Digital Technologies and a Modeling Approach to Learn Mathematics and Develop Problem Solving Competencies
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.
KeywordsDigital 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.
- 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
- 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
- 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.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
- 13.Mason, J., Johnston-Wilder, S.: Designing and Using Mathematical Tasks, 2nd edn. Tarquin, St Albans (2006)Google Scholar
- 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.National Council of Teachers of Mathematics (NCTM): Focus in high school mathematics: Reasoning and sense making. NCTM, Reston (2009)Google Scholar
- 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
- 19.Schoenfeld, A.H.: Reflections of an accidental theorist. J. Res. Math. Educ. 41(2), 104–116 (2010)Google Scholar
- 20.Simon, M.A.: Amidst multiple theories of learning in mathematics education. J. Res. Math. Educ. 40(5), 477–490 (2009)Google Scholar
- 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