Analysis of probabilistic reasoning in future natural sciences teachers
DOI:
https://doi.org/10.22600/1518-8795.ienci2022v27n3p254Keywords:
Probabilistic reasoning, Science teacher training, Scientific reasoning stylesAbstract
This article investigates the ways of reasoning of a group of students, future science teachers, of the degrees in physics, chemistry and biology of the National Pedagogical University of Colombia, by addressing three problematic situations whose analysis implies making use of basic concepts of probability, such as event independence and counting notions. It should be noted that this research is part of the development of the doctoral thesis of the first author. The analysis of the students' modes of reasoning expressed in their responses is carried out considering the probabilistic reasoning style as a theoretical framework, one of the six styles of scientific reasoning proposed in the philosophical approach of Ian Hacking. And, to establish the different modes of reasoning, the criteria of the phenomenographic methodology are used, which allows expressing these modes in the form of description categories that have current scientific knowledge as a reference. The results obtained allow us to show that many students make incipient probabilistic reasoning; biases such as the gambler's fallacy, the application of frequency probability to few data, and the prevalence of deterministic thinking are identified. These shortcomings constitute a limitation when approaching the study of scientific theories, such as quantum mechanics or the evolution of species, in which it is essential to carry out probabilistic reasoning to understand them.References
Agnelli, H. (2009). Relevancia de la enseñanza de la Probabilidad. Ciencias Económicas, 2(7), 11-21. https://doi.org/10.14409/ce.v2i11.1139
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 investigación en matemática educativa, 21(2), 131-156. https://doi.org/10.12802/relime.18.2121
Ausubel, D. P., Novak, J. D., & Hanesian, H. (1976). Psicología educativa: un punto de vista cognoscitivo. México, México: Trillas.
Bach, R., Pope, D., Liou, S. H., & Batelaan, H. (2013). Controlled double-slit electron diffraction. New Journal of Physics, 15(3), 033018. https://doi.org/10.1088/1367-2630/15/3/033018
Ballentine, L. E. (1998). Quantum mechanics: a modern development. World Scientific Publishing Company.
Bao, L. & Redish, E. (2002). Understanding probabilistic interpretations of physical systems: A prerequisite to learning quantum physics. American Journal of Physics, 70(3), 210-217. https://doi.org/10.1119/1.447541
Batanero, C. (2001). Didáctica de la Estadística. Granada, España: Universidad de Granada.
Batanero, C. (2005). Significados de la probabilidad em la educación secundaria. Relime, 8(3), 247-263. Recuperado de https://www.redalyc.org/articulo.oa?id=33508302
Batanero, C., & Díaz, C. (2012). Training school teachers to teach probability: reflections and challenges. Chilean Journal of Statistics, 3(1), 3-13. Recuperado de http://soche.cl/chjs/volumes/03/01/Batanero_Diaz(2012).pdf
Batanero, C., Godino, J. D., & Navarro-Pelayo, V. (1996). Razonamiento Combinatorio. Madrid, España: Editorial Síntesis.
Batanero, C., Godino, J. D., & Roa, R. (2004). Training teachers to teach probability. Journal of statistics Education, 12(1). https://doi.org/10.1080/10691898.2004.11910715
Bohm, D. (1989). Quantum theory. New York, United States of America: Dover Publications.
Calude, C. S., & Longo, G. (2016). Classical, quantum and biological randomness as relative unpredictability. Natural Computing, 15(2), 263-278. https://doi.org/10.1007/s11047-015-9533-2
Carletta, J. (1996). Assessing agreement on classification tasks: The kappa statistic. Computational Linguistics, 22(2), 249–254. Recuperado de https://aclanthology.org/J96-2004.pdf
Carnap, R. (1969). Fundamentación lógica de la física. Buenos Aires, Argentina: Sudamenricana
Castiblanco, A., Urquina, H., Bonilla, M., & Romero, J. (2004). Pensamiento Estadístico y Tecnologías Computacionales. Proyecto Incorporación de Nuevas Tecnologías al Currículo de Matemáticas de la Educación Básica Secundaria y Media de Colombia. Bogotá, D. C., Colombia: Ministerio de Educación Nacional Dirección de Calidad de la Educación Preescolar, Básica y Media. Recuperado de https://redaprende.colombiaaprende.edu.co/metadatos/recurso/pensamiento-estadistico-y-tecnologias-computaciona/
Castro, J. A. (2011). Estilos de razonamiento científico y enseñanza de la Biología: posibles conexiones y propuestas didácticas. Revista de Educación en Biología, 14(2), 5-12. Recuperado de https://revistas.unc.edu.ar/index.php/revistaadbia/article/view/22328
Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and psychological measurement, 20(1), 37-46. https://doi.org/10.1177/001316446002000104
Davisson, C., & Germer, L. H. (1927). Diffraction of electrons by a crystal of nickel. Physical Review, 30(6), 705. https://doi.org/10.1103/PhysRev.30.705
Deane, T., Nomme, K., Jeffery, E., Pollock, C., & Birol, G. (2016). Development of the statistical reasoning in biology concept inventory (SRBCI). CBE—Life Sciences Education, 15(1), ar5. https://doi.org/10.1187/cbe.15-060131
Donati, O., Missiroli, G. P., & Pozzi, G. (1973). An experiment on electron interference. American Journal of Physics, 41(5), 639-644. https://doi.org/10.1119/1.1987321
Dunn, P., Carey, M., Richardson, A. & McDonald, C. (2016). Learning the language of statistics: challenges and teaching approaches. Statistics Education Research Journal, 15(1), 8-27.
https://doi.org/10.52041/serj.v15i1.255
Esteban, J. M. & Martínez, S. (2008). Normas y prácticas en la ciencia. México, México: Universidad Nacional Autónoma de México. Recuperado de https://www.filosoficas.unam.mx/~sfmar/publicaciones/ESTEBAN-MARTINEZ%202008%20Normas%20y%20Practicas%20en%20la%20Ciencia.pdf
Fiedler, D., Sbeglia, G. C., Nehm, R. H., & Harms, U. (2019). How strongly does statistical reasoning influence knowledge and acceptance of evolution? Journal of Research in Science Teaching, 56(9), 1183-1206. https://doi.org/10.1002/tea.21547
Fischer, F., Chinn, C. A., Engelmann, K., & Osborne, J. (Eds.). (2018). Scientific reasoning and argumentation: The roles of domain-specific and domain-general knowledge. New York: Routledge.
Fonseca & Martínez, S. (2017). Heurísticas y el debate sobre la estructura normativa del Razonamiento. (Documento inédito). Recuperado de https://www.researchgate.net/publication/328052125_HEURISTICAS_Y_EL_DEBATE_SOBRE_LA_ESTRUCTURA_NORMATIVA_DEL_RAZONAMIENTO
Gal, I. (2002). Adults' statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1-25. https://doi.org/10.2307/1403713
Garfield, J., & Ben-Zvi, D. (2004). Research on statistical literacy, reasoning, and thinking: Issues, challenges, and implications. In D. Ben-Zvi y J. Garfield (Eds.) The challenge of developing statistical literacy, reasoning and thinking (pp. 397-409). Springer, Dordrecht. Recuperado de https://link.springer.com/chapter/10.1007/1-4020-2278-6_17
Garzón, I., De Cock, M., Zuza, K., Van Kampen, P., & Guisasola, J. (2014). Probing university students' understanding of electromotive force in electricity. American Journal of Physics, 82(1), 72-79. http://dx.doi.org/10.1119/1.4833637
Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., & Woloshin, S. (2007). Helping doctors and patients make sense of health statistics. Psychological science in the public interest, 8(2), 53-96. https://doi.org/10.1111/j.1539-6053.2008.00033.x
Greer, B., & Mukhopadhyay, S. (2005). Teaching and learning the Mathematization of uncertainty: Historical, cultural, social and political Contexts. In Jones G. (ed). Exploring probability in school. New York: Springer. Recuperado de https://link.springer.com/chapter/10.1007/0-387-24530-8_13
Guisasola, J., Zubimendi, J., Almundí, J., & Ceberio, M. (2008). Dificultades persistentes en el aprendizaje de la electricidad: estrategias de razonamiento de los estudiantes al explicar fenómenos de carga eléctrica. Enseñanza de las Ciencias, 26(2), 177–192. Recuperado de https://raco.cat/index.php/Ensenanza/article/view/118093/297681
Hacking, I. (1982). Language, truth and reason. En M. Hollis y S. Lukes (Eds.) Rationaly and relativism. MIT Pres p. 48-66.
Hacking, I. (2006)[1990]. La domesticación del azar. La erosión del determinismo y el nacimiento de las ciencias del caos. Sevilla, España: Gedisa Editorial.
Hacking, I. (2010). The Second Group of Styles. Probable Reasoning and its novelties. Texto de la lectura dada en el Instituto de Investigaciones Filosóficas, UNAM, 26 de abril de 2010.
Hacking, I. (2012). “Language, Truth and Reason” 30 years later. Studies in History and Philosophy of Science, 43, 2012, (pp. 599-609). https://doi.org/10.1016/j.shpsa.2012.07.002
Hacking, I. (2015). Probable Reasoning and its Novelties. En Arabatziz, T., Renn, J y Simoes, A. (Eds.) Relocating the History of Science (pp. 177 - 192). https://doi.org/10.1007/978-3-319-14553-2
Jönsson, C. (1974). Electron diffraction at multiple slits. American Journal of Physics, 42(1), 4-11. https://doi.org/10.1119/1.1987592
Kaplan, J., Fischer, D., & Rogness, N. (2009). Lexical ambiguity in statistics: What do students know about the words association, average, confidence, random and spread? Journal of Statistics Education, 17(3). https://doi.org/10.1080/10691898.2009.11889535
Kaplan, J. & Rogness, N. (2018). Increasing statistical literacy by exploiting lexical ambiguity of technical terms. Numeracy, 11(1) Article 3. https://doi.org/10.5038/1936-4660.11.1.3
Kind, P., & Osborne, J. (2017). Styles of scientific of reasoning: a cultural rationale for science education. Science Education, 101(1), 8-31. https//doi.org/10.1002/sce.21251
Marshman, E., & Singh, C. (2017). Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics. European Journal of Physics, 38(2), 025705. https://doi.org/10.1088/1361-6404/aa57d1
Martínez, S. (1997). De los efectos a las causas: Sobre la historia de los patrones de explicación científica. México, México: Paidós.
Martínez S. & Huang, X. (2011). Introducción. Hacia una filosofía de la ciencia centrada en prácticas. En S. Martínez, X. Huang y G. Guillaumin (Eds.) Historia, prácticas y estilos en la filosofía de la ciencia. Hacia una epistemología plural. México, México: Universidad Autónoma Metropolitana.
Martínez, S. & Huang, X. (2015). Hacia una filosofía de la ciencia centrada en prácticas. México, México: Bonilla Artigas Editores.
Marton, F. (1981). Phenomenography – Describing conceptions of the world around us. Instructional Science, 10, 177-200. https://doi.org/10.1007/BF00132516
Marton, F & Pong, W. (2005). On the unit of description in phenomenography. Higher Education Research & Development, 24(4), 335-348. https://doi.org710.1080/07294360500284706
Matthews, M. R. (2017). La enseñanza de la ciencia: un enfoque desde la historia y la filosofía de la ciencia. México, México: Fondo de Cultura Económica.
Merli, P. G., Missiroli, G. F., & Pozzi, G. (1976). On the statistical aspect of electron interference phenomena. American Journal of Physics, 44(3), 306-307. https://doi.org/10.1119/1.10184
MEN - Ministerio de Educación Nacional .(1998). Lineamientos Curriculares. Matemáticas. Recuperado de https://www.mineducacion.gov.co/1621/articles-89869_archivo_pdf9.pdf
MEN - Ministerio de Educación Nacional. (2006). Estándares Básicos de Competencias en Lenguaje, Matemáticas, Ciencias y Ciudadanas. Recuperado de: http://www.mineducacion.gov.co/1621/articles-340021 _recurso_1.pdf
MEN - Ministerio de Educación Naciona.l (2015a). Derechos básicos de aprendizaje. V. 1. Bogotá: MEN. Recuperado de https://www.colombiaaprende.edu.co/sites/default/files/files_public/2022-06/DBA_C.Naturales-min.pdf
MEN - Ministerio de Educación Nacional. (2015b). Derechos básicos de aprendizaje. V. 2. Bogotá: MEN. Recuperado de https://www.colombiaaprende.edu.co/sites/default/files/files_public/2022-06/DBA_Matematicas-min.pdf
Moreno, A., Cardeñoso, J. M., & González-García, F. (2014). El pensamiento probabilístico de los profesores de biología en formación. Bolema: Boletim de Educação Matemática, 28, 1418-1442. Recuperado de https://www.redalyc.org/pdf/2912/291232906021.pdf
Osborne, J., Rafanelli, S. & Kind, P. (2018). Toward a more coherent model for science education than the crosscutting concepts of the next generation science standards: The affordances of styles of reasoning. Journal of Research in Science Teaching, 55(7), 962-981. https://doi.org/10.1002/tea.21460
Pfannkuch, M. & M. Brown Constance (1996). Building on and Challenging Students' Intuitions About Probability: Can We Improve Undergraduate Learning?, Journal of Statistics Education, 4(1). https://doi.org/10.1080/10691898.1996.11910502
Sauvé, L. (2010). Educación científica y educación ambiental: un cruce fecundo. Enseñanza de las Ciencias, 28(1), 5-18. Recuperado de https://raco.cat/index.php/Ensenanza/article/view/189092/353371
Tonomura, A., Endo, J., Matsuda, T., Kawasaki, T., & Ezawa, H. (1989). Demonstration of single?electron buildup of an interference pattern. American Journal of Physics, 57(2), 117-120. https://doi.org/10.1119/1.16104
Tversky, A., & Kahneman, D. (1993). Probabilistic reasoning. Readings in philosophy and cognitive science, 43-68. Recuperado de http://csinvesting.org/wp-content/uploads/2012/07/amos_tversky_and_daniel_kahneman_-_probabilistic_reasoning2.pdf
Walsh, L. (2009). A Phenomenographic Study of Introductory Physics Students: approaches to Problem Solving and Conceptualization of Knowledge. (Tesis de Doctorado). Dublin Institute of Technology. https://doi.org/10.21427/D73598
Zapata L. (2011). ¿Cómo contribuir a la alfabetización estadística? Revista Virtual Universidad Católica del Norte, 1(33), 234-247. Recuperado de https://revistavirtual.ucn.edu.co/index.php/RevistaUCN/article/view/9
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Néstor Méndez-H, Isabel Garzón-B., Julio Alejandro Castro-M
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
IENCI is an Open Access journal, which does not have to pay any charges either for the submission or processing of articles. The journal has adopted the definition of the Budapest Open Access Initiative (BOAI), which states that the users have the right to read, write down, copy, distribute, print, conduct searches and make direct links with the complete texts of the published articles.
The author responsible for the submission represents all the authors of the work and when the article is sent to the journal, guarantees that he has the permission of his/her co-authors to do so. In the same way, he/she provides an assurance that the article does not infringe authors´ rights and that there are no signs of plagiarism in the work. The journal is not responsible for any opinions that are expressed.
All the articles are published with a Creative Commons License Attribution Non-commercial 4.0 International. The authors hold the copyright of their works and must be contacted directly if there is any commercial interest in the use of their works.
