Análisis de las Intuiciones y Conocimientos sobre Probabilidad de Estudiantes de Bachillerato
DOI:
10.37618/PARADIGMA.1011-2251.2021.p342-369.id1028Palabras clave:
Conocimientos, Enfoque frecuencial, Probabilidad, Experimento de diseño, Enfoque clásicoResumen
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.Descargas
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Amir, G. S. & Williams, J. S. (1999). Cultural influences on children’s probabilistic thinking. Journal of Mathematical Behavior, 18(1), 85-107. https://doi.org/10.1016/S0732-3123(99)00018-8.
Aspinwall, L. & Tarr, J. E. (2001). Middle school students’ understanding of the role sample size plays in empirical probability. Journal of Mathematical Behavior, 20, 229–245. https://doi.org/10.1016/S0732-3123(01)00066-9.
Ayres, P., & Way, J. (2000). Knowing the sample space or not: The effects on decision making. In T. Nakahara & M. Koyama (Eds), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 33-40). Hiroshima: PME Group.
Batanero, C. & Serrano, L. (1999). The meaning of randomness for secondary students. Journal for Research in Mathematics Education, 30, 558-567. https://doi.org/10.2307/749774.
Batanero, C., Navarro-Pelayo, V., & Godino, J. D. (1997). Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educational Studies in Mathematics, 32, 181-199. https://doi.org/10.1023/A:1002954428327.
Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. En G. A. Jones (Ed.), Exploring probability in school. challenges for teaching and learning. New York: Springer.
Begué, N., Batanero, C., Gea, M.M. y Beltrán-Pellicer, P. (2017). Comprensión del enfoque frecuencial de la probabilidad por estudiantes de Educación Secundaria Obligatoria. En J.M. Muñoz-Escolano, A. Arnal-Bailera, P. Beltrán-Pellicer, M.L. Callejo y J. Carrillo (Eds.), Investigación en Educación Matemática XXI (pp. 137-146). Zaragoza: SEIEM
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. En C. Batanero, G. Burril, & C. Reading (Eds.), Teaching statistics in school mathematics – challenges for teaching and teacher education (pp. 85-96). New York: Springer
Dantal, B. (1998). Comment les élèves de terminale perçoivent les concepts d’expérience aléatoire, d’événement et de probabilité. En Enseigner les probabilités au lycée. Ouvertures statistiques, enjeux épistémologiques, questions didactiques et idées d’activités (pp. 67-69). Grénoble: Commission inter-IREM Statistiques et Probabilités.
Denzin, N. K. & Lincoln, Y. S. (2011). Introduction. The discipline and practice of qualitative research. En N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (pp. 1-19). London: SAGE.
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. https://doi.org/10.1023/A:1002914202652.
Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgements in children in adolescence. Educational Studies in Mathematics, 22, 523-549. https://doi.org/10.1007/BF00312714.
Fischbein, E. & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96-105. https://doi.org/10.5951/jresematheduc.28.1.0096.
Flyvbjerg, B. (2011). Case study. En N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (pp. 301-316). London: SAGE.
Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. En G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39-63). Nueva York: Springer.
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 (Eds.), Proceedings of the First International Conference on Teaching Statistics (pp. 766-783). Sheffield, England: Teaching Statistics Trust.
Green, D. R. (1988). Children’s understanding of randomness: Report of a survey of 1600 children aged 7-11 years. En R. Davidson & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Statistics (pp. 287-291). Victoria, BC, Canada: University of Victoria.
Ireland, S. & Watson, J. (2009). Building a connection between experimental and theoretical aspects of probability. International Electronic Journal of Mathematics Education, 4(3), 339-370.
Jones, G. A., Langall, C. W., & Mooney, E. S. (2007). Research on probability. Responding to classroom realities. En F. K. Lester Jr. (Ed.). Second handbook of research on mathematics teaching and learning. Charlotte, NC: National Council of Teachers of Mathematics & Information Age Publishing.
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: Heuristics and biases (509-520). Cambridge: Cambridge University
Lee, H. S., Angotti, R. L., & Tarr, J. E. (2009). Making comparisons between observed data and expected outcomes: students’ informal hypothesis testing with probability simulation tools. Statistics Education Research Journal, 9(1), 68-96
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. Presenting plural perspective (509-532). New York: Springer.
Pfannkuch, M. & Ziedins, I. (2014). A modelling perspective on probability. En E. J. Chernoff, & B. Sriraman (Eds.). Probabilistic thinking. Presenting plural perspective (pp. 101-116). New York: Springer.
Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., Wild, C., & Ziedins, I. (2016). Probability modeling and thinking: what can we learn from practice? Statistics Education Research Journal, 15(2), 11-37.
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 education: Towards an evidence-based society. Proceedings of the Eighth International Conference on Teaching Statistics (ICOTS8, July, 2010), Ljubljana, Slovenia.
Sánchez, E., & Valdez, J. (2014). Reasoning development of a high school student about probability concept. En K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics. Flagstaff, AR: International Statistical Institute.
SEP (2017). Aprendizajes clave para la educación integral. Matemáticas, educación secundaria. Plan y programas de estudio. Ciudad de México: Secretaría de Educación Pública.
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 on mathematics teaching and learning (pp. 465-494). New York: Macmillan.
Shaughnessy, J. M., & Ciancetta, M. (2002). Students’ understanding of variability in a probability environment. In B. Philips (Ed.), Proceeding of the Sixth International Conference on the Teaching of Statistics [CD-ROM]. Cape Town, South Africa: International Statistical Institute.
Stohl, H., & Tarr, J. E. (2002). Developing notions of inference with probability simulation tools. Journal of Mathematical Behavior, 21(3), 319–337. https://doi.org/10.1016/S0732-3123(02)00132-3.
Stohl, H., Rider, R., & Tarr, J. (2004). Making connections between empirical and theoretical probability: Students’ generation and analysis of data in a technology environment. http://www.probexplorer.com/Articles/LeeRiderTarrConnectE&T.pdf.
Tarr, J. E. (2002). The confounding effects of “50-50 chance” in making conditional probability judgments. Focus on Learning Problems in Mathematics, 24, 35-53.
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 for teaching and learning (pp. 145-168). New York: Springer.
Watson, J. M., & Moritz, J. B. (2003). Fairness of dice: A longitudinal study of students’ beliefs and strategies for making judgments. Journal for Research in Mathematics Education, 34, 270-304. https://doi.org/10.2307/30034785.
Aspinwall, L. & Tarr, J. E. (2001). Middle school students’ understanding of the role sample size plays in empirical probability. Journal of Mathematical Behavior, 20, 229–245. https://doi.org/10.1016/S0732-3123(01)00066-9.
Ayres, P., & Way, J. (2000). Knowing the sample space or not: The effects on decision making. In T. Nakahara & M. Koyama (Eds), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 33-40). Hiroshima: PME Group.
Batanero, C. & Serrano, L. (1999). The meaning of randomness for secondary students. Journal for Research in Mathematics Education, 30, 558-567. https://doi.org/10.2307/749774.
Batanero, C., Navarro-Pelayo, V., & Godino, J. D. (1997). Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educational Studies in Mathematics, 32, 181-199. https://doi.org/10.1023/A:1002954428327.
Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. En G. A. Jones (Ed.), Exploring probability in school. challenges for teaching and learning. New York: Springer.
Begué, N., Batanero, C., Gea, M.M. y Beltrán-Pellicer, P. (2017). Comprensión del enfoque frecuencial de la probabilidad por estudiantes de Educación Secundaria Obligatoria. En J.M. Muñoz-Escolano, A. Arnal-Bailera, P. Beltrán-Pellicer, M.L. Callejo y J. Carrillo (Eds.), Investigación en Educación Matemática XXI (pp. 137-146). Zaragoza: SEIEM
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. En C. Batanero, G. Burril, & C. Reading (Eds.), Teaching statistics in school mathematics – challenges for teaching and teacher education (pp. 85-96). New York: Springer
Dantal, B. (1998). Comment les élèves de terminale perçoivent les concepts d’expérience aléatoire, d’événement et de probabilité. En Enseigner les probabilités au lycée. Ouvertures statistiques, enjeux épistémologiques, questions didactiques et idées d’activités (pp. 67-69). Grénoble: Commission inter-IREM Statistiques et Probabilités.
Denzin, N. K. & Lincoln, Y. S. (2011). Introduction. The discipline and practice of qualitative research. En N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (pp. 1-19). London: SAGE.
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. https://doi.org/10.1023/A:1002914202652.
Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgements in children in adolescence. Educational Studies in Mathematics, 22, 523-549. https://doi.org/10.1007/BF00312714.
Fischbein, E. & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96-105. https://doi.org/10.5951/jresematheduc.28.1.0096.
Flyvbjerg, B. (2011). Case study. En N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (pp. 301-316). London: SAGE.
Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. En G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39-63). Nueva York: Springer.
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 (Eds.), Proceedings of the First International Conference on Teaching Statistics (pp. 766-783). Sheffield, England: Teaching Statistics Trust.
Green, D. R. (1988). Children’s understanding of randomness: Report of a survey of 1600 children aged 7-11 years. En R. Davidson & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Statistics (pp. 287-291). Victoria, BC, Canada: University of Victoria.
Ireland, S. & Watson, J. (2009). Building a connection between experimental and theoretical aspects of probability. International Electronic Journal of Mathematics Education, 4(3), 339-370.
Jones, G. A., Langall, C. W., & Mooney, E. S. (2007). Research on probability. Responding to classroom realities. En F. K. Lester Jr. (Ed.). Second handbook of research on mathematics teaching and learning. Charlotte, NC: National Council of Teachers of Mathematics & Information Age Publishing.
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: Heuristics and biases (509-520). Cambridge: Cambridge University
Lee, H. S., Angotti, R. L., & Tarr, J. E. (2009). Making comparisons between observed data and expected outcomes: students’ informal hypothesis testing with probability simulation tools. Statistics Education Research Journal, 9(1), 68-96
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. Presenting plural perspective (509-532). New York: Springer.
Pfannkuch, M. & Ziedins, I. (2014). A modelling perspective on probability. En E. J. Chernoff, & B. Sriraman (Eds.). Probabilistic thinking. Presenting plural perspective (pp. 101-116). New York: Springer.
Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., Wild, C., & Ziedins, I. (2016). Probability modeling and thinking: what can we learn from practice? Statistics Education Research Journal, 15(2), 11-37.
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 education: Towards an evidence-based society. Proceedings of the Eighth International Conference on Teaching Statistics (ICOTS8, July, 2010), Ljubljana, Slovenia.
Sánchez, E., & Valdez, J. (2014). Reasoning development of a high school student about probability concept. En K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics. Flagstaff, AR: International Statistical Institute.
SEP (2017). Aprendizajes clave para la educación integral. Matemáticas, educación secundaria. Plan y programas de estudio. Ciudad de México: Secretaría de Educación Pública.
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 on mathematics teaching and learning (pp. 465-494). New York: Macmillan.
Shaughnessy, J. M., & Ciancetta, M. (2002). Students’ understanding of variability in a probability environment. In B. Philips (Ed.), Proceeding of the Sixth International Conference on the Teaching of Statistics [CD-ROM]. Cape Town, South Africa: International Statistical Institute.
Stohl, H., & Tarr, J. E. (2002). Developing notions of inference with probability simulation tools. Journal of Mathematical Behavior, 21(3), 319–337. https://doi.org/10.1016/S0732-3123(02)00132-3.
Stohl, H., Rider, R., & Tarr, J. (2004). Making connections between empirical and theoretical probability: Students’ generation and analysis of data in a technology environment. http://www.probexplorer.com/Articles/LeeRiderTarrConnectE&T.pdf.
Tarr, J. E. (2002). The confounding effects of “50-50 chance” in making conditional probability judgments. Focus on Learning Problems in Mathematics, 24, 35-53.
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 for teaching and learning (pp. 145-168). New York: Springer.
Watson, J. M., & Moritz, J. B. (2003). Fairness of dice: A longitudinal study of students’ beliefs and strategies for making judgments. Journal for Research in Mathematics Education, 34, 270-304. https://doi.org/10.2307/30034785.
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22-02-2021
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Martínez Pérez, S. A. ., & Sánchez Sánchez, E. A. . (2021). Análisis de las Intuiciones y Conocimientos sobre Probabilidad de Estudiantes de Bachillerato. PARADIGMA, 41(e1), 342–369. https://doi.org/10.37618/PARADIGMA.1011-2251.2021.p342-369.id1028
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