¿Qué estrategia es mejor para un problema de Fermi? Adaptabilidad de futuros maestros
Resumen
Los problemas de Fermi, adecuados para primaria, plantean una situación real y abierta que permite desarrollar y comparar múltiples estrategias, lo que requiere que los maestros sean adaptables (capaces de escoger la más apropiada). El objetivo de este trabajo es caracterizar y analizar la adaptabilidad de futuros maestros cuando resuelven estos problemas. Para ello, la investigación se divide en dos estudios. El Estudio 1 presenta una encuesta dirigida a expertos en educación matemática; el análisis de sus respuestas permite vincular las características contextuales de los problemas con estrategias, y estas, con criterios de adecuación (precisión, rapidez y rigor). Estos resultados conducen a una caracterización de adaptabilidad que nos permite abordar el Estudio 2 con futuros maestros, y se concluye que la mayoría de los resolutores adaptables usan estrategias de manera no sistemática.
Palabras clave
Adaptabilidad, Flexibilidad, Estimación, Modelización, Problemas de FermiCitas
Albarracín, L., Ferrando, I. y Gorgorió, N. (2021). The Role of Context for Characterising Students’ Strategies when Estimating Large Numbers of Elements on a Surface. International Journal of Science and Mathematics Education, 19, 1209-1227. https://doi.org/10.1007/s10763-020-10107-4
Albarracín, L. y Gorgorió, N. (2019). Using large number estimation problems in primary education classrooms to introduce mathematical modelling. International Journal of Innovation in Science and Mathematics Education, 27(2), 45-57. https://doi.org/10.30722/IJISME.27.02.004
Ärlebäck, J. B. (2009). On the use of realistic Fermi problems for introducing mathematical modelling in school. The Mathematics Enthusiast, 6(3), 331-364. https://doi.org/10.54870/1551-3440.1157
Blöte, A. W., Van der Burg, E. y Klein, A. S. (2001). Students’ flexibility in solving two-digit addition and subtraction problems: instruction effects. Journal of Educational Psychology, 93, 627-638. https://doi.org/10.1037/0022-0663.93.3.627
Carlson, J. E. (1997). Fermi problems on gasoline consumption. The Physics Teacher, 35(5), 308-309. https://doi.org/10.1119/1.2344696
Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 19-36. https://doi.org/10.31129/lumat.v3i1.1049
Durkin, K., Star, J. R. y Rittle-Johnson, B. (2017). Using comparison of multiple strategies in the mathematics classroom: lessons learned and next steps. ZDM Mathematics Education, 49, 585-597. https://doi.org/10.1007/s11858-017-0853-9
Efthimiou, C. J. y Llewellyn, R. A. (2007). Cinema, Fermi problems and general education. Physics Education, 42(3), 253. https://doi.org/10.1088/0031-9120/42/3/003
English, L. D. (2011). Data modeling in the beginning school years. En P. Sullivan y M. Goos (Eds.), Proceedings of the 34th Annual Conference of the Mathematics Education Research Group of Australia (pp. 226-234). MERGA.
Ferrando, I., Segura, C. y Pla-Castells, M. (2021). Analysis of the relationship between context and solution plan in modelling tasks involving estimations. En F. K. S. Leung, G. A. Stillman, G. Kaiser y K. L. Wong (Eds.), Mathematical Modelling Education in East and West (pp. 119-128). Cham: Springer. https://doi.org/10.1007/978-3-030-66996-6_10
Garcia Coppersmith, J. y Star, J. R. (2022). A Complicated Relationship: Examining the Relationship Between Flexible Strategy Use and Accuracy. Journal of Numerical Cognition, 8(3), 382-397. https://doi.org/10.5964/jnc.7601
Haberzettl, N., Klett, S. y Schukajlow, S. (2018). Mathematik rund um die Schule—Modellieren mit Fermi-Aufgaben. En K. Eilerts y K. Skutella (Eds.), Neue Materialien für einen realitätsbezogenen Mathematikunterricht 5. Ein ISTRON-Band für die Grundschule (pp. 31-41). Springer Spectrum. https://doi.org/10.1007/978-3-658-21042-7_3
Henze, J. y Fritzlar, T. (2010). Primary school children’s model building processes by the example of Fermi questions. En A. Ambrus y E. Vásárhelyi (Eds.), Problem Solving in Mathematics Education. Proceedings of the 11th ProMath conference (pp. 60-75). Eötvös Loránd University.
Heinze, A., Star, J. R. y Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41, 535-540. https://doi.org/10.1007/s11858-009-0214-4
Hickendorff, M. (2022). Flexibility and Adaptivity in Arithmetic Strategy Use: What Children Know and What They Show. Journal of Numerical Cognition, 8(3), 367-381. https://doi.org/10.5964/jnc.7277
Hickendorff, M., McMullen, J. y Verschaffel, L. (2022). Mathematical Flexibility: Theoretical, Methodological, and Educational Considerations. Journal of Numerical Cognition, 8(3), 326-334. https://doi.org/10.5964/jnc.10085
Huincahue-Arcos, J., Borromeo-Ferri, R. y Mena-Lorca, J. J. F. (2018). El conocimiento de la modelación matemática desde la reflexión en la formación inicial de profesores de matemática. Enseñanza de las Ciencias. Revista de investigación y experiencias didácticas, 36(1), 99-115. https://doi.org/10.5565/rev/ensciencias.2277
Klock, H. y Siller, H.-S. (2020). A Time-Based Measurement of the Intensity of Difficulties in the Modelling Process. En H. Wessels, G. A. Stillman, G. Kaiser, y E. Lampen (Eds.), International perspectives on the teaching and learning of mathematical modelling (pp. 163-173). Springer. https://doi.org/10.1007/978-3-030-37673-4_15
Ko, P. Y. y Marton, F. (2004). Variation and the secret of the virtuoso. En F. Marton y A. B. M. Tsui (Eds.), Classroom discourse and the space of learning (pp. 43-62). Erlbaum. https://doi.org/10.4324/9781410609762
Krawitz, J., Schukajlow, S. y Van Dooren, W. (2018). Unrealistic responses to realistic problems with missing information: what are important barriers? Educational Psychology, 38(10), 1221-1238. https://doi.org/10.1080/01443410.2018.1502413
Lemaire, P. y Siegler, R. S. (1995). Four aspects of strategic change: contributions to children’s learning of multiplication. Journal of experimental psychology: General, 124(1), 83. https://doi.org/10.1037/0096-3445.124.1.83
Levav-Waynberg, A. y Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. The Journal of Mathematical Behavior, 31(1), 73-90. https://doi.org/10.1016/j.jmathb.2011.11.001
Lu, X. y Kaiser, G. (2022). Creativity in students’ modelling competencies: conceptualisation and measurement. Educational Studies in Mathematics, 109(2), 287-311. https://doi.org/10.1007/s10649-021-10055-y
Newton, K. J., Lange, K. y Booth, J. L. (2020). Mathematical flexibility: Aspects of a continuum and the role of prior knowledge. The Journal of Experimental Education, 88(4), 503-515. https://doi.org/10.1080/00220973.2019.1586629
Nistal A. A., Van Dooren W. y Verschaffel L. (2012). Flexibility in Problem Solving: Analysis and Improvement. En N. M. Seel (Eds.), Encyclopedia of the Sciences of Learning. Springer. https://doi.org/10.1007/978-1-4419-1428-6_540
Obersteiner, A., Alibali, M. W. y Marupudi, V. (2022). Comparing fraction magnitudes: Adults’ verbal reports reveal strategy flexibility and adaptivity, but also bias. Journal of Numerical Cognition, 8(3), 398-413. https://doi.org/10.5964/jnc.7577
Okamoto, H., Hartmann, M. y Kawasaki, T. (2023). Analysis of the Relationship between Creativity in Fermi Problems Measured by Applying Information Theory, Creativity in Psychology, and Mathematical Creativity. Education Sciences, 13(3), 315. https://doi.org/10.3390/educsci13030315
Peter-Koop, A. (2009). Teaching and Understanding Mathematical Modelling through Fermi-Problems. En B. Clarke, B. Grevholm y R. Millman (Eds.), Tasks in primary mathematics teacher education (pp. 131-146). Springer. https://doi.org/10.1007/978-0-387-09669-8_10
Pla-Castells, M., Melchor, C. y Chaparro, G. (2021). MAD+. Introducing misconceptions in the temporal analysis of the mathematical modelling process of a Fermi problem. Education Sciences, 11(11), 747. https://doi.org/10.3390/educsci11110747
Segura, C., Ferrando, I. y Albarracín, L. (2021). Análisis de los factores de complejidad en planes de resolución individuales y resoluciones grupales de problemas de estimación de contexto real. Quadrante, 30(1), 31-51. https://doi.org/10.48489/quadrante.23592
Segura, C., Ferrando, I. y Albarracín, L. (2023). Does collaborative and experiential work influence the solution of real-context estimation problems? A study with prospective teachers. The Journal of Mathematical Behavior, 70, 101040. https://doi.org/10.1016/j.jmathb.2023.101040
Segura, C. y Ferrando, I. (2023). Pre-service teachers’ flexibility and performance in solving Fermi problems. Educational Studies in Mathematics, 113(2), 207-227. https://doi.org/10.1007/s10649-023-10220-5
Robinson, A. W. (2008). Don’t just stand there—teach Fermi problems! Physics Education, 43(1), 83-87. https://doi.org/10.1088/0031-9120/43/01/009
Sáenz, C. (2007). La competencia matemática (en el sentido de PISA) de los futuros maestros. Enseñanza de las Ciencias, 25(3), 355-366. https://doi.org/10.5565/rev/ensciencias.3701
Schoenfeld, A. H. (1982). Measures of problem-solving performance and of problem-solving instruction. Journal for Research in Mathematics Education, 13(1), 31-49. https://doi.org/10.2307/748435
Schukajlow, S., Krug, A. y Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance. Educational Studies in Mathematics, 89(3), 393-417. https://doi.org/10.1007/s10649-015-9608-0
Selter, C. (2009). Creativity, flexibility, adaptivity, and strategy use in mathematics. ZDM Mathematics Education, 41, 619-625. https://doi.org/10.1007/s11858-009-0203-7
Siegler, R. S. (1996). Emerging minds: The process of change in children ‘s thinking. Oxford: Oxford University Press. https://doi.org/10.1093/oso/9780195077872.001.0001
Sriraman, B. y Lesh, R. (2006). Modeling conceptions revisited. Zentralblatt für Didaktik derMathematik, 38, 247-254. https://doi.org/10.1007/BF02652808
Sriraman, B. y Knott, L. (2009). The mathematics of estimation: Possibilities for interdisciplinary pedagogy and social consciousness. Interchange, 40(2), 205-223. https://doi.org/10.1007/s10780-009-9090-7
Star, J. R. y Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and instruction, 18(6), 565-579. https://doi.org/10.1016/j.learninstruc.2007.09.018
Taggart, G. L., Adams, P. E., Eltze, E., Heinrichs, J., Hohman, J. y Hickman, K. (2007). Fermi Questions. Mathematics Teaching in the Middle School, 13(3), 164-167. https://doi.org/10.5951/MTMS.13.3.0164
Threlfall, J. (2002). Flexible Mental Calculation. Educational Studies in Mathematics, 50, 29-47. https://doi.org/10.1023/A:1020572803437
Van Dooren, W., Verschaffel, L. y Onghena, P. (2003). Preservice teachers’ preferred strategies for solving Arithmetic and Algebra word problems. Journal of Mathematics Teacher Education, 6(1), 27-52. https://doi.org/10.1023/A:1022109006658
Verschaffel, L., Luwel, K., Torbeyns, J. y Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24(3), 335-359. https://doi.org/10.1007/BF03174765
Publicado
Descargas
Derechos de autor 2023 Carlos Segura Cordero, Irene Ferrando
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
