Prospective Teachers’ Semiotic Conflicts in Computing Probabilities from a Two-Way Table

Carmen Batanero; José M. Contreras; Carmen Díaz; Ernesto Sánchez

doi:10.29333/iejme/288

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Carmen Batanero, José M. Contreras, Carmen Díaz, Ernesto Sánchez

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Abstract

The aim of this research was to assess the common knowledge of elementary probability in a sample of 183 prospective primary school teachers using and open-ended task, where teachers had to compute simple, compound and conditional probability from data presented in a two-way table. We base on theoretical ideas from the onto-semiotic approach to perform a semiotic analysis, in which we describe the mathematical objects and processes involved in the solutions of the tasks. Participants in the sample showed a weak common knowledge to compute simple, compound and conditional probabilities from a two-way table: they confused simple, compound and conditional probability; exchanged condition and event in conditional probabilities; confused probability and frequency or the union of events with the intersection. The semiotic analysis is used to provide and explanation for these errors in terms of semiotic conflicts. This list of difficulties expands what was found in previous research and may be used to reinforcing the preparation of prospective teachers to teach probability.

Keywords

assessment
simple
compound and conditional probability
teacher knowledge
2x2 tables

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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 10, Issue 1, January 2015, 3-16

https://doi.org/10.29333/iejme/288

Publication date: 04 Apr 2015

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How to cite this article

APA

Batanero, C., Contreras, J. M., Díaz, C., & Sánchez, E. (2015). Prospective Teachers’ Semiotic Conflicts in Computing Probabilities from a Two-Way Table . International Electronic Journal of Mathematics Education, 10(1), 3-16. https://doi.org/10.29333/iejme/288

Vancouver

Batanero C, Contreras JM, Díaz C, Sánchez E. Prospective Teachers’ Semiotic Conflicts in Computing Probabilities from a Two-Way Table . INT ELECT J MATH ED. 2015;10(1):3-16. https://doi.org/10.29333/iejme/288

AMA

Batanero C, Contreras JM, Díaz C, Sánchez E. Prospective Teachers’ Semiotic Conflicts in Computing Probabilities from a Two-Way Table . INT ELECT J MATH ED. 2015;10(1), 3-16. https://doi.org/10.29333/iejme/288

Chicago

Batanero, Carmen, José M. Contreras, Carmen Díaz, and Ernesto Sánchez. "Prospective Teachers’ Semiotic Conflicts in Computing Probabilities from a Two-Way Table ". International Electronic Journal of Mathematics Education 2015 10 no. 1 (2015): 3-16. https://doi.org/10.29333/iejme/288

Harvard

Batanero, C., Contreras, J. M., Díaz, C., and Sánchez, E. (2015). Prospective Teachers’ Semiotic Conflicts in Computing Probabilities from a Two-Way Table . International Electronic Journal of Mathematics Education, 10(1), pp. 3-16. https://doi.org/10.29333/iejme/288

MLA

Batanero, Carmen et al. "Prospective Teachers’ Semiotic Conflicts in Computing Probabilities from a Two-Way Table ". International Electronic Journal of Mathematics Education, vol. 10, no. 1, 2015, pp. 3-16. https://doi.org/10.29333/iejme/288