The charm of rational functions

Abstract

This work is being developed within the framework of the Fourth Educative Practicum’s Residency, which belongs to the mathematics’ teaching training course of studies. It was specifically carried out in a fifth year from the Oriented Cycle at Secondary School. Its main purpose is to present the basic mathematical fundamentals associated to the rational functions, making special emphasis on aspects such as domain, image, and asymptote. Furthermore, the didactic challenges associated to the ‘traditional’ teaching of these functions are explored through a revision of magazines and documents which deal with problems and interests regarding the teaching and learning aspects of this topic. The focus of this work is centered on the UNIPE’s perspective, which conceptualizes the rational functions as the quotient of two polynomials. It is highlighted that this approximation modifies the didactic challenges commonly associated with this topic’s teaching. The research is supplemented with the practicum, which was developed based on the references previously mentioned, and which invites us to reflect on the importance of a practicum which is based on the knowledgeable decision making to promote a bigger access to knowledge.