Educational experience on modelling for Panamanian mathematics teachers

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Published: Feb 19, 2024
Updated: 2024-02-19
Versions:
2024-02-19 (7)
DOI: https://doi.org/10.17163/alt.v19n1.2024.05
Keywords:
Diploma, Mathematical modelling, Mathematics teachers, Panama, Practising teachers, Teacher education.

Main Article Content

Carlos Ledezma
Universidad de Barcelona
https://orcid.org/0000-0001-9274-7619
Luisa Morales-Maure
Universidad de Panamá
https://orcid.org/0000-0003-3905-9002
Vicenc Font
Universidad de Barcelona
https://orcid.org/0000-0003-1405-0458

Abstract

Internationally, mathematical modelling has been gaining an important space in educational curricula, this is why the teaching of this process has been included in educational programmes for mathematics teachers. Due to this importance, in this study, an educational experience on modelling for practising secondary education mathematics teachers from the Panamanian school system is reported, whose objective is to analyse the solving procedures of these teachers to modelling problems and classify these solving procedures. The context is the Diploma Course in Mathematics Education Applied to Secondary Education, taught by the University of Panama, which included a submodule on modelling. The “modelling cycle from a cognitive perspective”, which was taught in the submodule, was used to analyse the solving procedures for three problems posed to the participating teachers, through the written productions that they uploaded to the virtual platform of the diploma course. Four solving procedures could be identified in the 40 productions analysed, which varied from not totally understanding the wording of the problems to developing a whole modelling cycle. With these results, it is intended to provide a first overview of the teaching and learning of modelling in the Panamanian context and to lay the foundations for possible curricular adaptations to mathematics teaching.

Article Details

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Vol. 19 No. 1 (2024): (January-June 2024): Teacher training
Section
Central Theme
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References

Abassian, A., Safi, F., Bush, S., y Bostic, J. (2020). Five different perspectives on mathematical modeling in athematics education. Investigations in Mathematics Learning, 12(1), 53–65. https://doi.org/10.1080/19477503.2019.1595360

Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. En G. Kaiser, W. Blum, R. Borromeo Ferri, y G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling: ICTMA 14 (pp. 15–30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3

Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? En S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and Attitudinal Challenges (pp. 73–96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9

Blum, W., y Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58. https://bit.ly/3IEeWA0

Blum, W., y Leiß, D. (2007). How do students and teachers deal with modelling problems? En C. Haines, P. Galbraith, W. Blum, y S. Khan (Eds.), Mathematical Modelling (ICTMA 12): Education, Engineering and Economics (pp. 222–231). Horwood. https://doi.org/10.1533/9780857099419.5.221

Blomhøj, M. (2004). Mathematical modelling: A theory for practice. En B. A. Clarke, D. M. Clarke, G. Emanuelsson, B. Johansson, D. V. Lambdin, F. Lester, A. Wallby, y K. Wallby (Eds.), International Perspectives on Learning and Teaching Mathematics (pp. 145–159). National Center for Mathematics Education.

Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86–95. https://doi.org/10.1007/bf02655883

Borromeo Ferri, R. (2007). Personal experiences and extra-mathematical knowledge as an influence factor on modelling routes of pupils. En D. Pitta-Pantazi y C. Philippou (Eds.), European Research in Mathematics Education V: Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2080–2089). University of Cyprus, ERME.

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

Breda, A., y Lima, V. M. d. R. (2016). Estudio de caso sobre el análisis didáctico realizado en un trabajo final de un máster para profesores de matemáticas en servicio. REDIMAT: Journal of Research in Mathematics Education, 5(1), 74–103. https://doi.org/10.17583/redimat.2016.1955

Cohen, L., Manion, L., y Morrison, K. (2018). Research Methods in Education (8ª ed.). Routledge.

Doerr, H. M., y English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136. https://doi.org/10.2307/30034902

English, L. (2003). Mathematical modelling with oung learners. En S. J. Lamon, W. A. Parker, y K. Houston (Eds.), Mathematical Modelling: A Way of Life – ICTMA 11 (pp. 3–17). Horwood.

English, L. D. (2013). Modeling with complex data in the primary school. En R. Lesh, P. L. Galbraith, C. Haines, y A. Hurford (Eds.), Modeling Students’ Mathematical Modeling Competencies: ICTMA 13 (pp 287–299). Springer. https://doi.org/10.1007/978-94-007-6271-8_25

García-Marimón, O. (2023). Evaluando la Idoneidad Didáctica de Participantes en el Diplomado Semipresencial de Estrategias para la Enseñanza Idónea de la Matemática para Maestros en Ejercicio en la República de Panamá [Tesis doctoral no publicada]. Universitat de Barcelona.

García-Marimón, O., Diez-Palomar, J., Morales-Maure, L., y Durán-González, R. E. (2021). Evaluación de secuencias de aprendizaje de matemáticas usando la herramienta criterios de idoneidad didáctica. BOLEMA: Boletim de Educação Matemática, 35(70), 1047–1072. http://doi.org/10.1590/1980-4415v35n70a23

Greefrath, G., Siller, H.-S., Klock, H., y Wess, R. (2022). Pre-service secondary teachers’ pedagogical content knowledge for the teaching of mathematical modeling. Educational Studies in Mathematics, 109(2), 383–407. https://doi.org/10.1007/s10649-021-10038-z

Kaiser, G., y Brand, S. (2015). Modelling ompetencias: Past development and further perspectives. En G. Stillman, W. Blum, y M. S. Biembengut (Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences (pp. 129–149). Springer. https://doi.org/10.1007/978-3-319-18272-8_10

Kuntze, S., Siller, H.-S., y Vogl, C. (2013). Teachers’ self-perceptions of their pedagogical content knowledge related to modelling – An empirical study with Austrian teachers. En G. A. Stillman, G. Kaiser, W. Blum, y J. P. Brown (Eds.), Teaching Mathematical Modelling: Connecting to Research and Practice (pp. 317–326). Springer. https://doi.org/10.1007/978-94-007-6540-5_26

Ledezma, C., Font, V., y Sala, G. (2022). Analysing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives. Mathematics Education Research Journal. Artículo individual. https://doi.org/10.1007/s13394-022-00411-3

Ledezma, C., Sol, T., Sala-Sebastià, G., y Font, V. (2022). Knowledge and beliefs on mathematical modelling inferred in the argumentation of a prospective teacher when reflecting on the incorporation of this process in his lessons. Mathematics, 10(18), Artículo 3339. https://doi.org/10.3390/math10183339

Lesh, R., y Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. En R. Lesh y H. M. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 3–33). Lawrence Erlbaum.

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

Maass, K., Artigue, M., Burkhardt, H., Doorman, M., English, L. D., Geiger, V., Krainer, K., Potari, D., y Schoenfeld, A. (2022). Mathematical modeling – A key to citizenship education. En N. Buchholtz, B. Schwarz, y K. Vorhölter (Eds.), Initiationen mathematikdidaktischer Forschung: Festschrift zum 70. Geburtstag von Gabriele Kaiser (pp. 31–50). Springer. https://doi.org/10.1007/978-3-658-36766-4_2

Manouchehri, A. (2017). Implementing mathematical modelling: The challenge of teacher educating. En G. Stillman, W. Blum, y G. Kaiser (Eds.), Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education (pp. 421–432). Springer. https://doi.org/10.1007/978-3-319-62968-1_35

Ministerio de Educación de Panamá. (2014a). Programa de Matemática – Décimo Grado. Autor. Disponible en: http://www.educapanama.edu.pa/sites/default/files/documentos/programas-educacion-media-academica-matematica-10-2014.pdf

Ministerio de Educación de Panamá. (2014b). Programa de Matemática – Undécimo Grado. Autor. Disponible en: http://www.educapanama.edu.pa/sites/default/files/documentos/Programas-Educacion-MEDIA-ACADEMICA-matematica-11-2014.pdf

Ministerio de Educación de Panamá. (2014c). Programa de Matemática – Duodécimo Grado. Autor. Disponible en: http://www.educapanama.edu.pa/sites/default/files/documentos/Prog-Educ-MEDIA-matematica-12-2014.pdf

Morales-Maure, L. (2019). Competencia de Análisis e Intervención Didáctica del Docente de Primaria en Panamá [Tesis doctoral, Universitat de Barcelona]. Dipòsit Digital de la Universitat de Barcelona. https://hdl.handle.net/2445/151343

Morales, L, Durán, R., Pérez, C., y Bustamante, M. (2019). Hallazgos en la formación de profesores para la enseñanza de la matemática desde la idoneidad didáctica: Experiencia de cinco regiones educativas de Panamá. Revista Inclusiones, 6(Número especial), 142–169.

Ng, K. E. D. (2010). Initial experiences of primary school teachers with mathematical modelling. En B. Kaur y J. Dindyal (Eds.), Mathematical Applications and Modelling: Yearbook 2010, Association of Mathematics Educators (pp. 129–147). World Scientific Publishing. https://doi.org/10.1142/7798_0008

Ng, K. E. D. (2013). Teacher readiness in mathematical modelling: Are there differences between pre-service and in-service teachers? En G. A. Stillman, G. Kaiser, W. Blum, y J. P. Brown (Eds.), Teaching Mathematical Modelling: Connecting to Research and Practice (pp. 339–348). Springer. https://doi.org/10.1007/978-94-007-6540-5_28

Organisation for Economic Co-operation and Development. (2019). PISA 2018 Assessment and Analytical Framework. OECD Publishing. https://doi.org/10.1787/b25efab8-en

Palm, T. (2007). Features and impact of the authenticity of applied mathematical school tasks. En W. Blum, P. L. Galbraith, H.-W. Henn, y M. Niss (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (pp. 201–208). Springer. https://doi.org/10.1007/978-0-387-29822-1_20

Preciado, A. P., Peña, F., Ortiz, Y. A., y Solares, A. (2023). Diversity of perspectives on mathematical modelling: A review of the international landscape. En G. Greefrath, S. Carreira, y G. A. Stillman (Eds.), Advancing and Consolidating Mathematical Modelling: Research from ICME-14 (pp. 43–57). Springer. https://doi.org/10.1007/978-3-031-27115-1_3

Pollak, H. (2007). Mathematical modelling – A conversation with Henry Pollak. En W. Blum, P. L. Galbraith, H.-W. Henn, y M. Niss (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (pp. 109–120). Springer. https://doi.org/10.1007/978-0-387-29822-1_9

Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. En A. H. Schoenfeld (Ed.), Mathematical Thinking and Problem Solving (pp. 53–70). Erlbaum.

Shahbari, J. A., y Tabach, M. (2019). Adopting the modelling cycle for representing prospective and practising teachers’ interpretations of students’ modelling activities. En G. A. Stillman y J. P. Brown (Eds.), Lines of Inquiry in Mathematical Modelling Research in Education (pp. 179–196). Springer. https://doi.org/10.1007/978-3-030-14931-4_10

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004

Wess, R., Klock, H., Siller, H.-S., y Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modelling. En F. K. S. Leung, G. A. Stillman, G. Kaiser, y K. L. Wong (Eds.), Mathematical Modelling Education in East and West (pp. 249–260). Springer. https://doi.org/10.1007/978-3-030-66996-6_21