Comparing probabilities in urns: A study with primary school students
DOI:
https://doi.org/10.15359/ru.35-2.9Keywords:
Probability comparison, proportional reasoning, primary education, statistical education, urns, Costa RicaAbstract
The study aimed to explore the strategies used by Costa Rican primary school students when comparing urn probabilities. The sample was intentional and consisted of 55 6th graders. Using an interpretive approach, we analyzed the children’s responses to a questionnaire of five probability comparison items taken from previous studies, including different levels of proportional reasoning. Results indicate that problems in the first levels of proportional reasoning were solved easily by students, while problems at higher levels increased in difficulty. One-variable strategies, which compare only the favorable or unfavorable cases in both urns, are predominant; although there are correspondence strategies, few students show complete proportional reasoning. Aside from slight variations, results are similar to previous studies, which suggests that this task is influenced more by the child’s level of maturity than the instruction received.
References
Alpízar, M., Barrantes, J., Bolaños, H., Céspedes, M., Delgado, E., Freer, D., Padilla, E. y Víquez, M. (2012). Aspectos relevantes sobre la formación docente en I y II ciclos en los temas probabilidad y estadística. EDUCARE, 16(2), 113-129. https://doi.org/10.15359/ree.16-2.7
Alpízar, M., Chavarría, L. y Oviedo, K. (2015). Percepción de un grupo de docentes de I y II ciclo de educación general básica de escuelas públicas de Heredia sobre los temas de estadística y probabilidad. Actualidades Investigativas en Educación, 15(1), 1-23.
Batanero, C. (2006). Razonamiento probabilístico en la vida cotidiana: Un desafío educativo. In P. Flores & J. Lupiáñez (Eds.), Investigación en el aula de matemáticas. Estadística y Azar, 1-17. Granada: Sociedad de Educación Matemática Thales. CD ROM.
Behr, M. J., Harel, G., Post, T. R. y Lesh, R. (1992). Rational number, ratio, and proportion. In D. D. A. Grows (Ed.), Handbook of research in mathematics teaching and learning (pp. 296-333). Macmillan.
Ben-Chaim, D., Keret, Y. e Ilany, B. S. (2012). Ratio and proportion: Research and teaching in mathematics teachers’ education. Sense Publisher. https://doi.org/10.1007/978-94-6091-784-4_2
Bisquerra, R. (1989). Métodos de investigación educativa. P.P.U.
Borovcnik, M. (2011). Strengthening the role of probability within statistics curricula. In Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education (pp. 71-83). Dordrecht. https://doi.org/10.1007/978-94-007-1131-0_11
Cañizares, M. J. (1997). Influencia del razonamiento proporcional y combinatorio y de creencias subjetivas en las intuiciones probabilísticas primarias [Doctoral dissertation]. Universidad de Granada, España. In Spanish.
Cañizares, M. J. y Batanero, C. (1997). Influencia del razonamiento proporcional y de las creencias subjetivas en la comparación de probabilidades. UNO, 14, 99-114.
Cerrón, W. (2019). La investigación cualitativa en educación. Horizonte de la Ciencia, 9(17), 1-8. https://doi.org/10.26490/uncp.horizonteciencia.2019.17.510.
Falk, R., Falk, R. y Levin, I. (1980). A potential for learning probability in young children. Educational Studies in Mathematics, 11, 181-204. https://doi.org/10.1007/BF00304355
Fischbein, E. y Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 15(1), 1-24. https://doi.org/10.1007/BF00380436
Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. In Exploring probability in school (pp. 39-63). Springer, Boston, MA. https://doi.org/10.1007/0-387-24530-8_3
Gil, J., León, J. y Morales, M. (2017). Los paradigmas de investigación educativa, desde una perspectiva crítica. Conrado, 13(58), 72-74.
Green, D. R. (1982). Probability concepts in school pupils aged 11-16 years [Doctoral dissertation]. University of Loughborough, United Kingdom.
Jones, G., Langrall, C. y Mooney, E. (2007). Research in probability: Responding to classroom realities. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 909-955). Information Age Publishing y NCTM.
Karplus, R., Pulos, S. y Stage, E. (1983). Early adolescents proportional reasoning on “rate” problems. Educational Studies in Mathematics, 14, 219-233. https://doi.org/10.1007/BF00410539
Krippendorff, K. (2013). Content analysis: An introduction to its methodology. SAGE.
Langrall, C. W. y Mooney, E. S. (2005). Characteristics of elementary school students’ probabilistic thinking. In Jones, G. (Ed.), Exploring probability in school. Challenges for teaching and learning (pp. 95-119). Dordrech, The Netherlands. https://doi.org/10.1007/0-387-24530-8_5
Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 557-568. https://doi.org/10.1007/BF00540060
MECD (2014). Real Decreto 126/2014, de 28 de febrero, por el que se establece el currículo básico de la Educación Primaria. Madrid: Autor.
Ministerio de Educación Pública (MEP). (2012). Programas de Estudio de Matemáticas. I, II Y III Ciclos de la Educación General Básica y Ciclo Diversificado. Autor.
National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. The Council.
Noelting, G. (1980a). The development of proportional reasoning and the ratio concept. Part I - Differentiation of stages. Educational Studies in Mathematics, 11(2), 217-253. https://doi.org/10.1007/BF00304357
Noelting, G. (1980b). The development of proportional reasoning and the ratio concept. Part II - problem-structure at successive stages; problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11(3), 331-363. https://doi.org/10.1007/BF00697744
Pérez Echeverría, M. P., Carretero, M. y Pozo, J. I. (1986). Los adolescentes ante las matemáticas: Proporción y probabilidad. Cuadernos de Pedagogía, 133, 9-13.
Piaget, J. (1975). Psicología de la inteligencia. Buenos Aires: Psique.
Piaget, J. e Inhelder, B. (1951). La genése de l'idée de hasard chez l'enfant. Presses Universitaires de France. In French.
Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31(5), 602-625. https://doi.org/10.2307/749889
Truran, J. (1994). Examination of a relationship between children's estimation of probabilities and their understanding of proportion. In J. P. Ponte y J. F. Matos (Eds.), Proceedings of the XVIII PME (pp. 337-344). Universidad de Lisboa.
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