An Exploratory Analysis of the Representations of Functions in the University Entrance Exam in Spain and Iran

Abstract

The University Entrance Exam (UEE) has an important impact on how math instructors teach mathematics to prepare students for this exam as well as how their students learn mathematics. Since the UEE is like a bridge between high school and university, its importance becomes twofold. However, research regarding this issue is very limited in mathematics education. The purpose of this research is to conduct an exploratory analysis of mathematics questions from the UEE in Spain and Iran from the point of view of representations of functions (i.e., algebraic, graphical, numerical and explanations with words). For this, the mathematics questions related to derivatives and integrals, which are two of the most important concepts in mathematics, from the last five years of the UEE in these two countries were considered to analyze them from the point of view of different representations. The results showed that most of the derivative and integral questions in the UEE in both countries were related to the algebraic representation. However, a very small percentage of the derivative and integral questions were related to the graphical and numerical representations and the relationships between the representations. At the end, suggestions to the curriculum planners and designers of mathematics questions of the UEEs are given.

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“…Lately, teachers have been emphasizing the mastery of problem-solving techniques akin to those found on the Konkoor (Farrokhi-Khajeh-Pasha et al, 2012). Acquiring these methods involves memorizing numerous formulas that have no utility outside of this specific exam context (Borji & Sánchez, 2019). In contrast, in a Canadian classroom, students are not required to memorize formulas, and teachers often provide them with a formula sheet during tests.…”

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“…(Behr et al, 1983). Various authors study the relationship between modes of representation of tasks and their understanding, or between the use of the concept image and its definition (Borji et al, 2018;Borji & Sánchez, 2019;Dahl, 2017;Pinto-Rojas & Parraguez, 2017). identified three levels of understanding of the derivative scheme (intra-inter-trans), which are based, among other aspects, on different modes of representation.…”

“…identified three levels of understanding of the derivative scheme (intra-inter-trans), which are based, among other aspects, on different modes of representation. Moreover, Borji and Sánchez (2019) concluded that the predominant mode of representation in secondary education is algebraic. For this reason, first-year undergraduate students may have difficulties in solving problems in other modes of representation or finding relations between them.…”