Del análisis de datos a la inferencia: Reflexiones sobre la formación del razonamiento estadístico (página 2)
Enviado por Guido Andrey Ojeda Torres
Dada la dificultad de integrar los conceptos involucrados en la inferencia estadística, tiene sentido sugerir que estas ideas deben ser desarrollados progresivamente en la mente de los alumnos, siguiendo los pasos sugeridos en este trabajo. Las nuevas directrices curriculares donde la educación estadística se introduce desde la escuela primaria proporcionan una oportunidad y un desafío para ayudar a los estudiantes a desarrollar su conocimiento y razonamiento estadístico. Debemos también reflexionar sobre la dosis exacta de formalización que se requieren para enseñar los conceptos estadísticos. En este sentido, la estadística puede ser paradigmática respecto a encontrar nuevas maneras de enseñar conceptos matemáticos avanzados a gran número de estudiantes e incluso para repensar el significado del pensamiento matemático avanzado (Artigue, Batanero, & Kent, 2007).
Agradecimientos: Se agradece el apoyo económico al proyecto EDU2010-14947 (MCIN) y grupo FQM126 (Junta de Andalucía).
Referencias
Abelson, R. P. (1997). On the surprising longevity of flogged horses: Why there is a case for the significance test? Psychological Science, 8(1), 12-14.
Albert, J. (2000). Using a sample survey project to assess the teaching of statistical inference, Journal of Statistical Education, 8. On line: www.amstat.org/publications/jse/.
Albert, J. H., & Rossman, A. (2001). Workshop statistics. Discovery with data. A bayesian approach.
Bowling Green. OH: Key College Publishing.
Artigue, M., Batanero, C., & Kent, P. (2007). Mathematics thinking and learning at post-secondary level.
En F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1011-1049). Greenwich, CT: Information Age Publishing, Inc., & National Council of Teachers of Mathematics.
Batanero, C. (2000). Controversies around significance tests. Mathematical Thinking and Learning, 2(1-2), 75-98.
Batanero, C. y Díaz, C. (2006). Methodological and didactical controversies around statistical inference.
Actes du 36iémes Journées de la Societé Française de Statistique. CD ROM. Paris: Societé Française de Statistique.
Batanero, C., Godino, J. D., Vallecillos, A., Green, D. R., & Holmes, P. (1994). Errors and difficulties in understanding elementary statistical concepts. International Journal of Mathematics Education in Science and Technology, 25(4), 527–547.
Birnbaum, I. (1982). Interpreting statistical significance. Teaching Statistics, 4, 24–27.
Borges, A., San Luis, C., Sánchez, J.A. y Cañadas, I. (2001). El juicio contra la hipótesis nula: muchos testigos y una sentencia virtuosa. Psicothema, 13 (1), 174-178.
Cabriá, S. (1994). Filosofía de la estadística. Valencia: Servicio de Publicaciones de la Universidad.
Castro-Sotos, A. E., Vanhoof, S., Noortgate, W. & Onghena, P. (2007). Students" misconceptions of statistical inference: A review of the empirical evidence from research on statistics education. Educational Research Review, 2 98–113
Chance, B., delMas, R. C., & Garfield, J. (2004). Reasoning About Sampling Distributions. In D.Ben-Zvi and J. Garfield (eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 295-323). The Netherlands: Kluwer.
Chow, L. S. (1996). Statistical significance: Rationale, validity and utility. London: Sage.
Cumming, G., Williams, J., & Fidler, F. (2004). Replication, and researchers" understanding of confidence intervals and standard error bars. Understanding Statistics, 3, 299-311.
Díaz, C. (2007). Introducción a la Inferencia Bayesiana. Granada: La autora.
Díaz, C., de la Fuente, I., & Batanero, C. (2008). Implications between learning outcomes in elementary
Bayesian inference. In R. Gras (Ed.), Statistical implicative analysis: theory and applications (pp. 163-183). Springer. Studies in Computational Intelligence 127.
Eddy, D. M. (1982). Probabilistic reasoning in clinical medicine: Problems and opportunities. En D.
Kahneman, P. Slovic y Tversky (Eds.), Judgement under uncertainty: Heuristics and biases. New York: Cambridge University Press.
Falk, R. (1986) Misconceptions of statistical significance, Journal of Structural Learning, 9, 83–96.
Falk, R., & Greenbaum, C. W. (1995) Significance tests die hard: The amazing persistence ofa probabilistic misconception, Theory and Psychology, 5 (1), 75-98.
Fidler, F. & Cumming, G. (2005, August). Teaching confidence intervals: problems and potential solutions. Trabajo presentado en la International Statistical Institute, 55th Session. Lisbon.
Fisher, R. A. (1935). The design of experiments. New York: Hafner Press.
Green, D. R. (1991). A longitudinal study of children"s probability concepts. En D. Vere-Jones (Ed.), Proceedings of the Third International Conference on Teaching Statistics (pp. 320-328). Voorburg: International Statistical Institute.
Hacking, I. (1990). The taming of chance. Cambridge, MA: Cambridge University Press.
Harlow, L. L., Mulaik, S. A., & Steiger, J. H. (1997). What if there were no significance tests? Mahwah, NJ: Lawrence Erlbaum.
Harradine, A., Batanero, C., & Rossman, A. (En prensa). Students and teachers" knowledge of sampling and inference. En C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education. Springer.
Jones, G. A. y Thornton, C. A. (2005). An overview of research into the teaching and learning of probability. En G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 65-92).. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases.
New York: Cambridge University Press.
Krauss, S., & Wassner, K. (2002). How significance tests should be presented to avoid the typical misinterpretations. En B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics. Cape Town, South Africa: International Association for Statistics Education. Online: www.stat.auckland.ac.nz/~iase/publications.
Lecoutre, B., & Lecoutre, M. P. (2001). Uses, abuses and misuses of significance tests in the scientific commumity: Won"t the Bayesian choice be unavoidable? International Statistical Review, 69(3)-399-417.
Lee, P. M. (2004). Bayesian statistics. An introduction. York, UK: Arnold.
Liu, Y., & Thompson, P. W. (2009). Mathematics teachers' understandings of proto-hypothesis testing. Pedagogies, 4 (2), 126-138.
MEC (2007). Real Decreto 1467/2007, de 2 de noviembre, por el que se establece la estructura del bachillerato y se fijan sus enseñanzas mínimas (Royal Decreet establihing the estructure and content of the high school curriculum).
Moore, D. S. (1997). New pedagogy and new content: the case of statistics. International Statistical Review, 635, 123-165.
Morrison, D. E., y Henkel, R. E. (Eds.). (1970). The significance tests controversy. A reader. Chicago: Aldine.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.
Reston, VA: NCTM. Online: standards.nctm.org/.
Nisbett, R. & Ross, L. (1980). Human inference: Strategies and shortcomings of social judgments.
Englewood Cliffs, NJ: Prentice Hall.
Rossman, A. (2008). Reasoning about informal statistical inference: One statistician"s view. Statistics
Education Research Journal, 7(2), 5-19. Online: http://www.stat.auckland.ac.nz/serj.
O"Hagan, A. y Forster, J. (2004). Bayesian inference. Vol. 2B en Kendall"s Advanced Theory of Statistics. London: Arnold.
Popper, K. R. (1967). La lógica de la investigación científica. Madrid: Tecnos. Rivadulla, A. (1991). Probabilidad e inferencia científica. Barcelona: Anthropos.
Rubin, A., Hammerman, J. K. L & Konold, C. (2006). Exploring informal inference with interactive visualization software. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics. Cape Town, South Africa: International Association for Statistics Education. Online: www.stat.auckland.ac.nz/~iase/publications.
Saldanha. L., & Thompson, P. (2002) Conceptions of sample and their relationship to statistical inference.
Educational Studies in Mathematics, 51, 257-270.
Sedlmeier, P. (1999). Improving statistical reasoning. Theoretical models and practical implications.
Mahwah, NJ: Erlbaum.
Vallecillos, A. (1994). Estudio teórico-experimental de errores y concepciones sobre el contraste estadístico de hipótesis en estudiantes universitarios Tesis Doctoral. Universidad de Granada, España.
Vallecillos, A. (1999). Some empirical evidence on learning difficulties about testing hypotheses.
Proceedings of the 52 session of the International Statistical Institute (Vol.2, pp. 201–204). Helsinki: International Statistical Institute.
Autor:
Carmen Batanero Bernabeu
Facultad de Educacion, Universidad de Granada
España
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