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Artículos

Vol. 27 No 1 (2024): Marzo

DISEÑO DE UNA TRAYECTORIA HIPOTÉTICA DE APRENDIZAJE PARA INTRODUCIR LA INFERENCIA ESTADÍSTICA INFORMAL EN PRIMARIA

DOI
https://doi.org/10.12802/relime.24.2711
Soumis
septembre 4, 2024
Publiée
2024-03-31

Résumé

Dans le cadre d'une étude de design développant une trajectoire d'apprentissage hypothétique pour l'inférence statistique informelle (ISI), des élèves de 3e et 4e année (n=23) ont été initiés aux concepts clés de la variabilité, de l'échantillonnage répété et de la distribution d'échantillonnage empirique. La trajectoire de cinq étapes avec une approche ludique de l'expérience aléatoire du lancer de deux pièces de monnaie comprenait : l'obtention d'échantillons ; la reconnaissance de l'incertitude et son expression avec le langage des possibilités ; le contraste des prédictions par l'échantillonnage répété ; la visualisation et la reconnaissance de la variabilité entre les échantillons ; l'attribution de niveaux de possibilités en tenant compte de la distribution d'échantillonnage empirique lors de la généralisation au-delà des données. Les résultats indiquent que les élèves des deux classes peuvent accéder aux concepts de ISI, en faisant des déductions informelles et en montrant des niveaux sophistiqués de raisonnement de ISI.

Références

  1. Arnold, P., Confrey, J., Jones, R., Lee, H., y Pfannkuch, M. (2018). Statistics learning trajectories. En D. Ben-Zvi et al. (Eds.), International handbook of research in statistics education (pp. 295–326). Springer. https://doi.org/10.1007/978-3-319-66195-7_9
  2. Ben-Zvi, D., Aridor, K., y Makar, K. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM Mathematics Education, 44(1), 913–925. https://doi.org/10.1007/s11858-012-0420-3
  3. Ben-Zvi, D. (2016). Three paradigms in developing student´s statistical reasoning. En S. Estrella (Ed.), XX Jornadas Nacionales de Educación Matemática (pp. 13–22). Universidad Católica de Valparaíso.
  4. Clements, D., y Sarama, J. (2004). Learning Trajectories in Mathematics Education. Mathematical Thinking and Learning, 6(2), 81–89. https://doi.org/10.1207/s15327833mtl0602_1
  5. Estrella, S. (2018). Data representations in Early Statistics: data sense, meta-representational competence and transnumeration. En A. Leavy et al. (Eds.), Statistics in Early Childhood and Primary Education – Supporting early statistical and probabilistic thinking, (pp. 239–256). Singapur: Springer. https://doi.org/10.1007/978-981-13-1044-7_14
  6. Estrella, S., Zakaryan, D., Olfos, R., y Espinoza, G. (2020). How teachers learn to maintain the cognitive demand of tasks through Lesson Study. Journal of Mathematics Teacher Education, 23(1), 293–310. https://doi.org/10.1007/s10857-018-09423-y
  7. Estrella, S., Vergara, A., y Gonzalez, O. (2021). Developing data sense: Making inferences from variability in tsunamis at primary school. Statistics Education Research Journal, 20(2), 16–16. https://doi.org/10.52041/serj.v20i2.413
  8. Estrella, S., Méndez-Reina, M., y Vidal-Szabó, P. (2023a). Exploring informal statistical inference in early statistics: a learning trajectory for third-grade students. Statistics Education Research Journal, 22(2), 1–16. https://doi.org/10.52041/serj.v22i2.426
  9. Estrella, S., Méndez-Reina, M., Salinas, R., y Rojas, T. (2023b). The Mystery of the Black Box: An Experience of Informal Inferential Reasoning. En G. Burrill et al. (Eds), Research on Reasoning with Data and Statistical Thinking, (pp. 191–210). ISBN 978-3-031-29458-7. SPRINGER. https://doi.org/10.1007/978-3-031-29459-4_16
  10. Garfield, J., y Ben-Zvi, D. (2008). Preparing school teachers to develop students’ statistical reasoning. En C. Batanero, G. Burrill, C. Reading, y A. Rossman (Eds.), Joint ICMI/IASE study: teaching statistics in school mathematics. Proceedings ICMI Study 18 and 2008 IASE. ICMI y IASE.
  11. Gravemeijer, K., Bowers, J., y Stephan, M. (2003). A hypothetical learning trajectory on measurement and flexible arithmetic. Journal for Research in Mathematics Education. Monograph, 12, 51–66.
  12. Konold, C., Higgins, T., Russell, S. J., y Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325. https://doi.org/10.1007/s10649-013-9529-8
  13. Langrall, C., Nisbet, S., Mooney, E., y Jansem, S. (2011). The Role of Context Expertise When Comparing Data. Mathematical Thinking and Learning, 13(1), 47–67. https://doi.org/10.1080/10986065.2011.538620
  14. Leavy, A., Meletiou-Mavrotheris, M., y Paparistodemou, E. (Eds.). (2018). Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking. Springer. https://doi.org/10.1007/978-981-13-1044-7
  15. Lobato, L., y Walters, C. (2017). A taxonomy of approaches to learning progressions. En J. Cai (Ed.), Compendium for Research in Mathematics Education (pp. 74–101). NCTM.
  16. Makar, K., y Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105. https://doi.org/10.52041/serj.v8i1.457
  17. Makar, K., Bakker, A., y Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1), 152–173. https://doi.org/10.1080/10986065.2011.538301
  18. Makar, K., y Rubin, A. (2018). Learning about statistical inference. En D. Ben-Zvi, K. Makar y J. Garfield (Eds.), International handbook of research in statistics education (pp. 261–294). Springer. https://doi.org/10.1007/978-3-319-66195-7_8
  19. Méndez-Reina, M., y Estrella, S. (2024). Razonamiento inferencial en Estadística Temprana: aspectos estructurales desde tipos de razonamiento de Peirce. En S. Estrella et al. (Eds.), Pensamiento Matemático: Aportes a la práctica docente desde la didáctica de la matemática. ISBN: 978-84-128559-8-2. España: GRAO.
  20. Moore, D. S. (2005). Estadística aplicada básica. Antoni Bosch.
  21. Pfannkuch, M. (2006). Informal inferential reasoning. En A. Rossman y B. Chance (Eds.), Proceedings ICOTS7: Working cooperatively in statistics education, Brazil.
  22. Pfannkuch, M., Arnold, P. y Wild, C. (2015). What I see is not quite the way it really is: students’ emergent reasoning about sampling variability. Educational Studies in Mathematics, 88, 343–360. https://doi.org/10.1007/s10649-014-9539-1
  23. Pratt, D., Johnston-Wilder, P., Ainley, J., y Mason, J. (2008). Local and global thinking in statistical inference. Statistics Education Research Journal, 7(2), 107–129. https://doi.org/10.52041/serj.v7i2.472
  24. Rossman, A. (2008). Reasoning about informal statistical inference: A statistician's view. Statistics Education Research Journal, 7(2), 5–19. https://doi.org/10.52041/serj.v7i2.467
  25. Rubin, A., Hammerman, J., y Konold, C. (2006). Exploring informal inference with interactive visualization software. En A. Rossman y B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings ICOTS7, Brazil.
  26. Sannomiya, M., Mashimo, T., y Yamaguchi, Y. (2021). Creativity training for multifaceted inferences of reason behind others’ behaviors. Thinking Skills and Creativity, 39, 100757. https://doi.org/10.1016/j.tsc.2020.100757
  27. Silvestre, E., Sánchez, E. A., e Inzunza, S. (2022). El razonamiento de estudiantes de bachillerato sobre el muestreo repetido y la distribución muestral empírica. Educación matemática, 34(1), 100–130. https://doi.org/10.24844/EM3401.04
  28. Simon, M. (2020). Hypothetical Learning Trajectories in Mathematics Education. En S. Lerman (ed.), Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-030-15789-0_72
  29. Soto, C., Gutiérrez de Blume, A., Jacovina, M., McNamara, D., Benson, N., y Riffo, B. (2019). Reading comprehension and metacognition: The importance of inferential skills. Cogent Education, 6(1), 1–20. https://doi.org/10.1080/2331186X.2019.1565067
  30. Steffe, L., y Thompson, P. (2000). Teaching experiment methodology: underlying principles and essential elements. En A. Kelly y R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267–306). Lawrence Erlbaum Associates.
  31. van Dijke-Droogers, M., Drijvers, P., y Bakker, A. (2020). Repeated sampling with a black box to e informal statistical inference accessible. Mathematical Thinking and Learning, 22(2), 116–138. https://doi.org/10.1080/10986065.2019.1617025
  32. van Dijke-Droogers, M., Drijvers, P., y Bakker, A. (2021). Introducing Statistical Inference: Design of a Theoretically and Empirically Based Learning Trajectory. International Journal of Science and Mathematics Education, 20(4), 1743–1766. https://doi.org/10.1007/s10763-021-10208-8
  33. Watson, J., Fitzallen, N., y Carter, P. (2013). Top Drawer Teachers: Statistics. Education Services Australia.
  34. Zieffler, A., Garfield, J., delMas, R., y Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistic Education Research Journal, 7(2), 40–58. https://doi.org/10.52041/serj.v7i2.469

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