¿Qué estrategia es mejor para un problema de Fermi? Adaptabilidad de futuros maestros

  1. Segura Cordero, Carlos 1
  2. Ferrando, Irene 1
  1. 1 Universitat de València
    info

    Universitat de València

    Valencia, España

    ROR https://ror.org/043nxc105

Revista:
Enseñanza de las ciencias: revista de investigación y experiencias didácticas

ISSN: 0212-4521,  2174-6486

Año de publicación: 2023

Volumen: 41

Número: 3

Páginas: 133-151

Tipo: Artículo

DOI: 10.5565/REV/ENSCIENCIAS.5978 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Enseñanza de las ciencias: revista de investigación y experiencias didácticas

Objetivos de desarrollo sostenible

Resumen

Fermi problems, suitable for primary school, pose a real and open situation that allows the development and comparison of multiple strategies. This requires teachers to be adaptive (able to choose the most appropriate strategy). The aim of this paper is to characterise and analyse the adaptability of prospective teachers when solving these problems. For this purpose, the research is divided into two studies. Study 1 presents a survey addressed to experts in mathematics education; the analysis of their answers makes it possible to link the contextual characteristics of the problems with strategies, and these with appropriateness criteria (accuracy, speed and rigour). These results lead to a characterisation of adaptability that allows us to approach Study 2 with pre-service teachers, finding that most adaptive solvers use strategies non-systematically.

Referencias bibliográficas

  • 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
Fuente de los datos: Dialnet