How to model a conic using five points: A classroom experience

Abstract

This paper presents a didactic experience involving six second-semester students enrolled in the Bachelor’s Degree in Applied Mathematics program in the Analytical Geometry course at a university in northern Mexico. Aiming to give greater meaning to the topic of conic sections, the students were assigned a project that required them to develop a mathematical model representing a conic. The experience was framed within an action research methodological approach. As part of the assignment, studenwwts modeled objects with conic shapes using three different processes: one using GeoGebra software tools, another using the quadrilateral method, and a third based on linear algebra techniques. The main outcomes revealed a significant departure from the traditional classroom model: the instructor adopted a more supportive and advisory role, students showed increased interest in completing the tasks, and communication between teacher and students improved, enabling more continuous and effective feedback. Collectively, these actions encouraged students to reflect on their own learning processes and become more aware of their academic needs.