Contenido principal del artículo

Carolina Guerrero Ortiz
Pontificia Universidad Católica de Valparaíso
Chile
https://orcid.org/0000-0001-8765-1815
Rita Borromeo Ferri
Universidad de Kassel
Alemania
https://orcid.org/0000-0001-8223-3729
Vol. 16 Núm. 4 (2022): (Julio, 2022), Artículos, Páginas 309-341
DOI: https://doi.org/10.30827/pna.v16i4.21329
Recibido: May 24, 2021 Aceptado: Apr 20, 2022 Publicado: Jun 23, 2022

Resumen

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.

Descargas

La descarga de datos todavía no está disponible.

Detalles del artículo

Citas

Andrews, P., & Sayers, J. (2012). Teaching linear equations: Case studies from Finland, Flanders and Hungary. Journal of Mathematical Behavior, 31(4), 476-488. https://doi.org/10.1016/j.jmathb.2012.07.002

Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554

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.), Cognitive activation in the mathematics classroom and professional competence of teachers - Results from the COACTIV project (pp. 25-48). Springer.

Birt, L., Scott, S., Cavers, D., Campbell, C., & Walters, F. (2016). Member checking: A tool to enhance trustworthiness or merely a nod to validation? Qualitative Health Research, 26(13), 1802-1811. https://doi.org/10.1177/1049732316654870

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 Congress on Mathematical Education (pp. 73-96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9

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, 8(3), 115-135. https://doi.org/10.30935/scimath/9551

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, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 1154-1161). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

Borromeo Ferri, R. (2021). Mandatory mathematical modelling in school! – What do we want the teachers to know? In F. Leung, G. Stillman, G. Kaiser, & K. Wong (Eds.), Mathematical modelling education in east and west (pp. 103-117). Springer. https://doi.org/10.1007/978-3-030-66996-6_12.

Borromeo Ferri, R., & Blum, W. (2010). Mathematical modelling in teacher education – Experiences from a modelling seminar. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 2046-2055). INRP.

Borromeo Ferri, R., & Blum, W. (2014). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), CERME 8 - Proceedings of the Eight Congress of the European Society for Research in Mathematics Education (pp. 1000-1009). Ankara.

Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modelling Dynamic events: a framework and a study. Journal for Research in Mathematics Education, 33(5), 352-378. https://doi.org/10.2307/4149958

Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149-158. https://doi.org/10.1007/s11858-005-0004-6

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. Journal Mathematics Teacher Education, 11(5), 395-415. https://doi.org/10.1007/s10857-008-9081-0

Doerr, H. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. L. Galbraith, H. W. Henn, and, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 69-78). Springer. https://doi.org/10.1007/978-0-387-29822-1_5

Doerr, H., & English, L. (2006). Middle grade teachers' learning through students' engagement with modelling tasks. Journal of Mathematics Teacher Education, 9(1), 5-32. https://doi.org/10.1007/s10857-006-9004-x

Doerr, H., Ärlebäck, J., & 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

Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19-25. https://www.jstor.org/stable/40247950

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. S. 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. 141-151). Springer. https://doi.org/10.1007/978-3-030-66996-6_12

Guerrero-Ortiz, C & Reyes-Rodríguez, A. (2021). Matices que dan forma a las concepciones sobre la modelización de futuros profesores. Revista electrónica de investigación en educación en ciencias. 16, 48-61. https://reiec.niecyt.exa.unicen.edu.ar/volumen-16-n%C3%BAmero-2-2021-actual

Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549. https://doi.org/10.2307/749690

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 Models. Mathematics, 9, 1569. https://doi.org/10.3390/math9131569

Moreno, A., Marín. M., & Ramírez-Uclés, R. (2021). Errores de profesores de matemáticas en formación inicial al resolver una tarea de modelización. PNA, 15(2), 109-136. https://doi.org/10.30827/pna.v15i2.20746

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 mathematics teachers. Mathematical Thinking and Learning, 20(3), 202-221. https://doi.org/10.1080/10986065.2018.1474532

Paolucci, C., & Wessels, H. (2017). An examination of preservice teachers’ capacity to create mathematical modelling problems for children. Journal of Teacher Education, 68(3) 330- 344. https://doi.org/10.1177/0022487117697636

Ramos-Rodríguez, E., Fernández-Ahumada, E., & Morales-Soto, A. (2022). Effective teacher professional development programs. A case study focusing on the development of mathematical modeling skills. Education Sciences, 12(1). https://doi.org/10.3390/educsci12010002

Sullivan, P., Knott, L., Yang, Y., Askew, M., Brown, L., Bartolini, M., …, Zodik, I. (2015). The relationships between task design, anticipated pedagogies, and student learning. In A. Watson & M. Ohtani (Eds.), Task design in Mathematics Education an ICMI study 22 (pp. 88-114). Springer. https://doi.org/10.1007/978-3-319-09629-2_3

Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421-456). NCTM.

Verschaffel, L., van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problems as exercises in mathematical modelling. Journal für Mathematikdidaktik, 1(1), 9-29. https://doi.org/10.1007/s13138-010-0007-x

Villa, J., & Ruiz, H. (2009). Modelación en educación matemática: una mirada desde los lineamientos y estándares curriculares colombianos. Revista Virtual Universidad Católica del Norte, 27(1), 1-21.

Wess, R., Klock, H., Siller, H-S., & Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modelling. In F. K. S. 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 (249-260). Springer. https://doi.org/10.1007/978-3-030-66996-6_21

Yin, R. (2014). Case study research design and methods (5th ed.). Sage.