics learning