High School Teachers’ Use of a Dynamic Geometry System to Formulate Conjectures and to Transit from Empirical to Geometric and Algebraic Arguments in Problem-Solving Approaches

  1. Santos-Trigo, Manuel
  2. Camacho-Machín, Matías 1
  3. Olvera-Martínez, Carmen
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

Libro:
Broadening the Scope of Research on Mathematical Problem Solving

ISSN: 2570-4729,  2570-4737

ISBN: 9783319998602,  9783319998619

Año de publicación: 2018

Páginas: 81-100

Tipo: Capítulo de Libro

DOI: 10.1007/978-3-319-99861-9_4 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

The aim of the study is to analyse and discuss ways of reasoning that high school teachers develop in a problem-solving environment that fosters the systematic use of digital technologies. Results indicate that they relied on a dynamic geometry system’s affordances to initially make sense of problem statements to formulate a set of conjectures or relationships that involve mathematical parameters’ behaviours. Initially these conjectures were empirically validated or through visual and quantitative arguments; but later the same arguments were a source to think with an algebraic support. Throughout the activities, the participants engaged in mathematical reflection to reconcile visual, geometric and algebraic or analytical approaches.

Referencias bibliográficas

  • Churchill, D., Fox, B., & King, M. (2016). Framework for designing mobile learning environments. In D. Churchill, J. Lu, T. K. F. Chiu, & B. Fox (Eds.), Mobile learning design, lectures notes in educational technologies (pp. 22–52). New York: Springer.
  • Cooney, T., Beckmann, S., & Lloyd, G. (2010). Developing essential understanding of functions for teaching mathematics in Grades 9–12. Reston, VA: National Council of Teacher of Mathematics.
  • Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to support reasoning and sense making. Reston, VA: National Council of Teacher of Mathematics.
  • Hoyles, C., & Noss, R. (2008). Next steps in implementing Kaput’s research programme. Educational Studies in Mathematics, 68, 85–97.
  • Kereluik, K., Mishra, P., Fahnoe, C., & Terry, L. (2013). What knowledge is of most worth: Teacher knowledge for 21st century learning. Journal of Digital Learning in Teacher Education, 29(4), 127–140.
  • Leung, A. (2011). An epistemic model of task design in dynamic geometry environment. ZDM Mathematics Education, 43, 325–336.
  • Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education, ICME-13 topical surveys. Cham: Springer.
  • Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teacher College Record, 108(6), 1017–1024.
  • National Council of Teacher of Mathematics. (2009). Focus in high school mathematics: Reasoning and sense making. Reston, VA: National Council of Teacher of Mathematics.
  • Sacristan, A. I., Calder, N., Rojano, T., Santos-Trigo, M., Friedlander, A., & Meissner, H. (2010). The influence and shaping of digital technologies on the learning -and learning trajectories- of mathematical concepts. In C. Hoyles & J. Lagrange (Eds.), Mathematics education and technology rethinking the terrain. The 17th ICMI study (pp. 179–226). New York: Springer.
  • Santos-Trigo, M. (2014). Problem solving in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 496–501). New York: Springer.
  • Santos-Trigo, M., & Camacho-Machín, M. (2009). Towards the construction of a framework to deal with routine problems to foster mathematical inquiry. Primus, 19(3), 260–279.
  • Santos-Trigo, M., & Moreno-Armella, L. (2016). The use of digital technologies to frame and foster learners’ problem solvers’ experiences. In P. Felmer et al. (Eds.), Posing and solving mathematical problems, Research in Mathematics Education (pp. 189–207). Cham: Springer. https://doi.org/10.1007/978-3-319-28023-3_12
  • Santos-Trigo, M., Moreno-Armella, L., & Camacho-Machín, M. (2016). Problem solving and the use of digital technologies within the mathematical working space framework. ZDM Mathematics Education, 48, 827–842. https://doi.org/10.1007/s11858-016-0757-0
  • Santos-Trigo, M., Reyes-Martínez, I., & Aguilar-Magallón, D. (2015). The use of digital technologies in extending mathematical problem solving reasoning. In L. Uden et al. (Eds.), Learning technologies for education in cloud, Communications in computer and information science (pp. 298–309). New York: Springer.
  • Santos-Trigo, M., Reyes-Martinez, I., & Aguilar-Magallón, D. (2016). Digital technologies and a modeling approach to learn mathematics and develop problem solving competencies. In L. Uden et al. (Eds.), Learning technologies for education in cloud, Communications in computer and information science (pp. 193–206). New York: Springer.
  • Santos-Trigo, M., & Reyes-Rodríguez, A. (2016). The use of digital technology in finding multiple paths to solve and extend an equilateral triangle task. International Journal of Mathematical Education in Science and Technology, 47(1), 58–81. https://doi.org/10.1080/0020739X.2015.1049228
  • Schoenfeld, A. H. (2009). An essay review of the NCTM high school curriculum project. Mathematics Teacher, 103(3), 168–171.
  • Schoenfeld, A. H. (2011). How we think. A theory of goal-oriented decision making and its educational application. New York: Routledge.
  • Schoenfeld, A. H. (2012). Toward professional development for teachers grounded in a theory of decision making. ZDM Mathematics Education, 43, 457–469. https://doi.org/10.1007/s1158-011-0307-8
  • Schoenfeld, A. H. (2015). How we think: A theory of human decision-making, with a focus on teaching. In S. J. Cho (Ed.), The proceedings of the 12th international congress on mathematical education (pp. 229–243). New York: Springer. https://doi.org/10.1007/978-3-319-12688-3_16
  • Trouche, L. (2016). Didactics of mathematics: Concepts, roots, interactions and dynamics from France. In J. Monaghan et al. (Eds.), Tools and mathematics, athematics education library (pp. 219–256). New York: Springer.