Skip to main navigation menu Skip to main content Skip to site footer

Artículos

Vol. 23 No. 1 (2020): March

HYPOTHESIS AND CONJECTURES IN THE DEVELOPMENT OF STOCHASTIC THINKING: CHALLENGES FOR ITS TEACHING AND TEACHERS TRAINING

DOI
https://doi.org/10.12802/relime.20.2313
Submitted
November 7, 2022
Published
2020-03-01

Abstract

This article reflects on the importance that the hypothesis-conjecture dialectic may have not only for the development of demonstrative reasoning, but also for the development of stochastic thinking in students. Reasons of a curricular type are argued for this, of a teaching approach based on problem solving, of a way of solving problems that considers simulation as a resolution method with heuristic content and, finally, in new proposals on mathematics. that the citizen of the 21st century will require and that includes data analysis in contexts of uncertainty. Consequently, a proposal for initial teacher training is presented that allows them to address such challenges.

References

  1. Batanero, C., Chernoff, E., Engel, J., Lee H., y Sánchez, E. (Eds.) (2016). Research on Teaching and Learning Probability, ICME-13 Topical Surveys, DOI: https://doi.org/10.1007/978-3-319-31625-3_1
  2. Begué, N., Batanero, C., y Gea, M. M. (2018). Comprensión del valor esperado y variabilidad de la proporción muestral en estudiantes de educación secundaria obligatoria. Enseñanza de las Ciencias36(2), 63-79.
  3. Bernoulli, J. (1987/1713). Ars conjectandi - 4ème partie. Rouen: IREM. (Original work published in 1713)
  4. Beth, B. (1989). Using simulation to model real-world problems. In M. Morris (Ed.) Studies in Mathematics Education. The teaching of statistics, 7, 95-100. Paris: UNESCO.
  5. Benson, C. T., & Jones, G. A. (1999). Assessing Students’ Thinking in Modeling Probability Contexts. The mathematics Educator 4(2), 1-21
  6. Borovcnik, M., & Kapadia, R. (2018). Reasoning with Risk: Teaching Probability and Risk as Tween Concepts. In C. Batanero & E. Chernoff (eds.), Teaching and Learning Stochastics,ICME-13 Monographs. DOI: https://doi.org/10.1007/978-3-319-72871-1_17
  7. Bunge, M. (2013). La ciencia. Su método y su filosofía. Pamplona: Laetoli
  8. Cardeñoso, J. M., Moreno, A., García-González, E., y Jiménez-Fontana, R. (2017). El sesgo de equiprobabilidad como dificultad para comprender la incertidumbre en futuros docentes argentinos. Avances de Investigación en Educación Matemática 11, 145 – 167
  9. Chaput, B., Girard, J. C., & Henry, M. (2011). Frequentist approach: Modelling and Simulation in Statistics and Probability Teaching. In C. Batanero, G. Burril, and C. Reading (eds.), Teaching Statistics in School Mathematics- Challenge for Teaching and Teachers Education: A Joint ICMI / IASE Study, (pp. 85-95). New York: Springe
  10. De Villiers, M., & Heideman, N. (2014). Conjecturing, Refuting and Proving within the Context of Dynamic Geometry. Learning and Teaching Mathematics, 17, 20-26.
  11. Devlin, K. (2018). The Mathematics People Really Need. Presentación disponible en http://curriculumredesign.org/wp-content/uploads/DEVLIN-talk-2018.pdf y vídeo en https://youtu.be/qBOnWZyq468, ambas visitada el 22 de junio de 2018
  12. Eichler, A., & Vogel, M. (2014). Three Approaches for Modelling Situations with Randomness. In E. J. Chernoff, B. Sriraman (eds.) (2014), Probabilistic Thinking, Presenting Plural Perspective (pp. 75-100). Dordrecht: Springer Science+Business Media
  13. Fernández, B., y Rodríguez, B. (2015). Del Ars Conjectandi al Valor de riesgo. Miscelánea matemática, 60, 25-45
  14. Ferrater Mora, J. (1965). Diccionario de Filosofía. Buenos Aires: Editorial Sudamericana
  15. Fiallo, J., & Gutiérrez, A. (2017). Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course. Educational Studies in Mathematics, 92(2), 145-167
  16. Furinghetti, F., Olivero F., & Paola, D. (2010). Students approaching proof through conjectures: snapshots in a classroom. International Journal of Mathematics Education in Science and Technology 32(3), 319-335. DOI: https://doi.org/10.1080/00207390120360
  17. Gordon, H. (1997). Discrete Probability. New York: Springer
  18. Huerta, M. P. (2002). El problema de la cueva. Elementos para un análisis didáctico de los problemas de probabilidad. Enseñanza de las Ciencias, 20(1), 75-86
  19. Huerta, M. P. (2015). La resolución de problemas de probabilidad con intención didáctica en la formación de maestros y profesores de matemáticas. En C. Fernández, M. Molina y N. Planas(eds.), Investigación en Educación MatemáticaXIX (pp. 105-119). Alicante: SEIEM
  20. Huerta, M. P. (2018). Preparing Teachers for Teaching Probability Through Problem Solving. In C.Batanero and E. J. Chernoff (eds.), Teaching and Learning Stochastics, ICME-13 Monographs(pp. 293-311). DOI: https://doi.org/10.1007/978-3-319-72871-1_17.
  21. Lakatos, I. (1976). Proofs and Refutations. Cambridge: Cambridge Academic Press.
  22. Lampert, M. (1990). When the Problem Is Not the Question and the Solution Is not the Answer: Mathematical Knowing and Teaching. American Educational Research Journal, 27(1), 29-63.
  23. Lecoutre, M. P. (1992). Cognitive models and problem spaces in purely random situations. Educational Studies in Mathematics, 23, 557-568.
  24. Llinares, S. (2018). Escribir narrativas. De observar a mirar profesionalmente. En L. J. Rodríguez-Muñiz, L. Muñiz-Rodríguez, A. Aguilar-González, P. Alonso, F. J. García García y A. Bruno (Eds.), Investigación en Educación Matemática XXII (pp. 39-50). Gijón: SEIEM
  25. Maaβ, K., & Doorman. (2013). A model for a widespread implementation of inquiry-based leaning. ZDM-International Journal on Mathematics Education, 45(6), 887-899.
  26. Makar, K. & Rubin, A. (2014). Informal statistical inference revisited. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9, July, 2014), Flagstaff, Arizona, USA. Voorburg, The Netherlands: International Statistical Institute.
  27. Martínez, M. L., Huerta, P. y González, E. (2018). Dificultades de los maestros y profesores en formación para identificar hipótesis y conjeturas en una tarea de probabilidad. En L. J. Rodríguez-Muñiz, L. Muñiz-Rodríguez, A. Aguilar-González, P. Alonso, F. J. García García y A. Bruno (Eds.), Investigación en Educación Matemática XXI (p.638). Gijón: SEIEM
  28. Martínez, M. L. y Huerta, M. P. (2015). Diseño e implementación de una situación de incertidumbreen una clase de educación infantil. Edma 0-6: Educación Matemática en la Infancia, 4(1), 24-36.
  29. Ministerio de Educación, Cultura y Deporte (MEC, 2014a). Real Decreto 126/2014 de 28 de febrero por que se establece el currículo básico de la Educación Primaria. Boletín Oficial del Estado de 1 de marzo de 2014. Madrid.
  30. Ministerio de Educación, Cultura y Deporte (MEC, 2014b). Real Decreto 1105/2014 de 26 de diciembre por que se establece el currículo básico de la Educación Secundaria Obligatoria y del Bachillerato. Boletín Oficial del Estado de 1 de enero de 2015. Madrid.
  31. Minyana, M. (2018). Hipòtesi i conjectures en el pensament estocàstic d’estudiants de 1er de Educació Secundària Obligatòria (12-13 anys). (Hypothesis and conjectures in 12-13 aged-students’ stochastic thinking). Trabajo de Fin de Máster de Investigación en Didácticas Específicas. Departament de Didàctica de la Matemàtica. Universitat de València.
  32. Pfannkuch, M. (2018). Reimaging Curriculum Approaches. In D. Ben-Zvi, K. Makar & J. Garfield (eds.) (2018), International Handbook of Research in Statistics Education (pp. 387-413). Springer International Handbooks of Education. https:// doi.org/10.1007/978-3-3319-66195-7_12
  33. NCTM (2018). Principles and Standards for School Mathematics. Disponible en https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf (visitado el 12 de julio de 2018)
  34. Poincaré, H. (1992). La Science et l’Hypothèse. Rueil-Malmason: La Bohème.
  35. Polya, G. (1966). Matemáticas y razonamiento plausible. Madrid: Tecnos.
  36. Popper, K. (1977). La lógica de la investigación científica. Madrid: Tecnos.
  37. Pratt, D. (2011). Re-connecting probability and reasoning about data in secondary school teaching. Proceedings of the 58th World Statistical Congress (pp. 890-899). Dublin.
  38. Saldanha, L., & Liu, Y. (2014). Challenges in Developing Coherent Probabilistic Reasoning: Rethinking Randomness and Probability from a Stochastic Perspective. In E. J. Chernoff, B. Sriraman (eds.) (2014), Probabilistic Thinking, Presenting Plural Perspective (pp. 367-398). Dordrecht: Springer Science+Business Media.
  39. Schup, H. (1989). Appropriate teaching and learning of stochastics in the middle grades (5-10). In M. Morris (Ed.) Studies in Mathematics Education. The teaching of statistics. (vol. 7), (pp. 101-121). Paris: UNESCO.
  40. Spiegelhalter, D., & Gage, J. (2014). What Can Education Learn from Real-World Communication of Risk and Uncertainty? The Mathematics Enthusiast 12(1-3), 4-10.
  41. Serrano, L., Batanero, C., Ortiz, J. J., & Cañizares M. J. (1998). Heurísticas y sesgos en el razonamiento probabilístico de los estudiantes de secundaria. Educación Matemática,10(1), 7-25.
  42. Shaughnessy, J. M. (1983). The psychology of inference and the teaching of probability and statistics: Two sides of the same coin? In R. W. Sholz (Ed.), Decision making under uncertainty(pp. 325-350). Amsterdam, The Netherlands: Elsevier.
  43. Wild, C. J., & Pfannkuch, M. (1999). Statistical Thinking in Empirical Enquiry. International Statistical Review 67 (3), 223-265.
  44. Zimmermann, G. (2002). Students’ reasoning about probability simulation during instruction. Doctoral Dissertation. Retrieved from https://www.stat.auckland.ac.nz/~iase/publications/dissertations/02.Zimmerman.Dissertation.pdf.

Downloads

Download data is not yet available.

Similar Articles

<< < 1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.