University Students’ Knowledge and Biases in Conditional Probability Reasoning

Carmen Díaz; Carmen Batanero

doi:10.29333/iejme/234

Full Text (PDF)

Carmen Díaz, Carmen Batanero

More Detail

Abstract

The research question in this study was assessing possible relationships between formal knowledge of conditional probability as well as biases related to conditional probability reasoning: fallacy of the transposed conditional; fallacy of the time axis; base rate fallacy; synchronic and diachronic situations; conjunction fallacy; and confusing independence and mutually exclusiveness. Two samples of university students majoring in psychology and following the same introductory statistics course were given the CPR test before (n = 177) and after (n = 206) formal teaching of conditional probability. Results indicate a systematic improvement in formal understanding of conditional probability and in problem solving capacity but little change in those items related to psychological biases.

Keywords

Conditional probability
biases
instruction

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2009, Volume 4, Issue 3, 131-162

https://doi.org/10.29333/iejme/234

Publication date: 12 Dec 2009

Article Views: 2793

Article Downloads: 2225

Open Access References How to cite this article

References

Bar-Hillel, M. (1983). The base rate fallacy controversy, in R. W. Scholz (Ed.). Decision making under uncertainty. Amsterdam: North Holland. 39–61.
Batanero, C., Henry, M. & Parzysz, B. (2005). The nature of chance and probability. In G. A. Jones (Ed.), Exploring probability in schools: Challenges for teaching and learning. New York: Springer. 15–37.
Borovcnik, M., Bentz, H. J., & Kapadia, R. (1991). A probabilistic perspective. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education. Dordrecht: Kluwer. 27–73.
Borovcnik, M. & Peard, R. (1996). Probability. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (Part 1). Dordrecht: Kluwer. 239–288.
Díaz, C. (2007). Viabilidad de la enseñanza de la inferencia bayesiana en el análisis de datos en psicología (Viability of teaching Bayesian inference in data analysis courses in psychology). Ph.D. Universidad de Granada.
Díaz, C. &, de la Fuente, E. I. (2006a). Assessing psychology students' difficulties with conditional probability and bayesian reasoning. In A. Rossman & B. Chance (Eds.), Proceedings of Seventh International Conference on Teaching of Statistics. Salvador de Bahia: International Association for Statistical Education, CD ROM.
Díaz, C. & de la Fuente, I. (2006b). Enseñanza del teorema de Bayes con apoyo tecnológico (Teaching the Bayes, theorem with technology support). In P. Flores & J. Lupiáñez (Eds.), Investigación en el aula de matemáticas. Estadística y Azar . Granada: Sociedad de Educación Matemática Thales. CD ROM.
Díaz, C. & de la Fuente, I. (2007a). Assessing psychology students' difficulties with conditional probability and Bayesian reasoning. International Electronic Journal of Mathematics Education, 2 (2), 128–148.
Díaz, C. & de la Fuente, I. (2007b). Dificultades en la resolución de problemas que involucran el Teorema de Bayes. Un estudio exploratorio en estudiantes de psicología (Difficulties in solving problems that involve Bayes’ theorem. An exploratory study with Psychology students). Educación Matemática, 18(2), 75–94.
Eddy, D. M.: 1982, Probabilistic reasoning in clinical medicine: Problems and opportunities. In D. Kahneman, P. Slovic & Tversky (Eds.), Judgement under uncertainty: Heuristics and biases. New York: Cambridge University Press.
Falk, R. (1986). Conditional probabilities: insights and difficulties. In R. Davidson & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Statistics. Victoria: International Statistical Institute. 292–297.
Falk, R. (1989). Inference under uncertainty via conditional probabilities. In R. Morris (Ed.), Studies in mathematics education. Vol.7. The teaching of statistics. Paris: UNESCO. 175–184.
Feller, W. (1973). Introducción a la teoría de las probabilidades y sus aplicaciones. México: Limusa.
Fischbein, E. & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 15, 1–24.
Gigerenzer, G. (1994). Why the distinction between single-event probabilities and frequencies is important for psychology? In G. Wright & P. Ayton (Eds.), Subjective probability. Chichester: Wiley. 129–161.
Gigerenzer, G. & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102, 684–704.
Gras, R. & Totohasina, A. (1995). Chronologie et causalité, conceptions sources d’obstacles épistémologiques à la notion de probabilité. Recherches en Didactique des Mathématiques, 15(1), 49–95.
Heitele, D. (1975). An epistemological view on fundamental stochastic ideas. Educational Studies in Mathematics, 6, 187–205.
Koehler, J. J. (1996) The base rate fallacy reconsidered: Descriptive, normative, and methodological challenges. Behavior and Brain Sciences, 19, 1–54.
Martignon, L. & Wassner, C. (2002). Teaching decision making and statistical thinking with natural frequencies. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics. Cape Town, South Africa: International Statistical Institute and International Association for Statistical Education, on line: http://www.stat.auckland.ac.nz/~iase.
Mises, R. von. (1952). Probability, statistics and truth. J. Neyman, O. Scholl, & E. Rabinovitch, (Trans.), London: William Hodge and company. (Original work published 1928).
Nisbett, R. & Ross, L. (1980). Human inference: Strategies and shortcomings of social judgments. Englewood Cliffs, NJ: Prentice Hall.
Ojeda, A. M. (1996). Contextos, representaciones y la idea de probabilidad condicional. In F. Hitt (Ed.), Investigaciones en matemáticas educativas. México: Grupo Editorial Iberoamericano. 291–310.
Pollatsek, A., Well, A. D., Konold, C. & Hardiman, P. (1987). Understanding conditional probabilities. Organization, Behavior and Human Decision Processes, 40, 255–269.
Pozo, J. I. (1987). Aprendizaje de la Ciencia y Pensamiento Causal, Madrid: Visor.
Sánchez, E. (1996). Dificultades en la comprensión del concepto de eventos independientes. In F. Hitt (Ed.), Investigaciones en Matemática Educativa. México: Grupo Editorial Iberoamericano. 389–404.
Sánchez, E. & Hernández, R. (2003). Variables de tarea en problemas asociados a la regla del producto en probabilidad. In E. Filloy (Coord.), Matemática educativa, aspectos de la investigación actual. México: Fondo de Cultura Económica. 295–313.
Sedlmeier, P. (1999). Improving statistical reasoning. Theoretical models and practical implications. Mahwah, NJ: Erlbaum.
Tarr, J. E. & Jones, G. A. (1997). A framework for assessing middle school students’ thinking in conditional probability and independence. Mathematics Education Research Journal, 9, 39–59.
Tarr, J. E. & Lannin, J. K. (2005). How can teachers build notions of conditional probability and independence? In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning. New York: Springer. 216–238.
Thorndike, R. L. (1991). Psicometría aplicada. Méjico: Limusa.
Totohasina, A. (1992). Méthode implicative en analyse de données et application á l’analyse de conceptions d’étudiants sur la notion de probabilité conditionnelle. Unpublished Ph.D. University of Rennes I.
Truran, J. M. & Truran, K. M. (1997). Statistical independence: One concept or two? In B. Phillips (Ed.), Papers from Statistical Education Presented at Topic Group 9, ICME 8. Victoria: Swinburne University of Technology. 87–100.
Tversky, A. & Kahneman, D. (1982a). Judgements of and by representativeness. In D. Kahneman, P. Slovic & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases. New York: Cambridge University Press. 84–98.
Tversky, A. & Kahneman, D. (1982b). Evidential impact of base rates. In D. Kahneman, P. Slovic & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases. New York: Cambridge University Press. 153–160.
Watson, J. M. & Moritz, J. B. (2002). School students’ reasoning about conjunction and conditional events. International Journal of Mathematical Education in Science and Technology, 33, 59–84.

How to cite this article

APA

Díaz, C., & Batanero, C. (2009). University Students’ Knowledge and Biases in Conditional Probability Reasoning. International Electronic Journal of Mathematics Education, 4(3), 131-162. https://doi.org/10.29333/iejme/234

Vancouver

Díaz C, Batanero C. University Students’ Knowledge and Biases in Conditional Probability Reasoning. INT ELECT J MATH ED. 2009;4(3):131-62. https://doi.org/10.29333/iejme/234

AMA

Díaz C, Batanero C. University Students’ Knowledge and Biases in Conditional Probability Reasoning. INT ELECT J MATH ED. 2009;4(3), 131-162. https://doi.org/10.29333/iejme/234

Chicago

Díaz, Carmen, and Carmen Batanero. "University Students’ Knowledge and Biases in Conditional Probability Reasoning". International Electronic Journal of Mathematics Education 2009 4 no. 3 (2009): 131-162. https://doi.org/10.29333/iejme/234

Harvard

Díaz, C., and Batanero, C. (2009). University Students’ Knowledge and Biases in Conditional Probability Reasoning. International Electronic Journal of Mathematics Education, 4(3), pp. 131-162. https://doi.org/10.29333/iejme/234

MLA

Díaz, Carmen et al. "University Students’ Knowledge and Biases in Conditional Probability Reasoning". International Electronic Journal of Mathematics Education, vol. 4, no. 3, 2009, pp. 131-162. https://doi.org/10.29333/iejme/234