Formation au raisonnement probabiliste

Auteurs

  • Carmen Batanero Universidad de Granada
  • María Magdalena Gea Serrano Gea Universidad de Granada
  • Rocío Álvarez-Arroyo Universidade de Granada

DOI :

https://doi.org/10.23925/1983-3156.2023v25i2p127-144

Mots-clés :

Raisonnement probabiliste, Culture probabiliste, Composants, Biais de raisonnement

Résumé

Bien que l'enseignement des probabilités ait été introduit ces dernières années dans de nombreux pays à partir de la primaire et qu'il s'étende à tous les niveaux de l'éducation, la recherche nous informe de fréquentes erreurs lors de son application dans des contextes quotidiens ou dans la prise de décisions professionnelles. Cet article commence par analyser la culture probabiliste, en tant que base du raisonnement probabiliste que chacun devrait acquérir. Ensuite, nous analysons les caractéristiques et les composantes de base de ce raisonnement et décrivons certains des biais les plus fréquents. Il se termine par quelques suggestions pour développer le raisonnement probabiliste des étudiants

Métriques

Chargements des métriques ...

Bibliographies de l'auteur

Carmen Batanero, Universidad de Granada

Tesis doctoral sobre procesos puntuales estocásticos y fiabilidad

María Magdalena Gea Serrano Gea, Universidad de Granada

Doctor en Educación

Rocío Álvarez-Arroyo , Universidade de Granada

PHD, University of Granada, Spain

Références

Alsina, Á. (2021). 'Ça commence aujourd'hui': alfabetización estadística y probabilística en la educación matemática infantil. PNA, 15(4), 243-266. https://doi.org/10.30827/pna.v15i4.21357

Álvarez-Arroyo, R., Lavela, J. F., y Batanero, C. (2022). Razonamiento probabilístico de estudiantes de bachillerato al interpretar datos de la COVID-19. Journal of Research in Mathematics Education, 11(2), 117-139. https://doi.org/10.17583/redimat.9741

Bar-Hillel, M., y Falk, R. (1982). Some teasers concerning conditional probabilities. Cognition, 11(2), 109-122. https://doi.org/10.1016/0010-0277(82)90021-X

Bar-Hillel, M., y Wagenaar, W. A. (1991). The perception of randomness. Advances in applied mathematics, 12(4), 428-454. https://doi.org/10.1016/0196-8858(91)90029-I

Batanero, C. (2006). Razonamiento probabilístico en la vida cotidiana: Un desafío educativo. En P. Flores y J. Lupiáñez (eds.), Investigación en el aula de matemáticas. Estadística y Azar (pp. 1-17). Sociedad de Educación Matemática Thales.

Batanero, C. (2015). Understanding randomness: Challenges for research and teaching. En K. Krainer y N. Vondrová (Eds.), Proceedings of the Ninth Conference of the European Society for Research in Mathematics Education (CERME9) (pp. 34-49). Praga, República Checa: ERME.

Batanero, C., Álvarez-Arroyo, R., Hernández-Solís, L. A. y Gea, M. M. (2021). El inicio del razonamiento probabilístico en educación infantil. PNA, 15(4), 267-288. https://doi.org/10.30827/pna.v15i4.22349

Batanero, C., y Borovcnik, M. (2016). Statistics and probability in high school. Sense Publishers.

Batanero, C., y Díaz, C. (2012). Training school teachers to teach probability: reflections and challenges. Chilean Journal of Statistics, 3(1), 3-13.Batanero, C., Henry, M., y Parzysz, B. (2005). The nature of chance and probability. En G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 15-37). Springer.

Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Pérez, L. y Sàngler, D. (2020). Pre-K-12 guidelines for assessment and instruction in statistics education II (Gaise II). American Statistical Association & National Council of Teachers of Mathematics.

Begué, N., Batanero, C. y Gea, M. (2018). Comprensión del valor esperado y variabilidad de la proporción muestral por estudiantes de educación secundaria obligatoria. Enseñanza de las Ciencias, 36(2), 63-79. https://doi.org/10.5565/rev/ensciencias.2256

Benjamin, D. J. (2019). Errors in probabilistic reasoning and judgment biases. En B. D. Bernheim, S. DellaVigna, y D. Laibson (Eds.), Handbook of behavioral economics - Foundations and applications, Vol. 2 (pp. 69–186). Elsevier. https://doi.org/10.1016/bs.hesbe.2018.11.002

Berry, D. A. (2008). The science of doping. Nature, 454(7205), 692-693. https://doi.org/10.1038/454692a

Böcherer-Linder, K., y Eichler, A. (2019). How to improve performance in Bayesian inference tasks: a comparison of five visualizations. Frontiers in Psychology, 10, 267. https://doi.org/10.3389/fpsyg.2019.00267

Borovcnik, M. (2011). Strengthening the role of probability within statistics curricula. En C. Batanero, G. Burrill, y C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A Joint ICMI/IASE Study (pp. 71-83). Springer.

Borovcnik, M. (2016). Probabilistic thinking and probability literacy in the context of risk. Educação Matemática Pesquisa, 18(3), 1491-1516.

Borovcnik, M. (2021). Mutual influence between different views of probability and statistical inference. Paradigma, 42(Extra 1), 221-256. https://doi.org/10.37618/PARADIGMA.1011-2251.2021.p221-256.id1024

Borovcnik, M., y Kapadia, R. (2014). A historical and philosophical perspective on probability. En E. J. Chernoff y B. Sriraman (Eds.), Probabilistic thinking: presenting plural perspectives (pp. 7-34). Springer.

Bryant, P., y Nunes, T. (2012). Children’s understanding of probability: a literature review. Nuffield Foundation.

Burns, Z., Chiu, A., Wu, G. (2010). Overweighting of small probabilities. En J. Cochran, L. A. Cox, P. Keskinocak, J. Kharoufeh y J. C. Smith (Eds.), Wiley Encyclopedia of Operations Research and Management Science. Jonh Wiley & Sons. https://doi.org/10.1002/9780470400531.eorms0634.

CEMat (2021). Bases para la elaboración de un currículo de matemáticas en educación no universitaria. CEMat. Disponible en https://matematicas.uclm.es/cemat/wp-content/uploads/bases2021.pdf

de la Fuente, I., y Díaz-Batanero, C. (2004). Razonamiento sobre probabilidad condicional e implicaciones para la enseñanza de la estadística. Épsilon, 59, 245-260.

Eichler, A. y Vogel, M. (2014). Three approaches for modelling situations with randomness. En E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking. Presenting plural perspectives (pp. 75-99). Springer. https://doi.org/10.1007/978-94-007-7155-0

Evans, D. (2015). Risk intelligence: How to live with uncertainty. Free Press.

Falk, R. (1986). Misconceptions of statistical significance. Journal of Structural Learning, 9(1), 83–96.

Fischbein (1975). The intuitive sources of probabilistic thinking in children (Vol.85). Reidel.

Fischbein, E., y Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28(1), 96-105.

Franklin, C., Kader. G., Mewborn, D., Moreno, J., Peck, R., Perry, M., y Scheaffer, R. (2007). Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 curriculum framework. American Statistical Association.

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). Springer.

Gigerenzer, G. (1994). Why the distinction between single-event probabilities and frequencies is important for psychology (and vice versa). En G. Wright, y P. Ayton (Eds.), Subjective probability (pp. 129-161). John Wiley & Sons.

Gigerenzer, G. (2002). Reckoning with risk: Learning to live with uncertainty. Penguin Books.

Gras, R. y Totohasina, A. (1995). Chronologie et causalité, conceptions sources d’obstacles épistémologiques à la notion de probabilité conditionnelle. Recherches en Didactique des Mathématiques, 15(1), 49-95.

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

Kahneman, D., Slovic, P. y Tversky, A. (Eds.). (1982). Judgement under uncertainty: heuristics and biases. Cambridge University Press.

Kahneman, D., y Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3(3), 430-454. https://doi.org/10.1016/0010-0285(72)90016-3

Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59-98. https://doi.org/10.1207/s1532690xci0601_3

Langer, E. J. (1975). The illusion of control. Journal of Personality and Social Psychology, 32(2), 311–328. https://doi.org/10.1037/0022-3514.32.2.311

Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23(6), 557-568. https://doi.org/10.1007/BF00540060

Lehrer, R. y Schauble, L. (2010). What kind of explanation is a model? En M. K. Stein (Eds.), Instructional explanations in the disciplines (pp. 9-22). Springer. https://doi.org/10.1007/978-1-4419-0594-9

Lilleholt, L. (2019). Cognitive ability and risk aversion: A systematic review and meta analysis. Judgment and Decision Making, 14(3), 234-279.

Martignon, L., y Wassner, C. (2002). Teaching decision making and statistical thinking with natural frequencies. En B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching of Statistics (ICOTS6). Ciudad del Cabo: IASE.

MEFP, Ministerio de Educación y Formación Profesional (2022a). Real Decreto 157/2022, de 1 de marzo, por el que se establecen la ordenación y las enseñanzas mínimas de la Educación Primaria. Madrid: MEFP.

MEFP, Ministerio de Educación y Formación Profesional (2022b). Real Decreto 217/2022, de 29 de marzo, por el que se establece la ordenación y las enseñanzas mínimas de la Educación Secundaria Obligatoria. Madrid: MEFP.

MEFP, Ministerio de Educación y Formación Profesional (2022c). Real Decreto 243/2022, de 5 de abril, por el que se establecen la ordenación y las enseñanzas mínimas del Bachillerato. Madrid: MEFP.

Méndez-Hincapié, N., Garzón-Barragán, I., y Castro-Moreno, J. A. (2022). Análisis del razonamiento probabilístico en futuros profesores de ciencias. Investigações em Ensino de Ciências, 27(3), 254-269. https://doi.org/10.22600/1518-8795.ienci2022v27n3p254

NCTM. (2000). Principles and standards for school mathematics. NCTM. Disponible en http://standards.nctm.org/

Schum, D. A. (2001). The evidential foundations of probabilistic reasoning. Northwestern University Press.

Sieroń, A. (2020). Does the COVID-19 pandemic refute probability neglect? Journal of Risk Research, 23(7-8), 855-861. https://doi.org/10.1080/13669877.2020.1772346

Stango, V., y Zinman, J. (2009). Exponential growth bias and household finance. The Journal of Finance, 64(6), 2807-2849. https://doi.org/10.1111/j.1540-6261.2009.01518.x

Steen, L. A. (1999). Twenty questions about mathematical reasoning. En L. V. Stiff y F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12 (pp 270-285). NCTM.

Thompson, W. C., y Schumann, E. L. (1987). Interpretation of statistical evidence in criminal trials: The prosecutor's fallacy and the defense attorney's fallacy. Law and Human Behavior, 11(3), 167.

Tversky, A., y Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive psychology, 5(2), 207-232. https://doi.org/10.1016/0010-0285(73)90033-9

Tversky, A., y Kahneman, D. (1982). Causal schemas in judgment under uncertainty. En D. Kahneman, P. Slovic y A. Tversky (Eds.), Judgement under uncertainty: Heuristics and biases (pp. 117-128). Cambridge University Press.

Van Dooren, W. (2014). Probabilistic thinking: Analyses from a psychological perspective. In E, Chernoff y B. Sriraman (Eds.), Probabilistic Thinking (pp. 123-126). Springer.

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Publiée

2023-08-20

Comment citer

BATANERO, C.; GEA, M. M. G. S.; ÁLVAREZ-ARROYO , R. Formation au raisonnement probabiliste. Educação Matemática Pesquisa, São Paulo, v. 25, n. 2, p. 127–144, 2023. DOI: 10.23925/1983-3156.2023v25i2p127-144. Disponível em: https://revistas.pucsp.br/index.php/emp/article/view/61213. Acesso em: 22 nov. 2024.

Numéro

Rubrique

NUMÉRO SPÉCIAL - COMMÉMORATION DES 25 ANS DE LA REVUE EDUCAÇÃO MATEMÁTICA PESQU