University of Valencia logo Logo Didactical, Historical and Epistemological Analysis of School Mathematics (ADHEME) Logo del portal

Group research publications

 

Research on the description of problem-solving processes in real-world contexts (modelling)

 

These first studies (2013–2017) aim to describe and characterise the procedure for solving modelling problems (understood as complex, open and defined problems in real contexts).

  • Gallart, C. & Ferrando, I.; García Raffi, L. M. (2014). Implementación de tareas de modelización abiertas en el aula de secundaria, análisis previo. In Investigación en Educación Matemática XVIII (pp. 327–336). Salamanca (Spain).
  • Gallart, C., Ferrando, I., & García Raffi, L. M. (2015). Análisis competencial de una tarea de modelización abierta. Números, 88, 93–103.
  • Ferrando, I., Gallart, C., & García-Raffi, L. M. (2017). Los niveles de codeterminación como herramientas para analizar las tareas de modelización matemática. In Évolutions contemporaines du rapport aux mathématiques et aux autres savoirs à l’école et dans la société (pp. 357–371). Available on: <https://citad4.sciencesconf.org>.
  • Gallart, C., Ferrando, I., García-Raffi, L. M., Albarracín, L., & Gorgorió, N. (2017). Design and implementation of a tool for analysing student products when they solve Fermi problems. In Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 265–275). Springer.
  • Gallart, C., Ferrando, I., & García-Raffi, L. M. (2017). Análisis de los procesos de resolución de tres tareas de modelización. Modelling in Science Education and Learning, 10(2), 137–152.
  • Ferrando, I., Albarracín, L., Gallart, C., García-Raffi, L. M., & Gorgorió, N. (2017). Análisis de los modelos matemáticos producidos durante la resolución de problemas de Fermi. Bolema: Boletim de Educação Matemática, 31, 220–242.

 

Research focused on the description and analysis of modelling proposals for secondary education students

 

These works present classroom proposals designed to incorporate modelling. Although approached from an educational research perspective, they are published in journals aimed at secondary education teachers, ensuring the transfer of research results.

  • Ferrando, I., & Segura, C. (2013). Una propuesta para trabajar la proporción desde el arte. Modelling in Science Education and Learning, 6, 61–71.
  • Ferrando, I., Castillo-Medina, J., & Pla-Castells, M. (2017). Videojuegos de estrategia en Educación Matemática: Una propuesta didáctica en secundaria. Epsilon, 97, 23–42.
  • Pla-Castells, M., Ferrando, I., & Robledo, M. F. (2019). A grandes problemas, grandes soluciones. Aula de innovación educativa, (282), 44–48.
  • Pla-Castells, M., García-Fernández, I., Gimeno, J., & Ferrando, I. (2019). Computer Animation to teach interpolation. Modelling in Science Education and Learning, 12(1), 31–46.

 

Research on teachers’ role in problem-solving in real-world contexts

 

Between 2013 and 2018, some members of the group have conducted research on teachers’ role in designing and implementing educational proposals based on modelling. 

  • Gallart, C. & Ferrando, I.; García-Raffi, L.M. (2015). El profesor ante la actividad modelizadora en el aula de secundaria. SUMA. Revista sobre la Enseñanza y Aprendizaje de las Matemáticas. 79, 9–16.
  • Calabuig, J. M., Ferrando, I., & Gallart, C.; García-Raffi, L. M.; Hurtado, D.; Sierra, L. (2015). La modelización como competencia transversal en el sistema educativo español. Uno. Revista de Didáctica de las Matemáticas, 69.
  • Ferrando, I., Segura, C., & Pla-Castells, M. (2017). Diseño de un curso de formación en línea para introducir la modelización como herramienta de enseñanza y aprendizaje de las matemáticas. In VIII Congreso Iberoamericano de Educación Matemática. Libro de actas (pp. 568–576). Madrid.
  • Gallart, C., Ferrando, I., & García-Raffi, L.M. (2018). Análisis del rol del profesor en la gestión de una actividad de modelización mediante un estudio de caso único. Ensayos, 33(2), 47–72.
  • Gallart, C., Ferrando, I., & García-Raffi, L. M. (2019) Modelización matemática en la educación secundaria: manual de uso. Modelling in Science Education and Learning. 12(1), 71–85.
  • Joglar, N.; Ferrando, I.; Abánades, M. A.; Arteaga, B.; Barrera, V.; Belmonte, J. M.; Crespo, R.; Fernández, I.; Fraile, A.; Hernández, E.; Liñán, M.; Macías, J.; Muñoz-Catalán, M. C.; Pla-Castells, M.; Ramírez, M.; Segura, C.; Tolmos, P.; Star, J. R. (2022) POEMat.ES: Pauta de observación de la enseñanza de matemáticas en educación secundaria. Avances de investigación en educación matemática, 20, 89–103.

 

Research on the impact of contextual or situational variables on the cognitive aspects of problem-solving in real-world contexts

 

Based on the results of publications analysing problem-solving in real-world contexts between 2013 and 2017, our team conducted research on the processes of solving estimation problems in real-world contexts (Fermi problems). Due to their characteristics, these problems enable to conduct detailed studies on the impact of the real context in which they are formulated on cognitive aspects, mainly problem-solving strategies.

  • Ferrando, I., Segura, C., & Pla-Castells, M. (2020). Relations entre contexte, situation et schéma de résolution dans les problèmes d’estimation. Canadian Journal of Science, Mathematics and Technology Education, 20, 557–573.
  • Ferrando, I., Segura, C., & Pla-Castells, M. (2021). Analysis of the Relationship between context and solution plan in modelling tasks involving estimations. In Mathematical Modelling Education in East and West. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 119–128). Springer.
  • Albarracín, L., Segura, C., Ferrando, I., & Gorgorió, N. (2022). Supporting mathematical modelling by upscaling real context in a sequence of tasks. Teaching Mathematics and its Applications: An International Journal of the IMA, 41(3), 183–197.
  • Segura, C., Ferrando, I., & Albarracín, L. (2023). Does collaborative and experiential work influence the solution of real-context estimation problems? A study with prospective teachers. The Journal of Mathematical Behavior, 70, 101040.

 

Research on cognitive (performance, flexibility and adaptability) and affective aspects during problem-solving in real-world contexts

 

These studies primarily analyse the performance, flexibility and adaptability of future teachers in solving Fermi problems, which are modelling problems that involve estimations in real contexts.

  • Ferrando, I. y Segura, C. (2020). Fomento de la flexibilidad matemática a través de una secuencia de tareas de modelización. Avances de investigación en educación matemática, 17, 84–97.
  • Segura, C. y Ferrando, I. (2021). Classification and Analysis of Pre-Service Teachers’ Errors in Solving Fermi Problems. Education Sciences, 11(8), 451–470.
  • Segura, C. y Ferrando, I. y Albarracín, L. (2021). Análisis de los factores de complejidad en planes de resolución individuales y resoluciones grupales de problemas de estimación de contexto real. Quadrante, 30(1), 31–51.
  • Segura, C. y Ferrando, I. (2023) ¿Qué estrategia es mejor para un problema de Fermi? Adaptabilidad de futuros maestros. Enseñanza de las Ciencias, 41(3), 133–151.
  • Segura, C.; Ferrando, I. (2023) Pre-service teachers’ flexibility and performance in solving Fermi problems. Educational Studies In Mathematics, 113, 207–227.
  • Ferrando, I., Segura, C., & Castillo-Medina, J. (in press). Regular and talented students’ behaviour when solving modelling tasks: are there differences? In Researching mathematical modelling education in disruptive/challenging times. Springer.
  • García-Cerdá, C., Segura, C., & Ferrando, I. (in press). Influence of the type of mathematical problems on students’ and pre-service teachers’ interest and performance. A replication and elaboration study. Implementation and Replication Studies in Mathematics Education.