Resumen

PEREYRA, Nora Elisa  y  HERRERA, Carlos Gabriel. Dificultades en la comprensión del concepto derivada de una función. Rev. electrón. investig. educ. cienc. [online]. 2020, vol.15, n.2, pp.48-58. ISSN 1850-6666.

The derivative of a function has been analysed by many authors in the field of Mathematics Education, and in general, the conclusions of their research agree that students have difficulties in understanding this mathematical concept. In this sense, the present work is based on the APOS theory. The research process in this theory involves the proposal of a cognitive model called genetic decomposition, through a student can construct a mathematical knowledge. It consists of a hypothesis about a detailed description of the constructions that students can make to learn a concept. Therefore, the aim of this work was to analyze the difficulties in the understanding of the mathematical concept of derivative of a function in the framework of the APOE theory, presenting a proposal of genetic decomposition, in order to carry out the research. Methodologically it is a descriptive case study.  For this purpose a data collection instrument was applied, which consisted in a set of  questions aimed to analyse whether students clearly identify the concept of a derivative of a function at a point, as well as the concept of a derivative function,  it has been possible to determine the predominant difficulties in the construction of the  concept of derivative, observing that the students present partial knowledge of the concept, showing inconveniences both to encapsulate in object, the process of determining the derivative of a function and to carry out the study of the behavior of functions, based on the sign of the first derivative.

Palabras clave : Derivative; Dificulties; APOS.

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