Keywords
Bidimensional distributions
Elements of meaning
Covariance
Correlation
Regression
How to Cite
Abstract
In this paper the meaning that the students of Secondary
Education (17 years of age) attach to the correlation and regression after
having received instruction on this topic, is characterized. The paper begins
with a revision of related literature, them the theoretical framework, the sample
and the questionnaire are described. The questionnaire contains 12 items
showing representative elements of meaning on bidimensional distributions,
correlation, covariance and regression. The difficulties and the correct and
erroneous answers of the students are analyzed and discussed, some of them are related to referred literature. We finalize with a summary and the
conclusions of the findings, useful results to plan teaching and to begin with
other research.
References
ALLOY, L. B. Y TABACHNIK, N. Assessment of covariation by humans and animals: The joint influence of prior expectations and current situational information. Psychological Review, v. 91, pp. 112-149, 1984.
ARKES, H. R. Y HARKNESS, A. R. Estimates of contingency between two dichotomous variables. Journal of Experimental Psychology: General, v. 112, n. 1, pp. 117-135, 1983.
BARBANCHO, A. G. Estadística elemental moderna. Barcelona: Ariel, 1973. 4ª edición, reimpresión de 1975.
BATANERO, M. C.; ESTEPA, A.; GODINO, J. D. Y GREEN, D. Intuitive strategies and preconceptions about association in contingency tables. Journal for Research in Mathematics Education, v. 27 n. 2, pp. 151-169, 1996.
BATANERO, M. C.; ESTEPA, A. Y GODINO, J. D. Students' understanding of Statistical association in a computer environments. In J. Garfield & G. Burrill (Eds .) Research on the Role of Technology in Teaching and Learning Statistics. Voorburg, The Netherlands: International Statistical Institute, pp. 191-205, 1997.
BATANERO, C.; GODINO, J. D. Y ESTEPA, A. Building the meaning of statistical association through data analysis activities (Research Forum). In A. Olivier & K. Newstead (Eds.). Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education. Stellenbosh (South Africa): University of Stellenbosh, 1998, v. 1, pp. 221- 236.
BATANERO, C. & GODINO, J. D. Understanding Graphical and Numerical Representations of Statistical Association in a computer environment. En: Pereira-Mendoza, L., Seu, L., Wee, T. y Wong, W.-K. (Eds.), Proceedings of the Fifth International Conference on Teaching of Statistics Voorburg (The Netherlands): ISI Permanent Office, 1998, v. 2, pp. 1017-1023.
BATANERO, C.; GODINO, J. Y ESTEPA, A. La construcción del significado de la asociación mediante actividades de análisis de datos: Reflexiones sobre el papel del ordenador en la enseñanza de la Estadística. En J. R. Pascual (Eds.). II Simposio de la Sociedad Española de Investigación en Educación Matemática (SEIEM). Pamplona: Universidad Pública de Navarra. 2001, pp. 151-169.
BEYTH-MAROM, R. (1982). Perception of correlation reexamined. Memory and Cognition, v. 10, n. 6, 1982, pp. 511-519.
BROUSSEAU, G. (1983). Les obstacles epistemologiques et les problemes en Mathematiques. Recherches en Didáctique des Mathématiques, v. 4, n. 2, 1983, pp. 165-198.
CROCKER, J. (1981) Judgment of covariation by social perceivers. Psychological Bulletin. 90, 2, 272-292.
CRUISE, R. J.; DUDLEY, R. L. Y THAYER, J. D. A Resource Guide for Introductory Statistics. Dubuque (Iowa): Kendall/Hunt Publishing Company, 1984.
ERLICK, D. E. Y MILLS, R. G. Perceptual quantification of conditional dependency. Journal of Experimental Psychology, v. 73, n. 1, pp. 9-14, 1967.
ESTEPA, A. Concepciones iniciales sobre la asociación estadística y su evolución como consecuencia de una enseñanza basada en el uso de ordenadores. Tesis doctoral. Barcelona: ETD Micropublicaciones, S.L. 1994.
ESTEPA, A. y BATANERO, M. C. Concepciones iniciales sobre la asociación estadística. Enseñanza de las Ciencias, Barcelona, España, v. 13, n. 2, pp. 155 – 170, 1995.
ESTEPA, A. Y BATANERO, M. C. Judgments of correlation in scatter plots: An empirical study of students' intuitive strategies and preconceptions. Hiroshima Journal of Mathematics Education, Hiroshima (Japan), v. 4, pp. 25-41, 1996.
ESTEPA, A., BATANERO, C. y SÁNCHEZ, F. T. Students’ understanding of regressión lines. In O. Zaslavsky (Ed.). Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education – PME 23, Vol. 2,. Haifa (Israel): Technion-Israel Institute of Technology, 1999, pp. 2-313, 2-320.
ESTEPA, A. y SÁNCHEZ, F. T. Desarrollo histórico de la idea de asociación estadística. Epsilon, N. 30, v, 10 f. 3, pp. 61 – 73, 1995.
ESTEPA, A. Y SÁNCHEZ, F.T. Correlation and regression in secondary school text books. En: Pereira-Mendoza, L., Seu, L., Wee, T. y Wong, W.-K. (Eds.), Proceedings of the Fifth International Conference on Teaching of Statistics (vol. 2), Voorburg (The Netherlands): ISI Permanent Office, 1998, pp. 671-676).
ESTEPA, A. Y SÁNCHEZ, F. T. Empirical Research On The Understanding Of Association And Implication For The Training Of Researchers. En C. Batanero (Ed.) Training Researchers in the Use of Statistics. Granada (Spain): International Association for Statistical Education. International Statistical Institute, 2001, pp. 37-51.
GODINO, J. D. (2003). Teoría de las Funciones Semióticas. Un enfoque ontológico-semiótico de la cognición e instrucción matemática. Universidad de Granada. Departamento de Didáctica de la Matemática, 2003, recuperable en (9-julio-07): http://www.ugr.es/~jgodino/funciones-semioticas/monografiatfs.pdf.
GODINO, J. D. Y BATANERO, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques, v. 14, n. 3, 1994, pp. 325-355.
HILDEBRAND, D. K., LANG, J. D. y ROSENTHAL, H. Analysis of nominal data. London:: Sage University Paper, 1977.
INHELDER, B. Y PIAGET, J. De la logique de l'enfant à la logique de l'adolescent. Paris: Presses Universitaires de France, 1955. (Traducción castellana, Primera reimpresión, 1985. Barcelona: Paidos).
JANVIER, C. Problems of representation in the teaching and learning of mathematics. Hillsdale, New Jersey: Lawrence Erlbaum Associates, Publishers, 1987a, n. p. 247.
JANVIER, C. Translation processes in Mathematics Education. En C. Janvier. Problems of representation in the teaching and learning of mathematics. Hillsdale, New Jersey: Lawrence Erlbaum Associates, Publishers, 1987b, pp. 27-32.
JENNINGS, D. L., AMABILE, T. M. Y ROSS, L. (1982). Informal covariation assessment: Data-based versus theory-based judgments. En D. Kahneman, P. Slovic y A. Tversky (Ed.), Judgment under uncertainty: Heuristics and biases. New York: Cambridge Universitary Press, 1982. pp. 211-230.
MORITZ, J. Reasoning about covariation. In D. Ben-Zvi & J. Garfield (Eds.). The Challenge of Developing Statistical Literacy, Reasoning and Thinking, n. p. 423. Dordrecht (The Nederlands): Kluwer Academic Publishers, 2004, pp. 227-255.
MORRIS, E. J. An investigation of students' conceptions and procedural stills in the statistical topic correlation. Centre for Information Technology in Education, Report n. 230, London: The Open University, 1997, n, p. 64.
MUÑIZ, J.; FIDALGO, A. M.; CUETO, E. Gª.; MARTÍNEZ, R. Y MORENO, R. Análisis de ítems. Madrid: Editorial “La Muralla”, 2005, n. p. 181.
MURPHY, G. L. Y MEDIN, D. L. The role of theories in conceptual coherence. Psychological Review, v. 92, n. 3, pp. 289-316, 1985.
NISBETT, R. Y ROSS, L. Human inference: strategies and shortcomings of social judgment. Nueva Jersey: Prentice Hall, 1980.
PEARSON, K. Notes on the history of correlation. Biometrika, 13, 25-45, 1920. En Pearson, E. S. y Kendall, M. (1970), (Eds.), Studies in the history of Statistics and Probability, 1970, v. 1. London: Charles Griffin, pp. 185-205.
PETERSON, C. R. Y BEACH, L. R. Man as an intuitive statistician. Psychological Bulletin, v. 68, n. 1, 1967, 29-46.
PÉREZ ECHEVERRIA, M. P. Psicología del razonamiento probabilístico. Madrid: Ediciones de la Universidad Autónoma de Madrid, 1990.
POZO, J. I. v. Aprendizaje de la ciencia y pensamiento causal. Madrid: Visor, 1987.
SMEDLUND, J. The concept of correlation in adults. Scandinavian Journal of Psychology, 4, 165-174, 1963.
SÁNCHEZ, F. T. Significado de la correlación y regresión para los estudiantes universitarios. Tesis doctoral. Departamento de Didáctica de la Matemática. Universidad de Granada, 1999.
SÁNCHEZ, F.T.; ESTEPA, A. Y BATANERO, C. Un estudio experimental de la estimación de la correlación a partir de diferentes representaciones. Enseñanza de las Ciencias, v. 18, n, 2, 297-310, 2000.
SIERSPINSKA, A. Some remarks on understanding in mathematics. For the learning of mathematics, v. 10, n. 3, pp. 24-36, 1991.
TANUR, J. M. (Ed.) Statistics: A guide to the Unknown. San Francisco: Holden Day, 1972.
TVERSKY, A. Y KAHNEMAN, D. (1982b). Judgment under uncertainty: Heuristics and biases. En D. Kahneman, P. Slovic y A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases. New York: Cambridge Universitary Press, 1982, pp. 3-20. (Traducido al español en M. Carretero y J. A. Garcia Madruga (1984). Lecturas de psicología del pensamiento. Razonamiento, solución de problemas y desarrollo cognitivo. Madrid: Alianza Editorial, 1984, pp. 169-184.
VERGNAUD, G. La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, v. 10, n. 2-3, pp. 133-170, 1990.
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