Análisis de las intuiciones y conocimientos sobre probabilidad de estudiantes de bachillerato

• Sandra Areli Martínez Pérez ^[1] ; Ernesto A Sánchez Sánchez ^[1]
  1. [1] DME, CINVESTAV, IPN CDMX, México
• Localización: Paradigma, ISSN 1011-2251, Nº. Extra 1, 2021, págs. 342-369
• Idioma: español
• DOI: 10.37618/paradigma.1011-2251.2021.p342-369.id1028
• Títulos paralelos:
  • Analysis of intuitions and knowledge about probability of high school students
  • Análise das intuições e conhecimento sobre probabilidade de alunos do ensino médio
• Enlaces
  • Texto completo
• Resumen
  • español

    El objetivo de esta investigación es hacer un diagnóstico de las intuiciones y conocimientos sobre conceptos básicos de probabilidad, en sus enfoques clásico y frecuencial, que exhiben los estudiantes de bachillerato antes de llevar a cabo con ellos un experimento de diseño sobre el enfoque frecuencial. Se aplicó un cuestionario de 10 ítems a 22 estudiantes de bachillerato (17-18 años) que habían estudiado temas de introducción a la probabilidad (hasta las distribuciones) del curso institucional que llevan. El cuestionario contiene tres preguntas para explorar su comprensión de algunos términos de probabilidad, seis problemas en situaciones de urnas y un problema con información incompleta, que explora las ideas espontáneas que surgen cuando intentan relacionar la probabilidad con contextos diferentes a los juegos de azar. Las respuestas se categorizaron para determinar los patrones presentes que permitan ofrecer características de sus conocimientos. Los resultados del análisis revelan conocimientos parciales de los términos experiencia aleatoria, frecuencia relativa y probabilidad que se relacionan más con nociones de sus vivencias personales que con las definiciones técnicas. Aunque calculan probabilidades clásicas y frecuenciales en situaciones simples de urnas, tienen dificultades en la consideración de resultados de extracciones sucesivas. La noción de repetibilidad de una experiencia aleatoria no emerge en algunas situaciones en que sería pertinente y se percibe que se basan en un modelo subjetivo que no requiere la repetibilidad del experimento.

  • English

    The objective of this research is to make a diagnosis of high school students’ intuitions and knowledge about basic concepts of probability, in its classical and frequentist approaches, before carrying out a design experiment on the frequentist approach . A 10-item questionnaire was given to 22 high school students (17-18 years old) who had studied introductory topics to probability ( until distributions) in the institutional course they were taking. The questionnaire contains three questions to explore their understanding of some probability terms, six problems in ballot box situations, and one ill-defined problem that explores the spontaneous ideas that arise when the students try to relate probability to contexts different to gambling. The responses were categorized to determine the patterns that help us to offer characteristics of their knowledge. The results of the analysis reveal partial knowledge of the terms random experience, relative frequency and probability that are more related to notions of their personal experiences than to the technical definitions. Although the students calculate classical and frequency probabilities in simple ballot box situations, they have difficulties in considering the results of successive draws. The notion of repeatability of a random experience does not emerge in some situations where it is relevant and we interpret that it is based on a subjective model that does not require the repeatability of the experiment.

  • português

    O objetivo desta pesquisa é fazer um diagnóstico das intuições e conhecimentos sobre os conceitos básicos de probabilidade, em suas abordagens clássica e frequencial, apresentados por alunos do ensino médio antes de realizar um experimento projetual sobre a abordagem frequencial com eles. Um questionário de 10 itens foi aplicado a 22 alunos do ensino médio (17-18 anos) que haviam estudado tópicos introdutórios à probabilidade (até as distribuições) do curso institucional que estão cursando. O questionário contém três perguntas para explorar a compreensão de alguns termos de probabilidade, seis problemas em situações de urna eleitoral e um problema mal definido que explora as ideias espontâneas que surgem quando tentam relacionar a probabilidade a contextos diferentes do jogo. As respostas foram categorizadas para determinar os padrões presentes que permitem oferecer características de seu conhecimento. Os resultados da análise revelam um conhecimento parcial dos termos experiência aleatória, frequência relativa e probabilidade, que estão mais relacionados com noções de suas experiências pessoais do que com definições técnicas. Embora calculem as probabilidades clássicas e de frequência em situações de urna simples, eles têm dificuldade em considerar os resultados de sorteios sucessivos. A noção de repetibilidade de uma experiência aleatória não surge em algumas situações onde seria relevante e é percebida como baseada em um modelo subjetivo que não requer repetibilidade do experimento.

• Referencias bibliográficas
  • Citas Amir, G. S. & Williams, J. S. (1999). Cultural influences on children’s probabilistic thinking. Journal of Mathematical Behavior,...
  • Aspinwall, L. & Tarr, J. E. (2001). Middle school students’ understanding of the role sample size plays in empirical probability. Journal...
  • Ayres, P., & Way, J. (2000). Knowing the sample space or not: The effects on decision making. In T. Nakahara & M. Koyama (Eds), Proceedings...
  • Batanero, C. & Serrano, L. (1999). The meaning of randomness for secondary students. Journal for Research in Mathematics Education, 30,...
  • Batanero, C., Navarro-Pelayo, V., & Godino, J. D. (1997). Effect of the implicit combinatorial model on combinatorial reasoning in secondary...
  • Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. En G. A. Jones (Ed.), Exploring probability in school....
  • Begué, N., Batanero, C., Gea, M.M. y Beltrán-Pellicer, P. (2017). Comprensión del enfoque frecuencial de la probabilidad por estudiantes de...
  • Birks, M. y Mills, J. (2015). Grounded theory. A practical guide. London: SAGE.
  • Chaput, B., Girard, J.-C, & Henry, M. (2011). Frequentistic approach: modelling and simulation instatistics and probability teaching....
  • Dantal, B. (1998). Comment les élèves de terminale perçoivent les concepts d’expérience aléatoire, d’événement et de probabilité. En Enseigner...
  • Denzin, N. K. & Lincoln, Y. S. (2011). Introduction. The discipline and practice of qualitative research. En N. K. Denzin & Y. S....
  • Fischbein, E. (1987). Intuition in science and mathematics. Dodrecht: Reidel.
  • Fischbein, E. & Grossman, A. (1997). Schemata and intuitions in combinatorial reasoning. Educational Studies in Mathematics, 34, 27-47....
  • Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgements in children in adolescence. Educational...
  • Fischbein, E. & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in...
  • Flyvbjerg, B. (2011). Case study. En N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (pp. 301-316). London:...
  • Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. En G. A. Jones (Ed.), Exploring...
  • Green, D. R. (1983). A survey of probability concepts in 3000 pupils aged 11-16 years. In D. R. Grey, P. Holmes, V. Barnett, & G. M. Constable...
  • Green, D. R. (1988). Children’s understanding of randomness: Report of a survey of 1600 children aged 7-11 years. En R. Davidson & J....
  • Ireland, S. & Watson, J. (2009). Building a connection between experimental and theoretical aspects of probability. International Electronic...
  • Jones, G. A., Langall, C. W., & Mooney, E. S. (2007). Research on probability. Responding to classroom realities. En F. K. Lester Jr....
  • Kahneman, D. (2012). Pensar rápido, Pensar despacio. Villatuerta, España: Debate.
  • Kahneman, D., & Tversky, A. (1982). Variants of uncertainty. En D. Kahneman, P. Slovic, & A. Tversky (Eds.). Judgment under uncertainty:...
  • Lee, H. S., Angotti, R. L., & Tarr, J. E. (2009). Making comparisons between observed data and expected outcomes: students’ informal hypothesis...
  • Miles, M. & Huberman, A. (1994). An expanded sourcebook qualitative data analysis (2a ed.). Londres: Sage Publications.
  • Mosteller, F. (1956). Fifty Challenging Problems in Probability with Solutions. New York: Dover.
  • Nilsson, P. (2014). Experimentation in probability teaching and learning. En Chernoff E. J., Sriraman, B. (Eds.). Probabilistic thinking....
  • Pfannkuch, M. & Ziedins, I. (2014). A modelling perspective on probability. En E. J. Chernoff, & B. Sriraman (Eds.). Probabilistic...
  • Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., Wild, C., & Ziedins, I. (2016). Probability modeling and thinking:...
  • Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31, 602–625. https://doi.org/10.2307/749889.
  • Sánchez, E., Hernández, A. (2010). A statistical game: the silent cooperation problem. En C. Reading (Ed.), Data and context in statistics...
  • Sánchez, E., & Valdez, J. (2014). Reasoning development of a high school student about probability concept. En K. Makar, B. de Sousa,...
  • SEP (2017). Aprendizajes clave para la educación integral. Matemáticas, educación secundaria. Plan y programas de estudio. Ciudad de México:...
  • SEP (2011). Plan de estudio 2011. Educación básica. Ciudad de México: Secretaría de Educación Pública
  • Shaughnessy J. M. (1992). Research in probability and statistics: Reflections and Directions. En D. A. Grouws (Ed.), Handbook of research...
  • Shaughnessy, J. M., & Ciancetta, M. (2002). Students’ understanding of variability in a probability environment. In B. Philips (Ed.),...
  • Stohl, H., & Tarr, J. E. (2002). Developing notions of inference with probability simulation tools. Journal of Mathematical Behavior,...
  • Stohl, H., Rider, R., & Tarr, J. (2004). Making connections between empirical and theoretical probability: Students’ generation and analysis...
  • Tarr, J. E. (2002). The confounding effects of “50-50 chance” in making conditional probability judgments. Focus on Learning Problems in Mathematics,...
  • Von Mises, R. (1957). Probability, statistics and truth. New York: Dover Publications, Inc.
  • Watson, J. M. (2005). The probabilistic reasoning of middle school students. In G. A. Jones (Ed.), Exploring probability in school: Challenges...
  • Watson, J. M., & Moritz, J. B. (2003). Fairness of dice: A longitudinal study of students’ beliefs and strategies for making judgments....