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Artículos

Vol. 23 No. 1 (2020): March

RELATIONSHIPS BETWEEN PROPORTIONAL THINKING AND PROBABILISTIC THINKING IN DECISION-MAKING SITUATIONS

DOI
https://doi.org/10.12802/relime.20.2311
Submitted
November 7, 2022
Published
2020-03-18

Abstract

Making decisions is a daily act in the human being, the greater the uncertainty, the more difficult it is to decide. Starting from a learning situation, consisting of deciding between two random games with dice, the relationship between proportional thinking and probabilistic thinking is studied, considering three states for proportional thinking and three types of probabilistic thinking. Under the approach of an instrumental case study, the decisions and arguments of Chilean high school students are analyzed. The results indicate that there are both beneficial and detrimental relationships between proportional and probabilistic thinking, and that the difficulties in determining probabilities are not necessarily due to the absence of the use of proportions. A teaching that considers the argumentation and learning of the sample space is recommended to channel the use of intuitive resources.

References

  1. Alvarado, H., Estrella, S., Retamal, L., & Galindo, M. (2018). Intuiciones probabilísticas en estudiantes de ingeniería: implicaciones para la enseñanza de la probabilidad. Revista Latinoamericana de Matemática Educativa, 21(2), 131-156. DOI: https://doi.org/10.12802/relime.18.2121.
  2. Anway, D., & Bennett, E. (2004, August). Common misperceptions in probability among students in an Elementary Statistics class. En B. Chance (Conference chair), ARTIST Roundtable Conference on Assessment in Statistics held at Lawrence University (pp. 1-4). Recuperado desde http://www.rossmanchance.com/artist/proceedings/AnwayBennett.pdf
  3. Ashline, G., & Frantz, M. (2009). Proportional reasoning and probability. Synergy Learning Nov / Dec, 8-10. Recuperado desde https://web.archive.org/web/20071010023424/http://cf.synergylearning.org/displaygrade.cfm?selectedgrade=1
  4. Batanero, C., Chernoff, E., Engel, J., Lee, H., & Sánchez, E. (2016). Research on Teaching and Learning Probability. En Research on Teaching and Learning Probability. ICME-13 Topical Surveys. Cham: Springer. DOI: https://doi.org/10.1007/978-3-319-31625-3_1
  5. Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. En Graham A. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 16-42). Boston, MA: Springer. DOI: https://doi.org/10.1007/0-387-24530-8_2
  6. Bellhouse, D. (2000). De Vetula: a medieval manuscript containing probability calculations. International Statistical Review, 68(2), 123-136. DOI: https://doi.org/10.2307/1403664
  7. Bennett, D. (2014). Sticking to your guns: a flawed heuristic for probabilistic decision-making. En E.J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking (pp. 261-281). Dordrecht: Springer. DOI: https://doi.org/10.1007/978-94-007-7155-0_14
  8. Borovcnik, M. (2011). Strengthening the role of probability within statistics curricula. En C. Batanero, G. Burrill & C. Reading (Eds.), Teaching Statistics in School MathematicsChallenges for Teaching and Teacher Education. A joint ICMI/IASE study: the 18th ICMI study (Vol. 14) (pp. 71-83). Dordrecht: Springer. DOI: https://doi.org/10.1007/978-94-007-1131-0_11
  9. Bryant, P., & Nunes, T. (2012). Children’s Understanding of Probability: A Literature Review (summary Report). London: Nuffield Foundation.
  10. Chernoff, E. J., & Zazkis, R. (2011). From personal to conventional probabilities: from sample set to sample space. Educational Studies in Mathematics, 77(1), 15-33. DOI: https://doi.org/10.1007/s10649-010-9288-8
  11. Chiesi, F., & Primi, C. (2010). Cognitive and non-cognitive factors related to students’ statistics achievement. Statistics Education Research Journal, 9(1), 6–26. Recuperado desde http://www.stat.auckland.ac.nz/~iase/serj/SERJ9%281%29_Chiesi_Primi.pdf
  12. Chiesi, F., & Primi, C. (2014). The interplay among knowledge, cognitive abilities and thinking styles in probabilistic reasoning: a test of a model. En E.J. Chernoff & B. Sriraman, B. (Eds.), Probabilistic thinking (pp. 195-214). Dordrecht : Springer. DOI: https://doi.org/10.1007/978-94-007-7155-0_11
  13. D’Alembert, J. (1784). Croix ou Pile. Dans Encyclopédie, ou Dictionnaire Raisonne des Sciences, des Arts et des Metiers, Vol. 4, pp. 512-513. Paris: Societe des Gens de Lettres. Recuperado desde https://gallica.bnf.fr/ark:/12148/bpt6k505351/f1.item.r=alember
  14. Díaz, C., & Batanero, C. (2009). University student’s knowledge and biases in conditional probability reasoning. International Electronic Journal of Mathematics Education, 4(3), 131-162. Recuperado desde http://www.iejme.com/article/university-students-knowledgeand-biases-in-conditional-probability-reasoning
  15. Engel, J., & Orthwein, A. (2018). The Six Loses: Risky Decisions Between Probabilistic Reasoning and Gut Feeling. En C., Batanero & E., Chernoff (Eds.), Teaching and Learning Stochastics, Advances in Probability Education Research, ICME-13 Monograph (pp. 261-274). Cham: Springer. DOI: https://doi.org/10.1007/978-3-319-72871-1_15
  16. Eriksson, K., & Simpson, B. (2010). Emotional reactions to losing explain gender differences in entering a risky lottery. Judgment and Decision Making, 5(3), 159. Recuperado desde http://journal.sjdm.org/10/10601/jdm10601.html
  17. Fielding-Wells, J. (2014). Where’s your evidence? Challenging young students’ equiprobability bias through argumentation. En T. Dunne (Conference chair), The 9th International Conference on Teaching Statistics (pp. 1-6). Recuperado desde https://iase-web.org/icots/9/proceedings/pdfs/ICOTS9_2B2_FIELDINGWELLS.pdf
  18. Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions Educational Studies in Mathematics, 15(1), 1-24. DOI: https://doi.org/10.1007/bf00380436
  19. Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel Publishing. DOI: https://doi.org/10.1007/978-94-010-1858-6
  20. Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. En Graham A. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 39 63). Boston, MA: Springer. DOI: https://doi.org/10.1007/0-387-24530-8_3
  21. Gandhi, H. (2018). Understanding Children’s Meanings of Randomness in Relation to Random Generators. En C., Batanero & E., Chernoff (Eds.), Teaching and Learning Stochastics, Advances in Probability Education Research, ICME-13 Monograph (pp. 181-200). Cham: Springer. DOI: https://doi.org/10.1007/978-3-319-72871-1_11
  22. Garfield, J., & Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: implications for research. Journal for Research in Mathematics Education, 19(1), 44–63. DOI: https://doi.org/10.2307/749110
  23. Garfield, J., & Ben‐Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372-396. DOI: https://doi.org/10.1111/j.1751-5823.2007.00029.x
  24. Gauvrit, N., & Morsanyi, K. (2014). The equiprobability bias from a mathematical and psychological perspective. Advances in cognitive psychology, 10(4), 119-130. Recuperado desde https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4310748/
  25. Gigerenzer, G. (2011). Decisiones Instintivas: la inteligencia del inconsciente. Barcelona: Editorial Ariel.
  26. Hoffrage, U., Krauss, S., Martignon, L., & Gigerenzer, G. (2015). Natural frequencies improve Bayesian reasoning in simple and complex inference tasks. Frontiers in psychology, 6, 1473. DOI: https://doi.org/10.3389/fpsyg.2015.01473
  27. Jones, G., Langrall, C., Thornton, C., & Mogill, A. (1999). Students’ probabilistic thinking in instruction. Journal for Research in Mathematics Education, 30(5), 487–519. DOI: https://doi.org/10.2307/749771
  28. Kahneman, D. (2012). Pensar rápido, pensar despacio. Barcelona: Penguin Random House.
  29. Kahneman, D., & Tversky, A. (1982). The psychology of preferences. Scientific American, 246(1), 160-173. DOI: http://dx.doi.org/10.1038/scientificamerican0182-160
  30. Kruger, J., Wirtz, D., & Miller, D. (2005). Counterfactual thinking and the first instinct fallacy. Journal of personality and social psychology, 88(5), 725-735. DOI: https://doi.org/10.1037/e413812005-243
  31. Laplace, P. (1814). Essai philosophique sur les probabilités. Paris: Mme Ve Courcier. Recuperado desde de https://www.e-rara.ch/zut/doi/10.3931/e-rara-3684.
  32. Lecoutre, M., Durand, J., & Cordier, J. (1990). A study of two biases in probabilistic judgments: Representativeness and equiprobability. En J. P. Caverni, J. M. Fabre & M. González (Eds.), Advances in Psychology: Cognitive Biases (pp. 563-575). Amsterdam: Elsevier. DOI: https://doi.org/10.1016/s0166-4115(08)61343-6
  33. Martignon, L. (2014). Fostering children’s probabilistic reasoning and first elements of risk evaluation. En E. J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking (pp. 149-160). Dordrecht: Springer. DOI: https://doi.org/10.1007/978-94-007-7155-0_9
  34. Ministerio de Educación de Chile (2014). Comprender la categoría de desempeño. En Autor (Ed.), Guía para comprender la categoría de desempeño y orientar las rutas de mejora (pp. 13-26). Recuperado de http://archivos.agenciaeducacion.cl/guia_para_comprender_categoria_de_desempeno.pdf
  35. Ministerio de Educación de Chile (2015). Matemática. En Autor (Ed.), Bases Curriculares 7° básico a 2° medio (pp. 93-106). Recuperado de http://www.curriculumnacional.cl/614/articles-37136_bases.pdf
  36. Morsanyi, K., Primi, C., Chiesi, F., & Handley, S. (2009). The effects and side-effects of statistics education: Psychology students’(mis-) conceptions of probability. Contemporary Educational Psychology, 34(3), 210-220. DOI: https://doi.org/10.1016/j.cedpsych.2009.05.001
  37. Nikiforidou, Z. (2019). Probabilities and Preschoolers: Do Tangible Versus Virtual Manipulatives, Sample Space, and Repetition Matter?. Early Childhood Education Journal, 47(6), 769-777. DOI: https://doi.org/10.1007/s10643-019-00964-2
  38. OECD (2016). PISA 2015 Results (Volume I): Excellence and Equity in Education. Paris: OECD Publishing. DOI: https://doi.org/10.1787/9789264266490-en
  39. Pratt, D., & Kazak, S. (2018). Research on Uncertainty. En Ben-Zvi, D., Makar, K., & Garfield, J. (Eds.), International Handbook of Research in Statistics Education (pp. 193-227), Cham: Springer. DOI: https://doi.org/10.1007/978-3-319-66195-7_6
  40. Reyes- Gasperini, D., & Cantoral, R. (2016). Empoderamiento docente: la práctica docente más allá de la didáctica… ¿qué papel juega el saber en una transformación educativa? Revista de la Escuela de Ciencias de la Educación, 2(11), 155-176. Recuperado de http://www.revistacseducacion.unr.edu.ar/ojs/index.php/educacion/article/viewFile/265/248
  41. Reyes- Gasperini, D. (2016). Empoderamiento docente y Socioepistemología. Un estudio sobre la transformación educativa en Matemáticas. México: Gedisa.
  42. Sedlmeier, P. (1999). Improving statistical reasoning: Theoretical models and practical implications. New York: Psychology Press. DOI: https://doi.org/10.4324/9781410601247
  43. Stake, R. (2007). Investigación con estudio de casos. Madrid: Morata.
  44. Van Dooren, W. (2014). Probabilistic thinking: analyses from a psychological perspective. En E. J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking (pp. 123-126). Springer, Dordrecht. DOI: https://doi.org/10.1007/978-94-007-7155-0_7
  45. Vergnaud, G. (1983). Multiplicative structures. En R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127-174). Orlando, FL: Academic Press.
  46. Vergnaud, G. (1997). The nature of mathematical concepts. En T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 5-28). Hove, England: Psychology Press.
  47. Watson, J., & Shaughnessy, M. (2004). Proportional Reasoning: Lessons from Research in Data and Chance. Mathematics Teaching in the Middle School, 10(2), 104-109. Recuperado desde https://www.researchgate.net/publication/234667935_Proportional_Reasoning_Lessons_from_Research_in_Data_and_Chance
  48. Zhu, L., & Gigerenzer, G. (2006). Children can solve Bayesian problems: The role of representation in mental computation. Cognition, 98(3), 287-308. DOI: https://doi.org/10.1016/j.cognition.2004.12.003

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