The Math Trail as a Learning Activity Model for M-Learning Enhanced Realistic Mathematics Education: A Case Study in Primary Education

  • Georgios Fessakis
  • Paschalina Karta
  • Konstantinos Kozas
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 715)


Seeking a systematic combination of the pedagogical model of m-learning with the Realistic Mathematics Education (RME) approach, this study concerns the use of math trail as a learning activity model that can take the advantages of mobile computing devices for the design of effective learning experiences in an authentic context. The paper presents the design and the study of the first pilot implementation of a math trail, using mobile devices for primary school students. In this math trail, the students are guided, through a digital map, to a sequence of preselected sites of a park where they solve specially designed math problems using data from the environmental context. The students measure real objects’ dimensions either with conventional instruments or by measurement applications of their tablet. According to the findings of the study, students solved the puzzles by applying mathematical knowledge, discussion and collaboration. The students applied and reinforced their knowledge through an effective and engaging learning activity. Moreover, the students were puzzled about the differences of the measurements by conventional and digital instruments and this confusion triggered social negotiation. Further research is needed for a grounded theory development about m-learning design for RME.


Learning design M-learning Realistic mathematics education Math trails 


  1. 1.
    Bouck, E.C., Flanagan, S., Miller, B., Bassette, L.: Technology in action. J. Spec. Educ. Technol. 27(4), 47–57 (2012)CrossRefGoogle Scholar
  2. 2.
    Cross, R.: Developing math trails. Math. Teach. 158, 38–39 (1997)Google Scholar
  3. 3.
    Traxler, J.: Defining mobile learning. In: Isaías, P., Borg, C., Kommens, P., Bonanno, P. (eds.), Proceedings of the IADIS International Conference on Mobile Learning, Qwara, Malta, pp. 261–266 (2005)Google Scholar
  4. 4.
    Zhang, Y.: Design of mobile teaching and learning in higher education: introduction. Handbook of Mobile Teaching and Learning, pp. 3–10 (2015)Google Scholar
  5. 5.
    Traxler, J.: Current state of mobile learning. Mob. Learn Transform. Deliv. Educ. Train. 1, 9–24 (2009)Google Scholar
  6. 6.
    Stevens, D., Kitchenham, A.: An analysis of mobile learning in education, business, and medicine. In: Kitchenham, A. (ed.) Models for Interdisciplinary Mobile Learning: Delivering Information to Students, pp. 1–25. IGI Global, Hersey (2011)Google Scholar
  7. 7.
    Martin, F., Ertzberger, J.: Here and now mobile learning: an experimental study on the use of mobile technology. Comput. Educ. 68, 76–85 (2013)CrossRefGoogle Scholar
  8. 8.
    Kukulska-Hulme, A., Traxler, J.: Mobile teaching and learning. In: Kukuluska-Hulme, A., Traxler, J., (eds.) Mobile Learning: A Handbook for Educators and Trainers, pp. 25–44 (2005)Google Scholar
  9. 9.
    Kraut, R.: UNESCO Policy Guidelines for Mobile Learning. UNESCO, France (2013)Google Scholar
  10. 10.
    Markouzis, D., Fessakis, G.: Interactive storytelling and mobile augmented reality applications for learning and entertainment—a rapid prototyping perspective. In: International Conference on Interactive Mobile Communication Technologies and Learning (IMCL) 2015, pp. 4–8 (2015)Google Scholar
  11. 11.
    Freudenthal, H.: Why to teach mathematics so as to be useful. Educ. Stud. Math. 1(1), 3–8 (1968)CrossRefGoogle Scholar
  12. 12.
    Van den Heuvel-Panhuizen, M., Drijvers, P.: Realistic mathematics education. In: Encyclopedia of Mathematics Education, pp. 521–525. Springer, Dordrecht (2014)Google Scholar
  13. 13.
    National Council of Teachers of Mathematics. In: Principles and Standards for School Mathematics, vol. 1 (2000)Google Scholar
  14. 14.
    Clements, D.H.: From exercises and tasks to problems and projects: unique contributions of computers to innovative mathematics education. J. Math. Behav. 19(1), 9–47 (2000)CrossRefGoogle Scholar
  15. 15.
    Koole, M.L.: A model for framing mobile learning. Mob. Learn. Transform. Deliv. Educ. Train. 1(2), 25–47 (2009)Google Scholar
  16. 16.
    Soykan, E., Uzunboylu, H.: New trends on mobile learning area: the review of published articles on mobile learning in science direct database. World J. Educ. Technol. 7(1), 31–41 (2015)Google Scholar
  17. 17.
    Daher, W.: Students’ perceptions of learning mathematics with cellular phones and applets. Int. J. Emerg. Technol. Learn. 4(1), 23–28 (2009)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Baya’a, N., Daher, W.: Students’ perceptions of mathematics learning using mobile phones. In: Proceedings of the International Conference on Mobile and Computer Aided Learning, vol. 4, pp. 1–9 (2009)Google Scholar
  19. 19.
    Bray, A., Oldham, E., Tangney, B.: Technology-mediated realistic mathematics education and the bridge21 model: a teaching experiment. In: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, Prague, pp. 2487–2493 (2015)Google Scholar
  20. 20.
    Cahyono, A.N., Ludwig, M.: MathCityMap: exploring mathematics around the city. Presented at the 13th International Congress on Mathematics Education (ICME-13), Hamburg (2016)Google Scholar
  21. 21.
    Zaranis, N.: Does the use of information and communication technology through the use of realistic mathematics education help kindergarten students to enhance their effectiveness in addition and subtraction? Presch. Prim. Educ. 5(1), 46–62 (2017). CrossRefGoogle Scholar
  22. 22.
    Zaranis, N., Baralis, G., Skordialos, E.: The use of ICT in teaching substraction to the first grade students. In: Proceedings of Fourteenth the IIER International Conference, Paris, France, pp. 99–104 (2015)Google Scholar
  23. 23.
    Widjaja, Y.B., Heck, A.: How a realistic mathematics education approach and microcomputer-based laboratory worked in lessons on graphing at an Indonesian Junior High School. J. Sci. Math. Educ. Southeast Asia 26(2), 1–51 (2003)Google Scholar
  24. 24.
    Fessakis, G., Bekri, A.-F., Konstantopoulou, A.: Designing a mobile game for spatial and map abilities of kindergarten children. In: 10th European Conference on Games Based Learning, ECGBL 2016, Scotland, pp. 183–192 (2016)Google Scholar
  25. 25.
    Shoaf, M.M., Pollak, H., Schneider, J.: Math Trails. COMAP, Lexington (2004)Google Scholar
  26. 26.
    Richardson, K.M.: Designing math trails for the elementary school. Teach. Child. Math. 11(1), 8–14 (2004)Google Scholar
  27. 27.
    Cobb, P., Confrey, J., diSessa, A., Lehrer, R., Schauble, L.: Design experiments in educational research. Educ. Res. 32(1), 9–13 (2003)CrossRefGoogle Scholar
  28. 28.
    Yin, R.: Case study Research. Design and Methods. Sage Publications, New Delhi (2014)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Georgios Fessakis
    • 1
  • Paschalina Karta
    • 1
  • Konstantinos Kozas
    • 1
  1. 1.University of the AegeanRhodesGreece

Personalised recommendations