Oportunidades de las tareas auténticas de modelación en el aprendizaje de la modelización matemática para la enseñanza. Un estudio con futuros profesores de matemáticas

Paula Andrea Rendón-Mesa; Monica Marcela Parra-Zapata; Jhony Alexander Villa-Ochoa

doi:10.17533/udea.unipluri.358071

Authors

Paula Andrea Rendón-Mesa Institución Educativa Pedro Luis Álvarez Correa (Caldas Antioquia) y Universidad de Antioquia (Medellín) https://orcid.org/0000-0001-6851-3302
Monica Marcela Parra-Zapata Institución Educativa Mariscal Robledo, y Universidad de Antioquia (Medellín) https://orcid.org/0000-0002-8844-0013
Jhony Alexander Villa-Ochoa Universidad de Antioquia https://orcid.org/0000-0003-2950-1362

DOI:

https://doi.org/10.17533/udea.unipluri.358071

Keywords:

mathematical modelling, prospective teacher education, authentic modelling tasks, authenticity

Abstract

Teacher learning on mathematical modelling is a significant goal of mathematics education. This article presents the results of a study conducted within a course designed for prospective teachers. Rooted in the principles of authentic learning, authentic tasks were designed to promote the prospective teacher's learning of mathematical modelling and its teaching. Data were collected from 18 prospective teachers across two groups of a mathematical modelling course at a public University. Analysis of documents, videos, and interviews evidenced the learning achieved by prospective teachers about learning environment configuration, use of context, and modelling project development. The results of this study provide empirical evidence regarding characteristics and components that configure authentic tasks that contribute to mathematical modelling learning and its teaching. Some implications regarding the way to integrate authenticity in mathematical modelling emerged from this study.

|Abstract

= 225 veces | PDF

= 52 veces|

Downloads

Author Biographies

Paula Andrea Rendón-Mesa, Institución Educativa Pedro Luis Álvarez Correa (Caldas Antioquia) y Universidad de Antioquia (Medellín)

Es profesora de la Institución Educativa Pedro Luis Álvarez Correa (Caldas Antioquia) y de la Universidad de Antioquia (Medellín). Integrante de la Red Colombiana de Modelación en Educación Matemática.

Monica Marcela Parra-Zapata, Institución Educativa Mariscal Robledo, y Universidad de Antioquia (Medellín)

Es profesora de la Institución Educativa Mariscal Robledo y de la Universidad de Antioquia (Medellín). Integrante de la Red Colombiana de modelación en Educacion Matemática RECOMEM.

Jhony Alexander Villa-Ochoa, Universidad de Antioquia

Es profesor de la Facultad de Educación de la Universidad de Antioquia e integrante de la Red Colombiana de Modelación en Educacion Matemática - RECOMEM.

References

Almeida, L. M. W., & Omodei, L. B. C. (2022). Autenticidade em Atividades de Modelagem Matemática: em busca de um design. Educação Matemática Pesquisa Revista Do Programa de Estudos Pós-Graduados Em Educação Matemática, 24(3), 108–144. https://doi.org/10.23925/1983-3156.2022v24i3p108-144

Barab, S. a., Squire, K. D., & Dueber, W. (2000). A co-evolutionary model for supporting the emergence of authenticity. Educational Technology Research and Development, 48(2), 37–62. https://doi.org/10.1007/BF02313400

Bernabeu-Martínez, M., Moreno, M., & Llinares, S. (2019). Experimentos de enseñanza. Características de una intervención basada en el aula de educación primaria para la enseñanza del concepto de polígono. Uni-Pluriversidad, 19(2), 103–123. https://doi.org/10.17533/udea.unipluri.19.2.07

Beswick, K. (2011). Putting context in context: an examination of the evidence for the benefits of ‘contextualised’ tasks. International Journal of Science and Mathematics Education, 9(2), 367–390. https://doi.org/10.1007/s10763-010-9270-z

Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In Trends in teaching and learning of mathematical modelling (pp. 15–30). Springer.

Blum, W., & Borromeo-Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.

Blum, W., Galbraith, P., Henn, H., & Niss, M. (Eds.). (2007). Modelling and Applications in Mathematics Education. The 14th ICMI Study (Vol. 10). Springer.

Bogdan, R., & Biklen, S. K. (2007). Qualitative Research for Education: An Introduction to Theories and Methods (fifth). Pearson.

Borba, M. C., & Villarreal, M. E. (2005). Humans-with-Media and the Reorganization of Mathematical Thinking (Vol. 39). Springer. https://doi.org/10.1007/b105001

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa

Braun, V., Clarke, V., Hayfield, N., & Terry, G. (2019). Thematic Analysis. In Handbook of Research Methods in Health Social Sciences (pp. 843–860). Springer Singapore. https://doi.org/10.1007/978-981-10-5251-4_103

Cáceres, M. J., Chamoso, J. M., & Cárdenas, J. A. (2015). Situaciones problemáticas auténticas propuestas por estudiantes para maestros. In C. Fernández, M. Molina, & N. Planas (Eds.), Investigación en Educación Matemática XIX (pp. 201–210). SEIEM.

Carmona-Mesa, J. A., Cardona Zapata, M. E., & Castrillón-Yepes, A. (2020). Estudio de fenómenos físicos en la formación inicial de profesores de Matemáticas. Una experiencia con enfoque STEM. Uni-Pluriversidad, 20(1), e2020101. https://doi.org/10.17533/udea.unipluri.20.1.02

Cetinkaya, B., Kertil, M., Erbas, A. K., Korkmaz, H., Alacaci, C., & Cakiroglu, E. (2016). Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course. Mathematical Thinking and Learning, 18(4), 287–314. https://doi.org/10.1080/10986065.2016.1219932

Didis, M. G., Erbas, A. K., Cetinkaya, B., Cakiroglu, E., & Alacaci, C. (2016). Exploring prospective secondary mathematics teachers’ interpretation of student thinking through analysing students’ work in modelling. Mathematics Education Research Journal, 28(3), 349–378. https://doi.org/10.1007/s13394-016-0170-6

Doerr, H. M., & Pratt, D. (2008). The learning of mathematics and mathematical modeling. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Research syntheses (pp. 259–285). Information Age.

García, M., Sánchez, V., Escudero, I., & Llinares, S. (2006). The Dialectic Relationship between Research and Practice in Mathematics Teacher Education. Journal of Mathematics Teacher Education, 9(2), 109–128. https://doi.org/10.1007/s10857-006-0003-8

Greefrath, G., & Vos, P. (2021). Video-based Word Problems or Modelling Projects—Classifying ICT-based Modelling Tasks. In F. Koon, S. Leung, G. A. Stillman, G. Kaisee, & K. L. Wong (Eds.), Mathematical Modelling Education in East and West (pp. 489–499). Springer International Publishing. https://doi.org/10.1007/978-3-030-66996-6_41

Herminio, M. J. G. B., & Borba, M. C. (2010). A Noção de Interesse em Projetos de Modelagem Matemática. Educação Matemática Pesquisa, 12(1), 111–127.

Herrington, J., & Parker, J. (2013). Emerging technologies as cognitive tools for authentic learning. British Journal of Educational Technology, 44(4), 607–615. https://doi.org/10.1111/bjet.12048

Herrington, J., Reeves, T. C., & Oliver, R. (2010). A guide to authentic e-learning. Routledge. https://doi.org/10.1111/j.1467-8535.2010.01154_4.x

Julie, C., & Mudaly, V. (2007). Mathematical Modelling of Social Issues in School Mathematics in South Africa. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and Applications in Mathematics Education (Vol. 10, Issue February, pp. 503–510). Springer US. https://doi.org/10.1007/978-0-387-29822-1_58

Kaiser, G. (2014). Mathematical Modelling and Applications in Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 396–404). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_101

Kaiser, G. (2017). The Teaching and Learning of Mathematical Modeling. In J. Cai (Ed.), Compendium for Research in Mathematics Education (pp. 267–291). NCTM.

Kaiser, G., & Schwarz, B. (2010). Authentic Modelling Problems in Mathematics Education—Examples and Experiences. Journal Für Mathematik-Didaktik, 31(1), 51–76. https://doi.org/10.1007/s13138-010-0001-3

Molina-Toro, J. F., Rendón-Mesa, P. A., & Villa-Ochoa, J. A. (2019). Research Trends in Digital Technologies and Modeling in Mathematics Education. EURASIA Journal of Mathematics, Science and Technology Education, 15(8), em1736. https://doi.org/10.29333/ejmste/108438

Niss, M. (1992). Applications and modelling in school mathematics—directions for future development. IMFUFA Roskilde Universitetscenter.

Niss, M. (2001). Issues and Problems of Research on the Teaching and Learning of Applications and Modelling. In J. F. Matos, W. Blum, K. Houston, & S. Carreira (Eds.), Modelling and Mathematics Education. ICTMA 9: Applications in Science and Technology (pp. 72–89). Horwood.

Ocampo-Arenas, M. C., & Parra-Zapata, M. M. (2022). Una experiencia de modelación matemática en educación primaria en un contexto de Educación Ambiental. Uni-Pluriversidad, 22(1), 1–16. https://doi.org/10.17533/udea.unipluri.348824

Parra-Zapata, M. M., Parra-Zapata, J. N., Ocampo-Arenas, M. C., & Villa-Ochoa, J. A. (2016). El Índice de Masa Corporal. Una experiencia de modelación y uso de modelos matemáticos para el aula de clase. Números. Revista de Didáctica de Las Matemáticas, 92, 21–33.

Ponte, J. P. (2014). Formação do professor de Matemática: Perspetivas atuais. In J. P. Ponte (Ed.), Práticas profissionais dos professores de Matemática (pp. 343–358). Instituto de Educação da Universidade de Lisboa.

Rellensmann, J., Schukajlow, S., & Leopold, C. (2017). Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance. Educational Studies in Mathematics, 95(1), 53–78. https://doi.org/10.1007/s10649-016-9736-1

Rendón-Mesa, P. A. (2016). Articulación entre la matemática y el campo de acción de la ingeniería de diseño de producto: aportes de la modelación matemática [Tesis de Doctorado en Educación (No publicado)]. Universidad de Antioquia.

Rendón-Mesa, P. A., Villa-Ochoa, J. A., & Suárez Téllez, L. (2021). Seminario Repensar las Matemáticas como estrategia para la formación de futuros profesores de matemáticas: caso de la modelación matemática. In A. Y. Soto Lazcano & L. Suárez-Téllez (Eds.), Repensar las didácticas específicas: una aportación multidisciplinaria a la enseñanza especializada (pp. 105–121). REDIECH.

Strobel, J., Wang, J., Weber, N. R., & Dyehouse, M. (2013). The role of authenticity in design-based learning environments: The case of engineering education. Computers & Education, 64, 143–152. https://doi.org/10.1016/j.compedu.2012.11.026

Stylianides, A. J., & Stylianides, G. J. (2013). Seeking research-grounded solutions to problems of practice: Classroom-based interventions in mathematics education. ZDM - Mathematics Education, 45(3), 333–341. https://doi.org/10.1007/s11858-013-0501-y

Vicente, S., & Manchado, E. (2016). Arithmetic word problem solving. Are authentic word problems easier to solve than standard ones? / Resolución de problemas aritméticos verbales. ¿Se resuelven mejor si se presentan como problemas auténticos? Infancia y Aprendizaje, 39(2), 349–379. https://doi.org/10.1080/02103702.2016.1138717

Villa-Ochoa, J. A. (2015). Modelación matemática a partir de problemas de enunciados verbales: un estudio de caso con profesores de matemáticas. Magis, Revista Internacional de Investigación En Educación, 8(16), 133–148. https://doi.org/10.11144/Javeriana.m8-16.mmpe

Villa-Ochoa, J. A., & Berrío, M. J. (2015). Mathematical Modelling and Culture: An Empirical Study. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical Modelling in Education Research and Practice, International Perspectives on the Teaching and Learning (pp. 241–250). Springer. https://doi.org/10.1007/978-3-319-18272-8_19

Villa-Ochoa, J. A., & López, C. M. J. (2011). Sense of Reality Through Mathematical Modelling. In G. Kaiser, W. Blum, R. Borromeo-Ferri, & G. A. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling (pp. 701–711). Springer. https://doi.org/10.1007/978-94-007-0910-2_67

Villa-Ochoa, J. A., Sánchez-Cardona, J., & Parra-Zapata, M. M. (2022). Modelación matemática en la perspectiva de la educación matemática. In M. Rodríguez, M. Pochulu, & F. Espinoza (Eds.), Educación matemática. Aportes a la formación docente desde distintos enfoques teóricos (pp. 67–89). Ediciones Universidad Nacional de General Sarmiento.

Villa-Ochoa, J. A., Sánchez-Cardona, J., & Rendón-Mesa, P. A. (2021). Formative Assessment of Pre-Service Teachers’ Knowledge on Mathematical Modeling. Mathematics, 9(8), 851. https://doi.org/10.3390/math9080851

Villarreal, M. E., Esteley, C. B., & Smith, S. (2018). Pre-service teachers’ experiences within modelling scenarios enriched by digital technologies. ZDM – Mathematics Education, 50(1–2), 327–341. https://doi.org/10.1007/s11858-018-0925-5

Widjaja, W. (2013). Building Awareness of Mathematical Modelling in Teacher Education: A Case Study in Indonesia. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching Mathematical Modelling: Connecting to Research and Practice (pp. 583–593). Springer Netherlands. https://doi.org/10.1007/978-94-007-6540-5_50