Modelización de la variabilidad muestral en diferentes metodologías de la inferencia
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Batanero, C. (2003). La simulación como instrumento de modelización en probabilidad. Educación y Pedagogía, 15(35), 3754.
Batanero, C. y Borovcnick, M. (2016). Statistics and probability in high school. Sense Publishers.
Batanero, C., Díaz-Batanero, C. y López-Martín, M. M. (2017). Significados del contraste de hipótesis, configuraciones epistémicas asociadas y algunos conflictos semióticos. Actas del Segundo Congreso International Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos. Disponible en: enfoqueontosemiotico.ugr.es/civeos.html
Batanero, C. Díaz-Batanero, C., López-Martín, M.M. y Roldán, A. F. (2020). Interval estimation: methodological approaches and understanding difficulties. BEIO, Boletín de Estadística e Investigación Operativa, 36(3), 269-291.
Biehler, R., Frischemeier, D. y Podworny, S. (2017). Reasoning about models and modelling in the context of informal statistical inference. Statistics Education Research Journal, 16(2), 8-12.
Blomhøj, M. y Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and its Applications 220, 123-139. https://doi.org/10.1093/teamat/22.3.123.
Blum, W., Galbraith, P. L., Henn, H. W. y Niss, M. (2007). Modelling and applications in mathematics education. Springer. https://doi.org/10.1007/978-0-387-29822-1_59
Bolstad, W. (2013). Introduction to Bayesian statistics, 2ª ed. Wiley.
Borovcnik, M. (2019). Informal and “informal” inference. Actas del Tercer Congreso Internacional Virtual de Educación Estadística. Disponible en www.ugr.es/local/fqm126/civeest.html
Burrill, G. y Biehler, R. (2011). Fundamental statistical ideas in the school curriculum and in training teachers. 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. 57-69). Springer.
Case, C. y Jacobbe, T. (2018). A framework to characterize student difficulties in learning information from a simulation-based approach, Statistics Education Research Journal, 17(2), 9-29. https://doi.org/10.52041/serj.v17i2.156
Castro-Sotos, A. E., Vanhoof, S., Noortgate, W. y Onghena, P. (2007). Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education. Educational Research Review, 2(2), 98-113. https://doi.org/10.1016/j.edurev.2007.04.001
Cevikbas, M., Kaiser, G. y Schukajlow, S. A. (2022). Systematic literature review of the current discussion on mathematical modelling competencies: State of the art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics 109, 205–236 (2022). https://doi.org/10.1007/s10649021101046
Chaput, B., Girard, J. C. y Henry, M. (2011). Frequentist approach: Modelling and simulation in statistics and probability teaching. 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. 85-95). Springer. https://doi.org/10.1007/978-94-007-1131-0_12
Cabriá, S. (1994). Filosofía de la estadística. Servicio de Publicaciones de la Universidad de Valencia.Cobb, G. W. (2007). The introductory statistics course: A Ptolemaic curriculum. Technology Innovations in Statistics Education, 1(1), 115. https://doi.org/10.5070/T511000028
Council of Chief State School Officers, CCSSO (2010). Common core state standards for mathematics. Council of Chief State School Officers: Disponible en: http://www.corestandards.org/Math/
de la Fuente, E. I. y Díaz-Batanero, C. (2004). Controversias en el uso de la inferencia en la investigación experimental. Metodología de las Ciencias del Comportamiento, 5(esp. 1), 161-167.
Díaz-Batanero, C. (2007). Viabilidad de la enseñanza de la inferencia bayesiana en el análisis de datos en psicología. Tesis doctoral. Universidad de Granada.
Doerr, H.M., Ärlebäck J.B. y Misfeldt M. (2017). Representations of modelling in mathematics education. En: Stillman G., Blum W. y Kaiser G. (Eds.), Mathematical modelling and applications. International perspectives on the teaching and learning of mathematical modelling (pp. 71-81). Springer
Doerr, H. M., Delmas, R. y Makar, K. (2017). A modeling approach to the development of students’ informal inferential reasoning. Statistics Education Research Journal, 16(2), 86-115. https://doi.org/10.52041/serj.v16i2.186
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7, 529-563.
Efron, B. y Tibshirani, R. J. (1993). An introduction to the bootstrap.
Chapman.Eichler, A. y Vogel, M. (2014). Three approaches for modelling situations with randomness. En E. Chernoff y B. Sriraman (Eds.), Probabilistic thinking (pp. 75-99). Springer. https://doi.org/10.1007/9789400771550_4
Gigerenzer, G. (1993). The superego, the ego and the id in statistical reasoning. En G. Keren y C. Lewis (Eds.), A handbook for data analysis in the behavioural sciences: Methodological issues (pp. 311-339).
Erlbaum.Godino, J. D. (1996). Mathematical concepts, their meanings and understanding. En L. Puig y A. Gutiérrez (Eds.), Proceedings of the 20th PME Conference (Vol. 2, pp. 417-424). Universidad de Valencia.
Godino, J. D. (2002). Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactique des Mathematiques, 22(23), 237-284.
Godino, J., Batanero, C. y Font, V. (2007). The ontosemiotic approach to research in mathematics education. ZDM - Mathematics Education, 39(12), 127-135. https://doi.org/10.1007/s1185800600041
Godino, J., Batanero, C. y Font, V. (2019). The ontosemiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 38-43.
Godino, J. D., Burgos, M. y Gea, M. M. (2021). Analysing theories of meaning in mathematics education from the ontosemiotic approach. International Journal of Mathematical Education in Science and Technology, 128. https://doi.org/10.1080/0020739X.2021.1896042
Hacking, I. (2006). The emergence of probability. A philosopfhical study of early ideas about probability, induction and statistical inference. Cambridge University Press.
Harradine, A., Batanero, C., y Rossman, A. (2011). Students and teachers’ knowledge of sampling and inference. 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. 235-246).
Springer.Hald, A. (2008). A history of parametric statistical inference from Bernoulli to Fisher, 1713-1935. Springer.
Hall, P. (2003) A short prehistory of the Bootstrap. Statistical Science, 18, 158–167.
Heitele, D. (1975). An epistemological view on fundamental stochastic ideas. Educational Studies in Mathematics, 6(2), 187-205.
Henry, M. (1997). Notion de modele et modélization en l'enseignement. En M. Henru (Ed.), Enseigner les probabilités au lycée (pp. 77-84.) Commission Inter-IREM.
Jones, G. A. y Thornton, C. A. (2005). An overview of research into the teaching and learning of probability. En G. Jones (Ed.), Exploring probability in school (pp. 65-92). Springer. https://doi.org/10.1007/0-387-24530-8_4
Kula, F. y Koçer, R. G. (2020). Why is it difficult to understand statistical inference? Reflections on the opposing directions of construction and application of inference framework. Teaching Mathematics and its Applications, 39(4), 248-265. https://doi.org/10.1093/teamat/hrz014
Ledesma, R. (2008). Introduccción al Bootstrap. Desarrollo de un ejemplo acompañado de software de aplicación. Tutorials in Quantitative Methods for Psychology, 4(2), 51-60.
Lecoutre, B., Lecoutre M. P. y Poitevineau J. (2007). Uses, abuses and misuses of significance tests in the scientific community: Won't the Bayesian choice be unavoidable? International Statistical Review, 69, 399-418. https://doi.org/10.1111/j.1751-5823.2001.tb00466.x
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
Lenhard, J. (2006). Models and statistical inference: The controversy between Fisher and Neyman–Pearson. The British journal for the philosophy of science, 57, 69-91.
Lipson, K. (2003) The role of the sampling distribution in understanding statistical inference. Mathematics Education Research Journal, 15, 270–287. https://doi.org/10.1007/BF03217383
Lu, X. y Kaiser, G. (2022). Creativity in students’ modelling competencies: conceptualisation and measurement. Educational Studies in Mathematica, 109, 287–311. https://doi.org/10.1007/s1064902110055y
Makar, K. y Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82-105.
Makar, K. y Rubin, A. (2018). Learning about statistical inference. En D. BenZvi, K, Makar y J.B. Garfield (Eds), International handbook of research in statistics education (pp. 261-294). Springer. https://doi.org/10.1007/9783319661957_8
Ministerio de Educación, Cultura y Deporte, MECD (2015). Real Decreto 1105/2014, de 26 de diciembre, por el que se establece el currículo básico de la Educación Secundaria Obligatoria y del Bachillerato. Madrid: Autor
Ministerio de Educación y Formación Profesional, MEFP (2022a). Real Decreto157/2022, de 1 de marzo, porel que se establece la ordenación y las enseñanzas mínimas de la Educación Primaria. Boletín Oficial del Estado, 52, 1-109.
Ministerio de Educación y Formación Profesional, MEFP (2022b). Real Decreto 217/2022, de 29 de marzo, porel que se establece la ordenación y las enseñanzas mínimas de la Educación Secundaria Obligatoria. Boletín Oficial del Estado, 76, 41571-41789.
Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy. Psychological methods, 5(2), 241. https://doi.org/10.1037/1082-989X.5.2.241
Niss, M y Blum, W. (2019). The learning and teaching of mathematical modelling. Routledge.
OECD (2013). PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. OECD.
Rivadulla, A. (1991). Probabilidad e inferencia científica. Barcelona: Anthropos.
Rossman, A. J. (2008). Reasoning about informal statistical inference: One statistician's view. Statistics Education Research Journal, 7(2), 5-19.
Saldanha, L. A. y Thompson, P. W. (2002) Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51, 257–270. https://doi.org/10.1023/A:1023692604014
Schukajlow, S., Kaiser, G. y Stillman, G. (2018). Empirical research on teaching and learning of mathematical modelling: A survey on the current state-of-the-art. ZDM - Mathematics Education, 50(1), 5-18. https://doi.org/10.1007/s11858-018-0933-5
Pfannkuch, M., BenZvi, D. y Budgett, S. (2018). Innovations in statistical modeling to connect data, chance and context. ZDM, 50(7), 1113-1123. https://doi.org/10.1007/s11858-018-0989-2
Pfannkuch, M., y Ziedins, I. (2014). A modelling perspective on probability. En E. Chernoff y B. Sriraman (Ed,), ProbabilisticThinking (pp. 101-116). Springer.
Watson, J. y Chance, B. (2012). Building intuitions about statistical inference based on resampling. Australian Senior Mathematics Journal, 26(1), 6-18.
Zieffler, A., Garfield, J. B., del Mas, R. y Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2), 5-19.
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