Estudio sobre la construcción de la noción de parábola con estudiantes de ingeniería

This article presents a snippet of a master's research, in which both the creation and the a priori and a posteriori analysis of the problem situation presented here were extracted from that research [1], whose advisor was the second author of this work. The need to investigate the parabola as a geometric locus arises from observing the difficulties encountered by engineering students during their first year of studies. This mathematical object is typically taught by first presenting the theoretical part followed by a series of repetitive exercises, prioritizing algebraic operations and neglecting the initial concepts of geometric locus. Furthermore, the exercises are far from being meaningful situations for future engineers, such as the geometric design of a parabolic antenna. Therefore, the purpose of this research is for students to discover, construct, and apply concepts related to the parabola in an engineering context. In this regard, the objective of this article is to analyze the interactions of first-year students in Electrical and Electronic Engineering at a public university in Lima, Peru, regarding the construction of the notion of the parabola as a geometric locus. The experimental part was conducted in person with university students aged between 17 and 19 years, in a pencil-and-paper environment. Didactic Engineering methodology was employed, allowing for the confrontation of a priori analysis with a posteriori analysis. Additionally, a bibliographic review was conducted to gain an overview of the main research studies related to the parabola as part of conics, using the dynamic software GeoGebra. This research observed the actions taken by students when facing the proposed problem situations, as well as the formulations developed by them, subsequently validating their results through semiotic representation records, which contributed to the construction of the parabola as a geometric locus.