Abstract
The study of the understanding of mathematical concepts is of great interest for research in Mathematics Education. In this sense, an investigation is carried out on the understanding of the concept of improper integral, a basic concept from the first courses of Bachelor of Mathematics for subsequent courses. The objective is to characterize the understanding of this mathematical concept through a proficiency model for this purpose, an instrument was designed that was applied to second-year university students. The research is qualitative exploratory and is based on the framework of the Theory of records of semiotic representations. 
 
Highlights
The present investigation is about the understanding of the Concept of Improper Integral of university students within the framework of Raymond Duval’s theory of semiotic representation
The study of the understanding of the mathematical concepts is a field of great interest for the investigation in Mathematical Education, in our investigation we deepen in the development of the understanding of this mathematical concept, with students of first and second year of Degree of Mathematics, in an age range of 18 to 22 years
By focusing on the role of visualization in mathematical materials, this study showed few graphic representations and few opportunities to work with different records, few applications or intra-mathematical references to the importance of the concept and few tasks Conceptually driven to go beyond practice with the application of convergence tests and prepare students for complex issues that employ the concept of the series where it is involved
Summary
The present investigation is about the understanding of the Concept of Improper Integral of university students within the framework of Raymond Duval’s theory of semiotic representation. Aspects of the theoretical view with which it was carried out mentioning elements of Advanced Mathematical Thought (PMA) and the Theory of Registries of Semiotic Representation (TRRS) (Duval, 1990, 1996, 2003, 2006) are presented. They mention the three cognitive activities that interest in this research, training, treatment and conversion, which are presented in the competence model (Socas, 2001), used to give evidence of the students’ understanding of the concept of improper integral In this sense, aspects of concept compression are mentioned
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