Tasks and Digital Tools

  • John Monaghan
  • Luc Trouche
Part of the Mathematics Education Library book series (MELI, volume 110)


This chapter considers scholastic tasks with digital tools. The first two sections consider tasks in ‘ordinary’ classrooms (tasks for learning) and issues relating to tasks using mathematical software. The first section presents examples of tasks with digital tools to highlight potential problems and opportunities for learning. The second section considers issues arising from the literature on tasks design with and without digital tools. The final section looks at task-tool issues in larger-than-the-individual classroom research and in assessment; it also comments of avenues for further development.


Task Design Digital Technology Graphic Calculator Mathematical Task Digital Tool 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abboud-Blanchard, M., & Vandebrouck, F. (2012). Analysing Teachers’ Practices in Technology Environments from an Activity Theoretical Approach. International Journal for Technology in Mathematics Education, 19(4), 159–163.Google Scholar
  2. Abdul Hussain, M., Monaghan, J., & Threlfall, J. (2012). Teacher-student development in mathematics classrooms: Interrelated zones of free movement and promoted actions. Educational Studies in Mathematics, 82(2), 285–302.CrossRefGoogle Scholar
  3. 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.CrossRefGoogle Scholar
  4. Artigue, M. (2005). The integration of symbolic calculators into secondary education: Some lessons from didactical engineering. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument. New York: Springer.Google Scholar
  5. Bokhove, C. (2013). Using crises, feedback and fading for online task design. In C. Margolinas (Ed.), Task Design in Mathematics Education. Proceedings of ICMI Study 22. Oxford. Retrieved from
  6. Bosch, M., & Chevallard, Y. (1999). La sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématique. Recherches en didactique des mathématiques, 19(1), 79–124.Google Scholar
  7. Brown, R. G. (2010). Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested? Educational Studies in Mathematics, 73(2), 181–203.CrossRefGoogle Scholar
  8. Chiappini, G. (2012). The transformation of ergonomic affordances into cultural affordances: The case of the Alnuset system. International Journal for Technology in Mathematics Education, 19(4), 135–140.Google Scholar
  9. Drijvers, P. (2009). Tools and tests: technology in national final mathematics examinations. In C. Winslow (Ed.), Nordic Research on Mathematics Education, Proceedings from NORMA08 (pp. 225–236). Rotterdam: Sense.Google Scholar
  10. Drijvers, P., Boon, P., Doorman, M., Bokhove, C., & Tacoma, S. (2013). RME principles for designing online tasks. In C. Margolinas (Ed.) Task Design in Mathematics Education. Proceedings of ICMI Study 22. Oxford. Retrieved from
  11. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: Reidel.Google Scholar
  12. Gueudet, G., Pepin, B., & Trouche, L. (2013). Textbooks’ Design and Digital Resources. In C. Margolinas (ed.), Task Design in Mathematics Education (pp. 327–337). ICMI Study 22, Oxford. Retrieved from
  13. Hoyles, C., Noss, R., Vahey, P., & Roschelle, J. (2013). Cornerstone mathematics: Designing digital technology for teacher adaptation and scaling. ZDM, The International Journal on Mathematics Education, 45(7), 1057–1070.CrossRefGoogle Scholar
  14. Johnson, D. C. (1981). Calculator exploration for concept reinforcement. Mathematics Teaching, 95, 28–29.Google Scholar
  15. Joubert, M. (2013). Using computers in classroom mathematical tasks: revisiting theory to develop recommendations for the design of tasks. In C. Margolinas (Ed.), Proceedings of ICMI Study 22 (pp. 71–79). Oxford, UK: ICMIGoogle Scholar
  16. Kaptelinin, V., & Nardi, B. (2006). Acting with technology: Activity theory and interaction design. Cambridge, MA: MIT Press.Google Scholar
  17. Kieran, C., & Drijvers, P. (2006). The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11(2), 205–263.CrossRefGoogle Scholar
  18. Kynigos, C. (2007). Using half-baked microworlds to challenge teacher educators’ knowing. International journal of computers for mathematical learning, 12(2), 87–111.Google Scholar
  19. Laborde, C. (2002). Integration of technology in the design of geometry tasks with Cabri-geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.CrossRefGoogle Scholar
  20. Lagrange, J.-b. (1999). Complex calculators in the classroom: Theoretical and practical reflections on teaching pre-calculus. International Journal of Computers for Mathematical Learning, 4(1), 51–81.CrossRefGoogle Scholar
  21. Lagrange, J.-B. (2000). L'intégration d’instruments informatiques dans l’enseignement: une approche par les techniques. Educational Studies in Mathematics, 43(1), 1–30.CrossRefGoogle Scholar
  22. Lagrange, J.-B. (2005). Using symbolic calculators to study mathematics. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 113–136). New York: Springer.CrossRefGoogle Scholar
  23. Lumb, S., Monaghan, J., & Mulligan, S. (2000). Issues arising when teachers make extensive Use of computer algebra. International Journal of Computer Algebra in Mathematics Education, 7(4), 223–240.Google Scholar
  24. Margolinas, C. (Ed.) (2013). Task Design in Mathematics Education. Proceedings of ICMI Study 22. Oxford. Retrieved from
  25. Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. York, England. QED Press.Google Scholar
  26. Monaghan, J. (2000). Some issues surrounding the use of algebraic calculators in traditional examinations. International Journal of Mathematical Education in Science and Technology, 31(3), 381–392.CrossRefGoogle Scholar
  27. Monaghan, J., Pool, P., Roper, T., & Threlfall, J. (2009). Open-start mathematics problems: An approach to assessing problem solving. Teaching Mathematics and its Applications, 28(1), 21–31.CrossRefGoogle Scholar
  28. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Springer.Google Scholar
  29. Perks, P., Prestage, S., & Hewitt, D. (2002). Does the software change the maths? Micromath, 18(1), 28–31.Google Scholar
  30. Prediger, S., Arzarello, F., Bosch, M., & Lenfant, A. (Eds.). (2008). Comparing, combining, coordinating—networking strategies for connecting theoretical approaches. ZDM, The International Journal on Mathematics Education, 40(2), 163–327.Google Scholar
  31. Rabardel, P. (1999). Éléments pour une approche instrumentale en didactique des mathématiques. In M. Bailleul, Actes de la dixième université d’été de didactique des mathématiques (pp. 203–213). ARDM, Caen.Google Scholar
  32. Robert, A. (2012). A Didactical Framework for Studying Students’ and Teachers’ Activities when Learning and Teaching Mathematics. International Journal for Technology in Mathematics Education, 19(4), 153–157.Google Scholar
  33. Roschelle, J., Tatar, D., Shechtman, N., & Knudsen, J. (2008). The role of scaling up research in designing for and evaluating robustness. Educational Studies in Mathematics, 68(2), 149–170.CrossRefGoogle Scholar
  34. Sahlberg, P., & Berry, J. (2003). Small group learning in mathematics: teachers’ and pupils’ ideas about groupwork in school. Painosalama Oy.Google Scholar
  35. Thomas, M. O., & Lin, C. (2013). Designing Tasks for Use With Digital Technology. Task Design in Mathematics Education Proceedings of ICMI Study 22, 109.Google Scholar
  36. Threlfall, J., Pool, P., Homer, M., & Swinnerton, B. (2007). Implicit aspects of paper and pencil mathematics assessment that come to light through the use of the computer. Educational Studies in Mathematics, 66(3), 335–348.CrossRefGoogle Scholar
  37. Trgalová, J., & Jahn, A.P. (2011). Quality issue in the design and use of resources by mathematics teachers. ZDM – The International Journal on Mathematics Education 45, 973–986.Google Scholar
  38. Trouche, L. (1998). Faire des mathématiques avec des calculatrices symboliques, conjecturer et prouver. 37 variations sur un thème imposé, IREM, Université Montpellier 2.Google Scholar
  39. 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.Google Scholar
  40. Warfield, V. (2006) Invitation to Didactique. (accessed 13 December 2015).
  41. Watson, A., & Mason, J. (2004). The exercise as mathematical object: Dimensions of possible variation in practice. In Proc. 24th Conf. of The British Society of Research in Learning Mathematics (Vol. 2, pp. 107–112).Google Scholar
  42. Watson, A., Ohtani, M., Ainley, J., Bolite-Frant, J., Doorman, M., Kieran, C., Leung, A., Margolinas, C., Sullivan, P., Thompson, D., & Yudong Yang, Y. (2013). Task Design in Mathematics Education – Introduction, Proceedings of ICMI Study 22, Oxford, England.Google Scholar
  43. Wertsch, J.V. (1998). Mind as action. Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • John Monaghan
    • 1
  • Luc Trouche
    • 2
  1. 1.Department of Mathematical SciencesUniversity of AgderKristiansandNorway
  2. 2.Institut Français de l’EducationEcole Normale Supérieure de LyonLyonFrance

Personalised recommendations