A Study and Research Path to Teach Conics in High School: conditions and constraints that affect its implementation

Abstract

In this work, we present a study of the conditions and constraints that affect a study and research path (SRP) when using it to teach conics (parabola, ellipse, and hyperbola) with a group of third-year High School students of Itabaiana/Sergipe/Brazil. The research followed the anthropological didactic theory methodology, which is based on the principles of didactical engineering and has four steps. In the first one, we developed epistemological and economic studies, in the second one we carried out the a priori analysis and the design of the SRP, which was implemented in the third step and, finally, the last one corresponds to the a posteriori analysis of the implementation. The design and management of the SRP were based on a reference epistemological model (REM), that shows conics present in three geometry models: synthetic, analytical, and linear. The results point to a set of conditions and constraints originated from the current teaching paradigm, in which the institution requires the teacher to comply with the content within a certain period; in which students, who are not used to classes based on inquiries, present difficulties in the process of elaborating questions, the use of reliable research sources, finding criteria to validate contents found on the internet, and when they work with synthetic geometry.

Palabras clave: Study and research path; Ecological study; ATD; Conics