Characterizing Probability Problems Posed in University Entrance Tests in Andalucia

The compulsory university entrance tests in Andalucia (Spain), which traditionally include a probability problem, often determine whether the student is admitted to study in his or her desired university program. Consequently, it is important to ensure that the content of the test is directly related to the content included in the high school curriculum. The aim of this research was to investigate the distribution of the main variables characterizing the probability problems posed in these tests in Andalucia. Specifically, we examined all the problems posed to students in the period 2003–2014 (n = 144 problems). We considered the following variables: type of experiment and sample space considered, type of probability that should be computed, theorems or properties needed to find the solution, format of the data, and context. The results of the analysis reveal the potential difficulty of the problems, as well as the relevance given to conditional probability in the tests, in comparison to other curricular contents.

[1]  M. Borovcnik.  Multiple perspectives on the concept of conditional probability. 'Perspectivas múltiples sobre el concepto del probabilidad condicional' , 2012 .

[2]  Klaus Krippendorff,et al.  Content Analysis: An Introduction to Its Methodology , 1980 .

[3]  M. Huerta.  Researching Conditional Probability Problem Solving , 2014 .

[4]  C. Batanero,et al.  The onto-semiotic approach to research in mathematics education , 2007 .

[5]  G. Gigerenzer,et al.  Representation facilitates reasoning: what natural frequencies are and what they are not , 2002, Cognition.

[6]  Paul Drijvers,et al.  One episode, two lenses , 2013 .

[7]  Carmen Díaz,et al.  Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning , 2007, International Electronic Journal of Mathematics Education.

[8]  G. Gigerenzer.  Why the distinction between single-event probabilities and frequencies is important for psychology (and vice versa). , 1994 .

[9]  A. Tversky,et al.  Judgments of and by Representativeness , 1981 .

[10]  Alexander Pollatsek,et al.  Understanding conditional probabilities , 1987 .

[11]  C. Wild,et al.  Statistical Thinking in Empirical Enquiry , 1999 .

[12]  María Carmen Díaz Batanero,et al.  Teaching Independence and Conditional Probability , 2010 .

[13]  C. Batanero,et al.  University Students’ Knowledge and Biases in Conditional Probability Reasoning , 2009, International Electronic Journal of Mathematics Education.

[14]  José Miguel Contreras,et al.  Evaluación de sesgos en el razonamiento sobre probabilidad condicional en futuros profesores de educación secundaria , 2012 .

[15]  Manfred Borovcnik,et al.  Statistics and Probability in High School , 2016 .