Problem Posing in Pre-service Secondary Mathematics Teacher Education: Insights of using GeoGebra

Authors

DOI:

https://doi.org/10.35763/aiem28.7550

Keywords:

Problem-posing, Problem-solving, Teacher Education, GeoGebra

Abstract

This research analyzes how the use of GeoGebra strengthens future teachers’ ability to reformulate problems. A qualitative analysis is applied, based on four phases of the problem formulation process (orientation, connection, generation and reflection), along with the categories established by Baumanns: reformulating to solve the problem and to inquire or investigate; formulating to generate new problems or to design them for didactic purposes. The results show that GeoGebra enabled participants to evaluate prior ideas and assess the feasibility of the problems they proposed. Additionally, visualization and dynamic approaches influenced both the reformulation and the formulation of new problems.

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References

Ayllón, M. F., Castro, E., & Molina, M. (2011). Invención de problemas y tipificación de problema “difícil” por alumnos de educación primaria. En M. Marín Rodríguez, G. Fernández García, L. J. Blanco Nieto, & M. Palarea Medina (Eds.), Investigación en Educación Matemática XV (pp. 277-286). SEIEM. https://www.seiem.es/acta/xv-2011-ciudad-real/

Ayllón, M. F., Gallego, J. L., & Gómez-Pérez, I. A. (2016). La actuación de estudiantes de educación primaria en un proceso de invención de problemas. Perfiles Educativos, 38(152), 51-67. https://doi.org/10.22201/iisue.24486167e.2016.152.57588

Baumanns, L. (2022). Mathematical problem posing. Springer Spektrum Wiesbaden. https://doi.org/10.1007/978-3-658-39917-7

Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. En F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing. Research in mathematics education (pp. 3-34). Springer.

https://doi.org/10.1007/978-1-4614-6258-3_1

Cai, J., & Rott, B. (2024). On understanding mathematical problem-posing processes. ZDM Mathematics Education, 56, 61-71.

https://doi.org/10.1007/s11858-023-01536-w

Camacho-Machín, M., Perdomo-Díaz, J., & Hernández, A. (2019). Actividades para la formación de profesores derivadas del uso de GeoGebra en la resolución de problemas. En E. Badillo, N. Climent, C. Fernández, & M. T. González (Eds.), Investigación sobre el profesor de matemáticas: práctica de aula, conocimiento, competencia y desarrollo profesional (pp. 371-394). Ediciones Universidad de Salamanca.

Chico, J., Montes, M., & Badillo, E. (2022). Transformaciones de la información en la formulación de problemas: Una mirada hacia los futuros maestros. En T. F. Blanco, C. Núñez-García, M. C. Cañadas, & J. A. González-Calero (Eds.), Investigación en Educación Matemática XXV (pp. 219-227). SEIEM. http://www.seiem.es/docs/actas/25/ActasXXVSEIEM.pdf

Cruz, M. (2006). A mathematical problem–formulating strategy. International Journal for Mathematics Teaching and Learning, 79-90.

García-Alonso, I., Bruno, A., Almeida, R., Sosa-Martín, D., & Perdomo-Díaz, J. (2022). Problemas de fracciones formulados por futuros profesores: Algunas características. En T. F. Blanco, C. Núñez-García, M. C. Cañadas, & J. A. González-Calero (Eds.), Investigación en Educación Matemática XXV (pp. 295-304). SEIEM.

https://www.seiem.es/2022/05/05/actas-xxv-seiem-santiago-de-compostela-2022/

Gómez-Chacón, I. M., & de la Fuente, C. (2018). Problem-solving and mathematical research projects: Creative processes, actions, and mediations. En N. Amado, S. Carreira, & K. Jones (Eds.), Broadening the scope of research on mathematical problem solving (pp. 347-373). Springer.

https://doi.org/10.1007/978-3-319-99861-9_15

Hernández, A., Perdomo-Díaz, J., & Camacho-Machín, M. (2023). Formulación de problemas matemáticos con GeoGebra. Un estudio inicial. Formación del Profesorado e Investigación en Educación Matemática, 15, 117-136. https://wp.ull.es/fpiem/numero-xv/

Jacinto, H., & Carreira, S. (2017). Mathematical problem solving with technology: The techno-mathematical fluency of a student-with-GeoGebra. International Journal of Science and Mathematics Education, 15, 1115-1136. https://doi.org/10.1007/s10763-016-9728-8

Jacinto, H., & Carreira, S. (2023). Knowledge for teaching mathematical problem-solving with technology: An exploratory study of a mathematics teacher’s proficiency. European Journal of Science and Mathematics Education, 11(1), 105-122. https://doi.org/10.30935/scimath/12464

Martín-Ferraz, A., Hernández, A., & Camacho-Machín, M. (2024). Reformulación de problemas matemáticos por futuros profesores de secundaria. Formación del Profesorado e Investigación en Educación Matemática, 16, 133-162. https://wp.ull.es/fpiem/2024/11/24/16_07-reformulacion-de-problemas-matematicos-por-futuros-profesores-de-secundaria/

Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. Addison-Wesley Publishing Company.

Montes, M., Chico, J., Martín-Díaz, J. P., & Badillo, E. (2024). Mathematics teachers’ specialized knowledge mobilized through problem transformation. Journal of Mathematical Behavior, 73, 101132. https://doi.org/10.1016/j.jmathb.2024.101132

Pólya, G. (1945). How to solve it? Princeton University Press.

Reyes-Rodríguez, A., Santos-Trigo, M., & Barrera-Mora, F. (2017). The construction of a square through multiple approaches to foster learners’ mathematical thinking. Teaching Mathematics and its Applications: An International Journal of the IMA, 36(3), 167-181. https://doi.org/10.1093/teamat/hrw022

Santos-Trigo, L. M. (2014). La resolución de problemas matemáticos. Fundamentos cognitivos. Trillas.

Santos-Trigo, M. (2024). Problem solving in mathematics education: Tracing its foundations and current research-practice trends. ZDM Mathematics Education, 56, 211-222. https://doi.org/10.1007/s11858-024-01578-8

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. https://doi.org/10.54870/1551-3440.1268

Santos-Trigo, M., Camacho-Machín, M., & Barrera-Mora, F. (2024). Focusing on foundational calculus ideas to understand the derivative concept via problem-solving tasks that involve the use of a dynamic geometry system. ZDM Mathematics Education, 56, 1287-1301.

https://doi.org/10.1007/s11858-024-01607-6

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. https://doi.org/10.1504/IJLT.2022.123686

Schoenfeld, A. (1985). Mathematical problem solving. Academic Press.

Published

2025-10-30

How to Cite

Hernández Hernández, A., Martín Ferraz, A., & Camacho Machín, M. (2025). Problem Posing in Pre-service Secondary Mathematics Teacher Education: Insights of using GeoGebra. Advances of Research in Mathematics Education, (28), 117–141. https://doi.org/10.35763/aiem28.7550

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