Digital Technology in Mathematics Education: Why It Works (Or Doesn’t)



The integration of digital technology confronts teachers, educators and researchers with many questions. What is the potential of ICT for learning and teaching, and which factors are decisive in making it work in the mathematics classroom? To investigate these questions, six cases from leading studies in the field are described, and decisive success factors are identified. This leads to the conclusion that crucial factors for the success of digital technology in mathematics education include the design of the digital tool and corresponding tasks exploiting the tool’s pedagogical potential, the role of the teacher and the educational context.


Didactical function Digital technology Instrumentation 



I thank Arthur Bakker, Vincent Jonker, Carolyn Kieran, Hussein Sabra and Luc Trouche for their helpful comments on the draft version of this paper.


  1. 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, 245–274.CrossRefGoogle Scholar
  2. Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Dissertation. CD Bèta Press, Utrecht.Google Scholar
  3. Bakker, A., & Gravemeijer, K. P. E. (2006). An historical phenomenology of mean and median. Educational Studies in Mathematics, 62, 149–168.CrossRefGoogle Scholar
  4. Bakker, A., & Hoffmann, M. H. G. (2005). Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students’ learning about statistical distribution. Educational Studies in Mathematics, 60, 333–358.CrossRefGoogle Scholar
  5. Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking of theories—an approach for exploiting the diversity of theoretical approaches. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 483–506). New York: Springer.CrossRefGoogle Scholar
  6. Bokhove, C. (2011). Use of ICT for acquiring, practicing and assessing algebraic expertise. Dissertation. CD-Bèta press, Utrecht.Google Scholar
  7. Bokhove, C., & Drijvers, P. (2012). Effects of a digital intervention on the development of algebraic expertise. Computers and Education, 58(1), 197–208.CrossRefGoogle Scholar
  8. Boon, P. (2009). A designer speaks: Designing educational software for 3D geometry. Educational Designer, 1(2). Retrieved June 19, 2012, from
  9. Burrill, G., Allison, J., Breaux, G., Kastberg, S., Leatham, K., & Sanchez, W. (Eds.). (2002). Handheld graphing technology in secondary mathematics: Research findings and implications for classroom practice. Dallas, TX: Texas Instruments.Google Scholar
  10. Cobb, P., McClain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21, 1–78.CrossRefGoogle Scholar
  11. Daher, W. (2010). Building mathematical knowledge in an authentic mobile phone environment. Australasian Journal of Educational Technology, 26(1), 85–104.Google Scholar
  12. Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41, 143–163.CrossRefGoogle Scholar
  13. Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Tool use and the development of the function concept: from repeated calculations to functional thinking. International Journal of Science and Mathematics Education, 10(6), 1243–1267.CrossRefGoogle Scholar
  14. Doorman, M., Drijvers, P., & Kindt, M. (1994). De grafische rekenmachine in het wiskundeonderwijs [The graphic calculator in mathematics education]. Utrecht: CD-Bèta press.Google Scholar
  15. Drijvers, P. (2003). Learning algebra in a computer algebra environment. Design research on the understanding of the concept of parameter. Dissertation. Freudenthal Institute, Utrecht. Retrieved from
  16. Drijvers, P. (2012). Teachers transforming resources into orchestrations. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources: Mathematics curriculum materials and teacher development (pp. 265–281). New York/Berlin: Springer.Google Scholar
  17. Drijvers, P., Boon, P., & Van Reeuwijk (2010a). Algebra and technology. In P. Drijvers (Ed.), Secondary algebra education, Revisiting topics and themes and exploring the unknown (pp. 179–202). Rotterdam: Sense.Google Scholar
  18. Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010b). The teacher and the tool; instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234.CrossRefGoogle Scholar
  19. Drijvers, P., Godino, J. D., Font, D., & Trouche, L. (2012). One episode, two lenses. A reflective analysis of student learning with computer algebra from instrumental and onto-semiotic perspectives. Educational Studies in Mathematics, 82(1), 23–49.CrossRefGoogle Scholar
  20. Drijvers, P., & Trouche, L. (2008). From artifacts to instruments: A theoretical framework behind the orchestra metaphor. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics (Vol. 2, pp. 363–392)., Cases and perspectives Charlotte, NC: Information Age.Google Scholar
  21. Freudenthal, H. (1991). Revisiting mathematics education, China lectures. Dordrecht: Kluwer.Google Scholar
  22. Fuglestad, A. B. (2007). Teaching and teachers’ competence with ICT in mathematics in a community of inquiry. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (pp. 2-249–2-258). Seoul, Korea.Google Scholar
  23. Graham, C. R. (2011). Theoretical considerations for understanding technological pedagogical content knowledge (TPACK). Computers and Education, 57, 1953–1960.CrossRefGoogle Scholar
  24. Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218.CrossRefGoogle Scholar
  25. Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments. The case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195–227.CrossRefGoogle Scholar
  26. Heid, M. K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19, 3–25.CrossRefGoogle Scholar
  27. Hoyles, C., & Lagrange, J.-B. (Eds.). (2010). Mathematics education and technology—Rethinking the terrain. New York/Berlin: Springer.Google Scholar
  28. Jaworski, B. (2006). Theory and practice in mathematics teaching development: critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9(2), 187–211.CrossRefGoogle Scholar
  29. 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
  30. Kieran, C., & Drijvers, P. (2012). The didactical triad of theoretical framework, mathematical topic, and digital tool in research on learning and teaching. Paper presented at the Colloque Hommage à Michèle Artigue, Paris, May 31, 2012.Google Scholar
  31. Koehler, M. J., Mishra, P., & Yahya, K. (2007). Tracing the development of teacher knowledge in a design seminar: Integrating content, pedagogy and technology. Computers and Education, 49, 740–762.CrossRefGoogle Scholar
  32. Lagrange, J.-B. (2000). L’intégration d’instruments informatiques dans l’enseignement: une approche par les techniques. Educational Studies in Mathematics, 43, 1–30.CrossRefGoogle Scholar
  33. Monaghan, J. (2005). Computer Algebra, instrumentation and the Anthropological Approach. Paper Presented at the 4th CAME Conference, October 2005. Accessed April 7, 2012.
  34. National Council of Teachers of Mathematics (2008). The role of technology in the teaching and learning of mathematics.
  35. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.Google Scholar
  36. 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.Google Scholar
  37. Peirce, C. S. (1931–1935). Collected papers of charles sanders peirce. Cambridge, MA: Harvard University Press.Google Scholar
  38. Pierce, R., & Ball, L. (2009). Perceptions that may affect teachers’ intention to use technology in secondary mathematics classes. Educational Studies in Mathematics, 71(3), 299–317.CrossRefGoogle Scholar
  39. Pierce, R., & Stacey, K. (2010). Mapping pedagogical opportunities provided by mathematics analysis software. Technology, Knowledge and Learning, 15(1), 1–20.Google Scholar
  40. Prensky, M. (2001). Digital game-based learning. New York: McGraw-Hill.Google Scholar
  41. Ruthven, K. (2007). Teachers, technologies and the structures of schooling. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the V Congress of the European Society for Research in Mathematics Education CERME5 (pp. 52–67). Larnaca, Cyprus: University of Cyprus.Google Scholar
  42. 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.CrossRefGoogle Scholar
  43. Sabra, H. (2011). Contribution à l’étude du travail documentaire des enseignants de mathématiques: les incidents comme révélateurs des rapports entre documentations individuelle et communautaire. [Contribution to the study of documentary work of mathematics teachers: incidents as indicators of relations between individual and collective documentation.] Dissertation. Lyon: Université Claude Bernard Lyon 1.Google Scholar
  44. Trouche, L. (2004). Managing 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.CrossRefGoogle Scholar
  45. Trouche, L., & Drijvers, P. (2010). Handheld technology: Flashback into the future. ZDM, The International Journal on Mathematics Education, 42(7), 667–681.CrossRefGoogle Scholar
  46. Voogt, J., Fisser, P., Pareja Roblin, N., Tondeur, J., & Van Braak, J. (2012). Technological pedagogical content knowledge—a review of the literature. Journal of Computer Assisted Learning, Online first,. doi: 10.1111/j.1365-2729.2012.00487.x.Google Scholar
  47. Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. New York: Cambridge University Press.CrossRefGoogle Scholar
  48. Wijers, M., Jonker, V., & Drijvers, P. (2010). MobileMath; exploring mathematics outside the classroom. ZDM, The International Journal on Mathematics Education, 42(7), 789–799.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Freudenthal Institute for Science and Mathematics EducationUtrecht UniversityUtrechtThe Netherlands

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