Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning

Carmen Díaz; Inmaculada de la Fuente

doi:10.29333/iejme/180

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Carmen Díaz, Inmaculada de la Fuente

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Abstract

In this paper we first describe the process of building a questionnaire directed to globally assess formal understanding of conditional probability and the psychological biases related to this concept. We then present results from applying the questionnaire to a sample of 414 students, after they had been taught the topic. Finally, we use Factor Analysis to show that formal knowledge of conditional probability in these students was unrelated to the different biases in conditional probability reasoning. These biases also appeared unrelated in our sample. We conclude with some recommendations about how to improve the teaching of conditional probability.

Keywords

Conditional Probability Reasoning
Assessment

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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, Volume 2, Issue 3, October 2007, 128-148

https://doi.org/10.29333/iejme/180

Publication date: 12 Dec 2007

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References

Batanero, C., Henry, M., & Parzysz (2005). The nature of chance and Probability. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning, (pp. 20-42). New York: Springer.
Bar-Hillel, M. (1983). The base rate fallacy controversy. In R. W. Scholz (Ed.), Decision making under uncertainty. (pp 39 – 61). Amsterdam: North Holland.
Bar-Hillel, M., & Falk, R. (1982). Some teasers concerning conditional probabilities. Cognition 11, 109-22.
Callingham, R. (2006). Assessing statistical literacy: a question of interpretation? In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil: International Statistical Institute and International Association for Statistical Education. On line: http://www. stat.auckland.ac.nz/~iase.
Cosmides, L., & J. Tooby. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition, 58, 1-73.
Díaz, C., & de la Fuente, I. (2006). Assessing psychology students’ difficulties with conditional probability and bayesian reasoning. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil: International Statistical Institute and International Association for Statistical Education. On line: http://www. stat.auckland.ac.nz/~iase.
Eddy, D. M. (1982). Probabilistic reasoning in clinical medicine: Problems and opportunities. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgement under uncertainty: Heuristics and biases (pp. 249-267). New York: Cambridge University Press.
Estepa, A. (1993). Concepciones iniciales sobre la asociación estadística y su evolución como consecuencia de una enseñanza basada en el uso de ordenadores (Initial conceptions on statistical association and its evolution after a teaching experiment based on the use of computers). Unpublished Ph.D. University of Granada, Spain.
Falk, R. (1986). Conditional probabilities: insights and difficulties. In R. Davidson, & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Sta¬tistics. (pp. 292–297). Victoria, Canada: International Statistical Institute.
Falk, R. (1989). Inference under uncertainty via conditional probabilities. In R. Morris (Ed.), Studies in mathematics education: Vol.7. The teaching of statistics (pp. 175-184). Paris: UNESCO.
Feller, W. (1968). An introduction to probability theory and its applications (Vol. 1). New York: Wiley.
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 (and vice-versa). In G. Wright, & P. Ayton (Eds.), Subjective probability (pp. 129 – 161). Chichester: Wiley.
Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats (pp. 129-161). Psychological Review, 102, 684 – 704.
Gras, R., & Totohasina, A. (1995). Chronologie et causalité, conceptions sources d’obstacles épistémologiques à la notion de probabilité (Chronology and causality, conceptions causing epistemological obstacles to the notion of probability). Recherches en Didactique des Mathématiques, 15(1), 49 – 95.
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. Online: http://www.stat.auckland.ac.nz/~iase.
Millman, J., & Greene, J. (1989). The specification and development of test of achievement and ability. In R. L. Linn (Ed.), Educational Measurement (pp. 335 – 366). London: Macmillan.
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 (Contexts, representations and conditional probability). In F. Hitt (Ed.), Investigaciones en matemáticas educativas (pp.291-310). México: Grupo Editorial Iberoamericano.
Pollatsek, A., Well, A. D., Konold, C., & Hardiman, P. (1987). Understanding conditional probabilities. Organization, Behavior and Human Decision Processes, 40, 255 – 269.
Rossman, A., & Short, T. (1995). Conditional probability and education reform: Are they compatible? Journal of Statistics Education, 3(2). On line: http://www.amstat.org/publications/jse.
Sánchez, E. (1996). Dificultades en la comprensión del concepto de eventos independientes (Difficulties in understanding independent events). In F. Hitt (Ed.), Investigaciones en Matemática Educativa (pp. 389–404). México: Grupo Editorial Iberoamericano.
Sánchez, E., & Hernández, R. (2003). Variables de tarea en problemas asociados a la regla del producto en probabilidad (Task variables in product rule problems in probability). In E. Filloy (Coord.), Matemática educativa, aspectos de la investigación actual (pp. 295 –313). México: Fondo de Cultura Económica.
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 (pp.216-238). New York: Springer.
Totohasina, A. (1992). Méthode implicative en analyse de données et application á l’analyse de concetpions d’étudiants sur la notion de probabilité conditionnelle (Implicative data analysis and application to analyse students’ conceptions on conditional probability). 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, (pp. 87–100). Hawthorn, Victoria, Australia: Swinburne University of Technology.
Tversky, A., & Kahneman, D. (1982 a). Judgements of and by representativeness. In D. Kahneman P. Slovic & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 84-98). New York: Cambridge University Press.
Tversky, A., & Kahneman, D. (1982 b). Evidential impact of base rates. In D. Kahneman P. Slovic & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 153-160). New York: Cambridge University Press.

How to cite this article

APA

Díaz, C., & Fuente, I. D. L. (2007). Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning. International Electronic Journal of Mathematics Education, 2(3), 128-148. https://doi.org/10.29333/iejme/180

Vancouver

Díaz C, Fuente IDL. Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning. INT ELECT J MATH ED. 2007;2(3):128-48. https://doi.org/10.29333/iejme/180

AMA

Díaz C, Fuente IDL. Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning. INT ELECT J MATH ED. 2007;2(3), 128-148. https://doi.org/10.29333/iejme/180

Chicago

Díaz, Carmen, and Inmaculada de la Fuente. "Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning". International Electronic Journal of Mathematics Education 2007 2 no. 3 (2007): 128-148. https://doi.org/10.29333/iejme/180

Harvard

Díaz, C., and Fuente, I. D. L. (2007). Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning. International Electronic Journal of Mathematics Education, 2(3), pp. 128-148. https://doi.org/10.29333/iejme/180

MLA

Díaz, Carmen et al. "Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning". International Electronic Journal of Mathematics Education, vol. 2, no. 3, 2007, pp. 128-148. https://doi.org/10.29333/iejme/180