Prospective Secondary School Mathematics Teachers’ Use of Digital Technologies to Represent, Explore and Solve Problems

  1. Hernández, Alexánder 1
  2. Perdomo-Díaz, Josefa 1
  3. Camacho-Machín, Matías 1
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

Libro:
Problem Posing and Problem Solving in Mathematics Education

ISBN: 9789819972043,  9789819972050

Año de publicación: 2023

Páginas: 73-90

Tipo: Capítulo de Libro

DOI: 10.1007/978-981-99-7205-0_5 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

This research aims to analyze the work done by a group of prospective secondary school mathematics teachers while solving mathematics problems using GeoGebra. Our focus is on analyzing the Mathematical Activity as they progress solving one problem, through the different problem-solving episodes (Santos-Trigo & Camacho-Machín, 2013): understanding, exploration and the search for multiple approaches. The results show evidence of mathematical processes and activities that include extending and posing new problems and finding novel paths to reason and solve the tasks with technology. We could observe them to generate and pursue new routes to represent mathematical objects, transforming representations, formulating conjectures and observing and justifying relationships and conjectures.

Referencias bibliográficas

  • Conner, A., Wilson, P., & Kim, H. (2011). Building on mathematical events in the classroom. ZDM Mathematics Education, 43, 979–992.
  • Contreras, J. (2014). Solving optimization problems with dynamic geometry software: The airport problem. Journal of Mathematics Education at Teacher College, 5(2), 17–27.
  • Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48–62. https://doi.org/10.1016/j.jmathb.2014.11.001
  • Heid, M., Wilson, P. S., & Blume, G. W. (Eds.). (2015). Mathematical understanding for secondary teaching: A framework and classroom-based situations. NCTM and IAP.
  • Hernández, A. (2021). Resolución de problemas con GeoGebra en la formación inicial de profesores de matemáticas: Un análisis desde la actividad matemática. Unpublished Doctoral Thesis. Universidad de La Laguna, Spain. https://riull.ull.es/xmlui/handle/915/26865
  • Hernández, A., Perdomo-Díaz, J., & Camacho-Machín, M. (2020). Mathematical understanding in problem solving with GeoGebra: A case study in initial teacher education. International Journal of Mathematical Education in Science and Technology, 51(2), 208–223. https://doi.org/10.1080/0020739X.2019.1587022
  • Iranzo, N., & Fortuny, J. M. (2009). La influencia conjunta del uso de GeoGebra y Lápiz y Papel en la adquisición de competencias del alumno. Enseñanca de las ciencias, 27(3), 433–446. https://doi.org/10.5565/rev/ensciencias.3653
  • Jacinto, H., & Carreira, S. (2017). Mathematical problem solving with technology: Techno-mathematical fluency of a student-with-GeoGebra. International Journal of Science and Mathematics Education, 1115–1136. https://doi.org/10.1007/s10763-016-9728-8
  • Kilpatrick, J. (2015). Background for the mathematical understanding framework. In M. K. Heid, P. Wilson, & G. W. Blume (Eds.), Mathematical understanding for secondary teaching: A framework and classroom-based situations (pp. 1–8). NCTMand IAP.
  • Leung, A. (2017). Exploring techno-pedagogic task design in the mathematics classroom. In A. Leung & A. Baccaglini-Frank (Eds.), Digital technologies in designing mathematics education tasks (pp. 3–16). Springer. https://doi.org/10.1007/978-3-319-43423-0_1
  • Santos-Trigo, M. (2019) Mathematical problem solving and the use of digital technologies. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical problem solving, current themes, trends and research ICME-13 monographs, (pp. 62–89). Springer. https://doi.org/10.1007/978-3-030-10472-6_4
  • Santos-Trigo, M., & Camacho-Machín, M. (2013). Framing the use of computational technology in problem solving approaches. The Mathematical Enthusiast, 10(1&2), 279–302.
  • Santos-Trigo, M., & Reyes-Martínez, I. (2018). High school prospective teachers’ problem-solving reasoning that involves the coordinated use of digital technologies. International Journal of Mathematical Education, 50(1), 1–20.
  • Santos-Trigo, M., Reyes-Martínez, I., & Gómez-Arciga, A. (2022). A conceptual framework to structure remote learning scenarios: A digital wall as a reflective tool for students to develop mathematics problem-solving competencies. International Journal of Learning Technology, 17(1), 27–52.
  • Santos-Trigo, M., Reyes-Martínez, I., & Ortega-Moreno, F. (2015). Fostering and supporting the coordinated use of digital technologies in mathematics learning. International Journal Learning Technology, 10(3), 251–270.
  • Thurm, D., & Barzel, B. (2022). (2022) Teaching mathematics with technology: A multidimensional analysis of teacher beliefs. Educational Studies in Mathematics, 109, 41–63. https://doi.org/10.1007/s10649-021-10072-x
  • Zbiek, R. M., & Heid, M. (2018). Making connections from the secondary classroom to the abstract algebra course: A mathematical activity approach. In N. H. Wasserman (Ed.), Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers, (pp. 189–210). Springer. https://doi.org/10.1007/978-3-319-99214-3_10