Digital Technologies and a Modeling Approach to Learn Mathematics and Develop Problem Solving Competencies

  • Manuel Santos-TrigoEmail author
  • Isaid Reyes-Martínez
  • Daniel Aguilar-Magallón
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 620)


This study is framed within a conceptual approach that integrates modeling, problem solving, and the use of digital technologies perspectives in mathematical learning. It focuses on the use of a Dynamic Geometry System (GeoGebra) to construct mathematical models as a means to represent and explore mathematical relationships. In particular, we analyze and document what ways of reasoning high school students exhibit as a result of working on a mathematical task in problem solving sessions. Results show that the students rely on a set of technology affordances to dynamically visualize, represent and explore mathematical relations. In this process, the students’ discussions became relevant not only to explain their approaches; but also to contrast, and eventually refine, their initial models and ways of reasoning.


Digital technologies Modeling Problem solving Mathematics learning 



The authors would like to acknowledge the support received from Conacyt (project reference 168543) during the development of this research.


  1. 1.
    Blum, W., Galbraith, P.L., Henn, H.-W., Niss, M. (eds.): Modelling and Applications in Mathematics Education. Springer, New York (2007)zbMATHGoogle Scholar
  2. 2.
    Cai, J.: Commentary on problem solving heuristics, affect, and discrete mathematics: a representational discussion. In: Sriraman, B., English, L. (eds.) Theories of Mathematics Education, pp. 252–257. Springer, New York (2010)Google Scholar
  3. 3.
    Carlson, M.P., Bloom, I.: The cyclic nature of problem solving: an emergent multidimensional problem-solving framework. Educ. Stud. Math. 58, 45–75 (2005)CrossRefGoogle Scholar
  4. 4.
    Cobb, P.: Putting philosophy to work: coping with multiple theoretical perspectives. In: Lester, F. (ed.) Second Handbook of Research on Mathematics Teaching and Learning, vol. 1, pp. 3–38. Information Age Publishing, Greenwich (2007)Google Scholar
  5. 5.
    Engelbrecht, J.: Adding structure to the transition process to advance mathematical activity. Int. J. Math. Educ. Sci. Technol. 41(2), 143–154 (2010)CrossRefGoogle Scholar
  6. 6.
    English, L., Sriraman, B.: Problem solving for the 21st century. In: Sriraman, B., English, L. (eds.) Theories of Mathematics Education: Seeking New Frontiers, pp. 263–290. Springer, New York (2010)CrossRefGoogle Scholar
  7. 7.
    Jackiw, N., Sinclair, N.: Sounds and pictures: dynamism and dualism in dynamic geometry. ZDM Math. Educ. 41, 413–426 (2009)CrossRefGoogle Scholar
  8. 8.
    Kelly, A.E., Lesh, R.A.: Handbook of Research Design in Mathematics and Science Education. Lawrence Erlbaum Associates, Mahwah (2000)zbMATHGoogle Scholar
  9. 9.
    Kilpatrick, J., Swafford, J., Bradford, F. (eds.): Adding it Up: Helping Children Learn Mathematics. National Academic Press, Washington, D.C. (2001)Google Scholar
  10. 10.
    Lesh, R., Doerr, H.M.: Symbolizing, communicating, and mathematizing: key components of models and modeling. In: Cobb, P., Yackel, E., McClain, K. (eds.) Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design, pp. 361–383. Lawrence Erlbaum Associates, Mahwah (2000)Google Scholar
  11. 11.
    Lesh, R., Sriraman, B.: Re-conceptualizing mathematics education as a design science. In: Sriraman, B., English, L. (eds.) Theories of Mathematics Education, Seeking New Frontiers, pp. 123–146. Springer, New York (2010)CrossRefGoogle Scholar
  12. 12.
    Lester Jr., F.K.: On the theoretical, conceptual, and philosophical foundation for research in mathematics education. In: Sriraman, B., English, L. (eds.) Theories of Mathematics Education: Seeking New Frontiers, pp. 67–85. Springer, New York (2010)CrossRefGoogle Scholar
  13. 13.
    Mason, J., Johnston-Wilder, S.: Designing and Using Mathematical Tasks, 2nd edn. Tarquin, St Albans (2006)Google Scholar
  14. 14.
    Moreno-Armella, L., Santos-Trigo, M.: The use of digital technologies in mathematical practices: reconciling traditional and emerging approaches. In: English, L., Kirshner, D. (eds.) Handbook of International Research in Mathematics Education, 3rd edn, pp. 595–616. Taylor and Francis, New York (2016)Google Scholar
  15. 15.
    National Council of Teachers of Mathematics (NCTM): Focus in high school mathematics: Reasoning and sense making. NCTM, Reston (2009)Google Scholar
  16. 16.
    Santos-Trigo, L.: Problem solving in mathematics education. In: Lerman, S. (ed.) Encyclopedia of Mathematics Education, 1st edn, pp. 496–501. Springer, Netherlands (2014)Google Scholar
  17. 17.
    Santos-Trigo, M., Reyes-Rodriguez, A.: The use of digital technology in finding multiple paths to solve and extend an equilateral triangle task. Int. J. Math. Educ. Sci. Technol. 47(1), 58–81 (2016)CrossRefGoogle Scholar
  18. 18.
    Schoenfeld, A.H.: Bharath Sriraman and Lyn English: Theories of mathematics education: seeking new frontiers. ZDM Int. J. Math. Educ. 42, 503–506 (2010)CrossRefGoogle Scholar
  19. 19.
    Schoenfeld, A.H.: Reflections of an accidental theorist. J. Res. Math. Educ. 41(2), 104–116 (2010)Google Scholar
  20. 20.
    Simon, M.A.: Amidst multiple theories of learning in mathematics education. J. Res. Math. Educ. 40(5), 477–490 (2009)Google Scholar
  21. 21.
    Trouche, L.: Managing the complexity of human/machine interactions in computerized learning environments: guiding students’ command process through instrumental orchestrations. Int. J. Comput. Math. Learn. 9(3), 281–307 (2004)CrossRefGoogle Scholar
  22. 22.
    Zbiek, R.M., Heid, M.K., Blume, G.W.: Research on technology in mathematics education. In: Lester Jr., F.K. (ed.) Second Handbook of Research on Mathematics Teaching and Learning, pp. 1169–1207. Information Age Publishing, NCTM, Charlotte (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Manuel Santos-Trigo
    • 1
    Email author
  • Isaid Reyes-Martínez
    • 1
  • Daniel Aguilar-Magallón
    • 1
  1. 1.Mathematics Education DepartmentCentre for Research and Advanced Studies, Cinvestav-IPNMexico CityMexico

Personalised recommendations