Didactic proposal of binomial distribution for undergraduate students incorporating technology
Main Article Content
Abstract
This paper describes the application process of a design for the teaching of binomial distribution which incorporates the use of Fhatom software. Thirty-five Chilean high school students (15 to 18 years old) participated in the experience. The teaching design includes manipulative, computational and algebraic representations, as well as some of the recommendations of the GAISE project. A task with a context close to the students is proposed, and its solution implies the generation of sampling distributions. Based on this information, several questions are proposed that allow conjecturing about the concept and characteristics of the binomial distribution, which are later formalized. Trough the development of the proposal, the students were able to understand some concepts of the binomial distribution.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The published works are the property of their authors, who may make use of them for subsequent publications, always including the original edition (original title, Ensino em Re-Vista, volume, number, pages). All articles in this journal are the sole responsibility of their authors, and no legal responsibility for their content rests with the Journal or EDUFU.
References
ALPÍZAR, M. Herramientas tecnológicas en el proceso de enseñanza y aprendizaje de la estadística. Cuadernos de investigación y formación en educación matemática, n. 3, p. 96-115. 2007.
BARGAGLIOTTI, A.; FRANKLIN, C.; ARNOLD, P.; GOULD, R.; JOHNSON, S.; PEREZ, L.; SPANGLER, D. Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II) A Framework for Statistics and Data Science Education. Virginia: American Statistical Association and National Council of Teachers of Mathematics, 2020.
BATANERO, C.; GARFIELD, J.; OTTAVIANI, M. G.; TRURAN, J. Research in statistical education: Some priority questions. Statistical Education Research Newsletter, v. 1, n. 2, p. 2-6. 2000.
BATANERO, C.; SÁNCHEZ, E. What is the nature of high school student’s conceptions and misconceptions about probability? En G. A. Jones (ed.), Exploring probability in school: Challenges for teaching and learning, p. 241-266. New York: Springer. 2005. Disponible en: https://doi.org/10.1007/0-387-24530-8_11. Revisado 16 de Julio, 2023.
BATANERO, C.; CHERNOFF, E. J.; ENGEL, J.; LEE, H.; SÁNCHEZ, E. Research on teaching and learning probability. ICME-13. Topical Survey series. New York, NY: Springer. 2016.
BATANERO, C.; BOROVCNIK, M. Statistics and probability in high school. Rotterdam: Sense Publishers. 2016.
BEGUÉ, N.; BATANERO, C.; GEA, M. M. Argumentos de los estudiantes de bachillerato en la generación de muestras de la distribución binomial. En CONTRERAS, J. M.; GEA, M. M.; LÓPEZ-MARTÍN M. M.; MOLINA-PORTILLO, E. (Eds.), Actas del Tercer Congreso Internacional Virtual de Educación Estadística. 2019. Disponible en: www.ugr.es/local/fqm126/civeest.html. Revisado 16 de Julio, 2023.
BEGUÉ, N.; DIAZ-LEVICOY, D.; BATANERO, C.; GEA, M. M.. Lanzamiento a una canasta de baloncesto: interpretación de una situación binomial por estudiantes de Bachillerato. En: ZACARIAS, J.; CRUZ, H.; VELASCO, F.; JUAREZ, B.; VASQUEZ, V. H.; TAJONAR, F.; REYES, H.; SALGADO, G. (Eds.), Innovación en los Procesos de Enseñanza y Aprendizaje de lo Estadístico y lo Estocástico. Puebla, 2021. p. 19-34.
BIEHLER, R.; BEN-ZVI, D.; BAKKER, A.; MAKAR, K. Technology for enhancing statistical reasoning at the school level. In M. A. (Ken) Clements et al. (Eds.), Third International Handbook of Mathematics Education (pp. 643-689) Springer International Handbooks of Education 27. 2013. DOI: https://doi.org/10.1007/978-1-4614-4684-2_21.
CISTERNAS, G.; DIAZ-PALLAUTA, J.; DIAZ-LEVICOY D. Aproximación a la distribución de Poisson incorporando el uso de tecnología desde el Enfoque Ontosemiótico. Educação Matemática Debate, v. 5, n. 11, p. 1-25. 2021. DOI: https://doi.org/10.46551/emd.e202112.
CHANCE, B.; BEN-ZVI, D.; GARFIELD, J.; MEDINA, E. The Role of Technology in Improving Student Learning of Statistics. Technology Innovations in Statistics Education, v.1, n. 1. 2007. DOI: http://dx.doi.org/10.5070/T511000026.
ENGEL, J. Statistical literacy for active citizenship: a call for data science education. Statistics Education Research Journal, v.16, n.1, p. 44-49. 2017. DOI: https://doi.org/10.52041/serj.v16i1.213.
FISCHBEIN, E. Intuition in science and mathematics. Reidel. 1987.
GAL, I. Towards" probability literacy" for all citizens: Building blocks and instructional dilemmas. En Exploring probability in school: Challenges for teaching and learning. Boston, MA: Springer US, 2005. p. 43-71.
GARCÍA-GARCÍA, J.; ARREDONDO, E.; MÁRQUEZ, M. Desarrollo de la noción de distribución binomial en estudiantes de bachillerato con apoyo de tecnología. Revista Paradigma, v. 39, n. 2, p. 92 – 106. 2018.
GARCÍA, L. Necesidad de una educación digital en un mundo digital. Revista Iberoamericana de Educación a Distancia (RIED). v.22, n. 2, p. 9-22. 2019. DOI: http://dx.doi.org/10.5944/ried.22.2.23911.
GARFIELD, J.; BEN-ZVI, D.; CHANCE, B.; MEDINA, E.; ROSETH, C.; ZIEFFLER, A. Developing students’ Statistical reasoning: connecting research and teaching practice. Dordrecht: Springer, 2008.
IZCARA, S. Manual de investigación cualitativa. Fontamara. 2014.
KONOLD, C. Informal conceptions of probability. Cognition and Instruction, v. 6, n. 1, p. 59-98. 1989. Disponible en: http://www.jstor.org/stable/3233463.
LANDÍN, P.; SÁNCHEZ, E.. Niveles de razonamiento probabilístico de estudiantes de bachillerato frente a tareas de distribución binomial. Educação Matemática Pesquisa, v. 12, n. 3, p. 598-618. 2010.
MINISTERIO DE EDUCACIÓN (MINEDUC). Bases Curriculares 3º y 4º medio. Unidad de Currículum y Evaluación. 2019. Disponible en: https://bibliotecadigital.mineduc.cl/bitstream/handle/20.500.12365/14364/bases%203%c2%b0%204%c2%b0.pdf?sequence=1&isAllowed=y. Revisado el 11 de julio, 2023.
MINISTERIO DE EDUCACIÓN (MINEDUC). Programa de Estudio Matemática 3º medio. Unidad de Currículum y Evaluación. 2020. Disponible en: https://www.curriculumnacional.cl/614/articles-140137_programa.pdf. Revisado el 10 de septiembre, 2023.
MUÑIZ-RODRÍGUEZ, L.; RODRÍGUEZ-MUÑIZ, L. J.; ALSINA, A.. Deficits in the statistical and probabilistic literacy of citizens: Effects in a world in crisis. Mathematics, v. 8, n. 11, p. 1-20, 2020. DOI: https://doi.org/10.3390/math8111872.
PALLAUTA, J.; ARTEAGA, P. Niveles de complejidad semiótica en gráficos y tablas Estadísticas, v. 108, p. 13-22, 2021.
PRATT, D.; DAVIES, N.; CONNOR, D. The role of technology in teaching and learning Statistics. En: BATANERO, C.; BURRILL, G.; READING, C. (Ed.), Teaching statistics in school mathematics. Challenges for teaching and teacher education. A joint ICMI/IASE. New York: Springer, 2011, p. 97-107. DOI: https://doi.org/10.1007/978-94-007-1131-0_13.
RIDGWAY, J. Why engage with civic statistics? In J. Ridgway (Ed.), Statistics for empowerment and social engagement (pp. 1-13). Cham: Springer. 2022. DOI: https://doi.org/10.1007/978-3-031-20748-8_1.
SALINAS-HERRERA, J.; SALINAS-HERNÁNDEZ, U. Teaching and Learning the Notion of Normal Distribution Using a Digital Resource. Can. J. Sci. Math. Techn. Educ. v. 22, p. 576–590. 2022. DOI: https://doi.org/10.1007/s42330-022-00226-1.
SÁNCHEZ, E.; LANDÍN, P. Fiabilidad de una jerarquía para evaluar el razonamiento probabilístico acerca de la distribución binomial. En: Marín, Margarita; Fernández, Gabriel; Blanco, Lorenzo J.; Palarea, María Mercedes (Eds.), Investigación en Educación Matemática XV. Ciudad Real: SEIEM. 2011. p. 533-542. Disponible en: http://funes.uniandes.edu.co/1837/. Revisado el 07 de julio, 2023.