Abstract:

The usefulness of probability for daily life, the way in which probability reasoning support decision making and the instrumental role of probability in various curricular areas and professional work has been stated by Batanero, Contreras, Díaz, and Sánchez (2015) but other authors have also written about its teaching and learning.

In this work we present the semiotic conflicts of an explanatory study with 120 Portuguese secondary school students (ages from 15 to 17) in the northern Portugal, in the academic year 2013/2014, in solving two problems that involve the use of conditional probability, events independence, the theorem of total probability and the Bayes formula. The Onto-Semiotic Approach (Godino, Batanero & Font, 2007) was adopted in order to identify and describe the semiotic conflicts - the disparity between the student’s interpretation of a mathematical expression and the meaning of the same expression in a mathematics or school institution (Batanero, Contreras, Díaz, & Sánchez, 2015) - that arose in the answers of the students in a survey. The survey was presented in a 50 minute class and had 11 multiple choice questions and students were asked to write the reasons of their choice. In this paper we analyse the answers to questions 4 (based on absolute frequencies) and 9 (based on relative frequencies), and both of them were designed to detect the semiotic conflicts of the students’ answers that are referred in the literature.

As a result the semiotic conflicts referred in the literature were identified and analysed in order to support a plan proposal for classroom approach and its further research.

References:
[1] Batanero, C., Contreras, J. M. y Díaz, C. & Sánchez, E. (2015). Prospective teachers’ semiotic conflicts in computing probabilities from a two-way table. Mathematics Education, 10 (1), 3-16. Accessible in: http://www.ugr.es/~batanero/documentos /Mathedu.pdf
[2] Godino, J. D., Batanero, C. & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39 (1-2), 127-135.

Keywords:

Probability, probability reasoning, students, semiotic conflicts.