Pre-service teachers’ challenges in implementing mathematical modelling: Insights into reality

• Autores: Carolina Guerrero Ortiz , Rita Borromeo Ferri
• Localización: PNA: Revista de investigación en didáctica de la matemática, ISSN-e 1887-3987, Vol. 16, Nº. 4, 2022 (Ejemplar dedicado a: (Julio, 2022)), págs. 309-341
• Idioma: inglés
• DOI: 10.30827/pna.v16i4.21329
• Títulos paralelos:
  • Los desafíos de los profesores en formación en la implementación de la modelación matemática. Una mirada en torno a la realidad
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    El modelado se ha vuelto obligatorio en los programas de estudio de muchos países, a menudo sin brindar a los profesores la capacitación necesaria para abordar este desafío. Mediante un estudio cualitativo, analizamos las tareas diseñadas por futuros profesores de matemáticas de secundaria. Identificamos cómo movilizan sus conocimientos para enseñar modelación en ausencia de formación para ello, elementos como traducción entre lenguajes, reconocimiento de datos desconocidos, covariación y uso de representaciones para la comprensión y resolución de problemas, fueron identificados. Los resultados también revelan que los participantes tienden a crear problemas verbales cuando intentan enseñar modelación por primera vez.

  • English

    Modelling has become mandatory in the school curricula in many countries across the globe, often without providing teachers the training needed to address this challenge. With a qualitative case study, we analyzed the tasks designed by secondary mathematics pre-service teachers. We recognized how participants manage their knowledge for teaching modelling in the absence of training. Elements of knowledge for teaching such as translation between languages, recognizing unknown data, covariation, and usefulness of representations for understanding and solving problems, were identified. Our results also reveal that future teachers have a tendency to create word problems when first attempting to teach modelling.

• Referencias bibliográficas
  • Andrews, P., & Sayers, J. (2012). Teaching linear equations: Case studies from Finland, Flanders and Hungary. Journal of Mathematical...
  • Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5),...
  • Bardin, L. (1986). El análisis de contenido. Akal.
  • Baumert, J., & Kunter, M. (2013). The COACTIV model of teachers’ professional competence. In M. Kunter, J. Baumert, W. Blum, et al. (Eds.),...
  • Birt, L., Scott, S., Cavers, D., Campbell, C., & Walters, F. (2016). Member checking: A tool to enhance trustworthiness or merely a nod...
  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we Know, what can we do? In S. Cho (Ed.), Proceedings of the 12th International...
  • Blum, W., Galbraith, P., Henn, H.-W., & Niss, M. (Eds.) (2007). Modelling and applications in mathematics education. Springer. https://doi.org/10.1007/978-0-387-29822-1
  • Bolsad, O. (2020). Secondary teachers’ operationalisation of mathematical literacy. European Journal of Science and Mathematics Education,...
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95. https://doi.org/10.1007/BF02655883
  • Borromeo Ferri, R. (2018). Learning how to teach mathematical modelling in school and teacher education. Springer.
  • Borromeo Ferri, R. (2019). Assessing teaching competencies for mathematical modelling. In U. T. Jankvist, M. van den Heuvel-Panhuizen, &...
  • Borromeo Ferri, R. (2021). Mandatory mathematical modelling in school! – What do we want the teachers to know? In F. Leung, G. Stillman, G....
  • Borromeo Ferri, R., & Blum, W. (2010). Mathematical modelling in teacher education – Experiences from a modelling seminar. In V. Durand-Guerrier,...
  • Borromeo Ferri, R., & Blum, W. (2014). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons....
  • Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modelling Dynamic events: a framework...
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes....
  • Cohen L., & Manion L. (2002). Métodos de investigación educativa. La Muralla.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems....
  • Doerr, H. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. L. Galbraith,...
  • Doerr, H., & English, L. (2006). Middle grade teachers' learning through students' engagement with modelling tasks. Journal of...
  • Doerr, H., Ärlebäck, J., & Misfeldt, M. (2017). Representations of modelling in mathematics education. In G. Stillman, W. Blum, &...
  • Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2),...
  • Greer, B. (1997). Modelling reality in mathematics classrooms: the case of word problems. Learning and Instruction, 7(4), 293-307. https://doi.org/10.1016/S0959-4752(97)00006-6
  • Guerrero-Ortiz, C. (2021). Pre-service mathematics teachers’ technological pedagogical content knowledge: The case of modelling. In F. K....
  • Guerrero-Ortiz, C & Reyes-Rodríguez, A. (2021). Matices que dan forma a las concepciones sobre la modelización de futuros profesores....
  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level...
  • Maaß, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285-311. https://doi.org/10.1007/s13138-010-0010-2
  • MINEDUC (2016). Matemática. Programa de estudio 8º básico. Ministerio de Educación Chile.
  • MINEDUC (2018a). Currículum Nacional. Actualización y vigencia curricular. Ministerio de Educación Chile.
  • MINEDUC (2018b). Programa de Estudio 3° Medio, Matemática. Unidad de Currículo y Evaluación. Ministerio de Educación Chile.
  • Montejo-Gámez, J., Fernández-Ahumada, E., & Adamuz-Povedano, N. (2021). A Tool for the Analysis and Characterization of School Mathematical...
  • Moreno, A., Marín. M., & Ramírez-Uclés, R. (2021). Errores de profesores de matemáticas en formación inicial al resolver una tarea de...
  • OECD (2013). PISA 2012 Assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. OECD Publishing.
  • Oropesa, C., Cortez, R., & Bennett, A. (2018). The emergence of mathematical modeling competencies: An investigation of prospective secondary...
  • Paolucci, C., & Wessels, H. (2017). An examination of preservice teachers’ capacity to create mathematical modelling problems for children....
  • Ramos-Rodríguez, E., Fernández-Ahumada, E., & Morales-Soto, A. (2022). Effective teacher professional development programs. A case study...
  • Sullivan, P., Knott, L., Yang, Y., Askew, M., Brown, L., Bartolini, M., …, Zodik, I. (2015). The relationships between task design, anticipated...
  • Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai...
  • Verschaffel, L., van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problems as exercises in mathematical modelling....
  • Villa, J., & Ruiz, H. (2009). Modelación en educación matemática: una mirada desde los lineamientos y estándares curriculares colombianos....
  • Wess, R., Klock, H., Siller, H-S., & Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modelling....
  • Yin, R. (2014). Case study research design and methods (5th ed.). Sage.