Making sense of modelling: the case of a group of pre-service teachers
DOI:
https://doi.org/10.48489/quadrante.23937Keywords:
Future teachers, mathematical modelling, sense, experience, educational trajectoriesAbstract
This paper addresses the results from a study about the production of meanings related to mathematical modelling processes by four mathematics pre-service teachers from an Argentinian national university, who were engaged in mathematical modelling activities. Specifically, we ask: What meanings do pre-service teachers give to Mathematical Modelling? Do these meanings vary? And if so, what variations become evident as pre-service teachers engage in different activities? To produce relevant information to answer the above questions, qualitative research was developed through a case study. Within the framework of the research, we designed a teaching proposal that was implemented by the teacher in charge of a course on Space geometry. When reporting and analysing the information produced, the characteristics of the teacher training environment are specified, as well as the main moments and activities that framed the mathematical work and the reflective processes experienced by the future teachers. Based on the conducted analysis, both the meanings produced by the pre-service teachers, as a group or individually, and their variations are delineated and documented. Based on the results of the study, brief contributions are made concerning the training of pre-service mathematics teachers.
References
Abel, T., Searcy, M. E., & Salinas, T. (2020). Sense-making with the mathematical modelling process: Developing a framework for faculty practice. In G. Stillman, G. Kaiser, & C. Lampen (Eds.), Mathematical modelling education and sense-making (pp.119-128). Springer. https://doi.org/10.1007/978-3-030-37673-4_11
Araújo, J. (2019). Toward a framework for a dialectical relationship between pedagogical practice and research. In G. A. Stillman, & J. P. Brown (Eds.), Lines of inquiry in mathematical modelling research in education (pp. 21-36). Springer. https://doi.org/10.1007/978-3-030-14931-4_2
Bajtín, M. (2010). Yo también soy. Taurus.
Bassanezi, R. (1994). Modelling as a teaching-learning strategy. For the Learning of Mathematics, 14(2), 31-35.
Bassanezi, R. (2002). Ensino-aprendizagem con modelagem matemática: Uma nova estratégia. Contexto.
Bishop, A. (1991). Enculturación matemática. La educación matemática desde una perspectiva cultural. Paidós.
Blomhøj, M. (2004). Mathematical modelling - A theory for practice. In B. Clarke, D. Clarke, G. Emanuelsson, B. Johannsson, D. Lambdin, F. Lester, A. Walby, & K. Walby (Eds.), International perspectives on learning and teaching mathematics (pp. 145-159). National Center for Mathematics Education.
Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer. https://doi.org/10.1007/978-3-319-68072-9
Borromeo Ferri, R. (2021). Mandatory mathematical modelling in school: What do we want the teachers to know? In F. K. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modelling education in East and West: International perspectives on the teaching and learning of mathematical modelling (pp. 103-118). Springer.
Britzman, D. P. (2003). Practice makes practice. University of New York.
Buenrostro, P., & Ehrenfeld, N. (2019). Math teachers sensemaking and enactment of the discourse of "Perseverance". In S. Otten, A. G. Candela, Z. de Araujo, C. Haines, & C. Munter (Eds.), Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 451-459). University of Missouri.
Carter, K. (1993). The place of story in the study of teaching and teacher education. Educational Researcher, 22(1), 5-18. https://doi.org/10.3102/0013189X022001005
Confrey, J. (2005). The evolution of design studies as methodology. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 135-152). Cambridge University Press.
Cruz, M. F., Esteley, C., & Scaglia, S. (2018). Validar, justificar, demostrar en voces de futuros profesores en matemática. Memorias de la VII Reunión Pampeana de Educación Matemática (Vol 7, pp. 105-116). Santa Rosa de la Pampa, Universidad Nacional de La Pampa, Facultad de Ciencias Exactas y Naturales.
Cruz, M. F., Esteley, C., & Scaglia, S. (2020). Una experiencia de formación para futuros profesores: producir matemática en un contexto de modelización matemática vinculada con fenómenos geométricos. Educación Matemática, 32(1), 193-220. https://doi.org/10.24844/EM3201.09
da Ponte, J. P., Segurado, M. I., & Oliveira, H. (2003). A collaborative project using narratives: What happens when pupils work on mathematical investigations? In A. Perter-Koop, V. Santos-Wagner, C. Breen, & A. Begg (Eds.), Collaboration in teacher education: Examples from the context of mathematics education (pp. 85-97). Kluwer. https://doi.org/10.1007/978-94-017-1072-5_7
Denzin, N. K. & Lincoln, Y. S. (2018). The SAGE handbook of qualitative research (5th Ed.). SAGE.
Dewey, J. (1958). Experiencia y educación. Losada.
Doerr, H. M., Ärlebäck, J. B., & Misfeldt, M. (2017). Representations of modelling in mathematics education. In G. Stillman, W., Blum, & G. Kaiser (Eds.), Mathematical modelling and applications. Crossing and researching boundaries in mathematics education (pp. 71-82). Springer. https://doi.org/10.1007/978-3-319-62968-1_6
Durandt, R., & Lautenbach, G. (2020). Pre-service teachers’ sense-making of mathematical modelling through a Design-Based Research strategy. In G. Stillman, G. Kaiser, & C. Lampen (Eds.), Mathematical modelling education and sense-making (pp. 431-442). Springer. https://doi.org/10.1007/978-3-030-37673-4_37
Esteley, C. (2014). Desarrollo profesional en escenarios de modelización matemática: Voces y sentidos. Editorial de la Facultad de Filosofía y Humanidades de la Universidad Nacional de Córdoba.
Gazzetta, M. (1989). A modelagem como estratégia de aprendizagem da Matemática em cursos de aperfeiçoamento de profesores (Tesis de maestría). Universidade Estadual Paulista, São Paulo, Brasil.
Goos, M. (2020). Communities of practice in mathematics teacher education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Second Edition (pp. 107-110). Springer. https://doi.org/10.1007/978-3-030-15789-0_26
Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. (pp. 503-510). Springer.
Kaiser, G. (2020). Mathematical modelling and applications in education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Second Edition. (pp. 553-561). Springer.
Kazez, R. (2009). Los estudios de casos y el problema de la selección de la muestra: aportes del sistema de matrices de datos. Subjetividad y procesos cognitivos, 13(1), 71-89.
Keazer, L. M., & Menon, R. S. (2015/6). Reasoning and sense making begins with the teacher. The Mathematics Teacher, 109(5), 342–349. https://doi.org/10.5951/mathteacher.109.5.0342
Lakatos, I. (1986). Pruebas y refutaciones. La lógica del descubrimiento matemático. Alianza.
Lamb, J., & Visnovska, J. (2015). Developing statistical numeracy: The model must make sense. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 363–373). Springer.
Larrosa, J. (2003). Entre las lenguas. Lenguaje y educación después de Babel. Laertes.
Lave, J. (1991). La cognición en la práctica. Paidós.
Lewis, S. T. (2021). Theorizing ‘Modelling as Bridge’ between content and vehicle. In F. K. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modelling education in East and West: International perspectives on the teaching and learning of mathematical modelling. (pp. 45-54). Springer.
Lingefjärd, T. (2013). Teaching mathematical modeling in teacher education: Efforts and results. In X-S. Yang (Ed.), Mathematical modeling with multidisciplinary applications (pp. 57–80). John Wiley & Sons.
Mina, M., Esteley, C., & Alterman, N. (2019). Sobre la modelización matemática en diseños curriculares. El caso del Ciclo Básico de la Educación Secundaria de la Provincia de Córdoba. Resúmenes de las XI Jornadas de Investigación en Educación. Área de Educación de la Facultad de Filosofía y Humanidades, Universidad Nacional de Córdoba. 9 al 11 de octubre de 2019. (Tomo II, pp. 119-130). https://rdu.unc.edu.ar/handle/11086/12877
Sadovsky, P. (2005). Enseñar matemática hoy. Zorzal.
Sevinc, S. & Lesh, R. (2018). Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses. ZDM Mathematics Education, 50, 301-314. https://doi.org/10.1007/s11858-017-0898-9
Stake, R. (1998). Investigación con estudio de casos. Morata.
Stillman, G., Blum, W., & Biembengut, S. (Eds.). (2015). Mathematical modelling in education research and practice cultural, social and cognitive influences. Springer.
Stillman, G., Blum, W., & Kaiser, G. (Eds.). (2017). Mathematical modelling and applications. Crossing and researching boundaries in mathematics education. Springer.
Stillman, G., & Brown, J. (Eds.). (2019). Lines of inquiry in mathematical modelling research in education. Springer.
Stillman, G., Kaiser, G., Blum, W., & Brown, J. (Eds.). (2013). Teaching mathematical modelling: Connecting to research and practice. Springer.
Stillman, G., Kaiser, G., & Lampen, C. (Eds.). (2020). Mathematical modelling education and sense-making. Springer.
The Design-Based Research Collective. (2003). Design-Based Research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5-8. https://doi.org/10.3102/0013189X032001005
Vezub, L. F. (2013). Hacia una pedagogía del desarrollo profesional docente: modelos de formación continua y necesidades formativas de los profesores. Páginas de Educación, 6(1), 97-124.
Villa-Ochoa, J., Castrillón-Yepes, A., & Sánchez-Cardona, J. (2017). Tipos de tareas de modelación para la clase de matemática. Espaço Plural, 18(36), 219-251.
Villarreal, M., & Esteley, C. (2017). Futuros profesores de matemática: Narrativas de sus primeras prácticas en escenarios de modelización. In S. Smith, M. Villarreal, D. Fregona, & F. Viola (Eds.), Formación de profesores que enseñan matemática y prácticas educativas en diferentes escenarios. Aportes para la educación matemática (pp. 25-50). Universidad Nacional de Córdoba.
Villarreal, M., Esteley, C., & Smith, S. (2018). Pre-service teachers working in mathematical modelling scenarios with digital technologies. ZDM Mathematics Education 50, 327-341. https://doi.org/10.1007/s11858-018-0925-5
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) belongs to Quadrante. Nevertheless, we encourage articles to be published in institutional or personal repositories as long as their original publication in Quadrante is identified and a link to the journal's website is included.
