Um modelo didático de referência baseado em atividades de estudo e investigação para o ensino de cônicas na escola básica - Siqueira, Carlos Alberto Fernandes de (2021)
This research aims to identify which contributions can emerge from the study of the three dimensions of the didactic problem and contribute to the construction of a Reference Didactic Model associated with the development of Study and Research Activities aimed at teaching and learning conics in basic education. We used as theoretical reference the Anthropological Theory of didactics and adopted the methodology of documentary research. According to this theory, we made a study of these three dimensions in which, in the epistemological dimension we identified the knowledge and the reasons of being of conicals, throughout history, inserted in the synthetic geometry, analytical, linear, projective and taxi and we built an Epistemological Model of Reference involving each of these geometries in which we explain the praxeologies involved. In the economic-institutional dimension, we identified the dominant model for the teaching of conics in primary school, based on a historical study, in Brazilian teaching, through the curricula that followed and textbooks adopted in different periods. In the ecological dimension we built a food chain, in the sense of TAD, explaining which mathematical contents allow feeding the teaching of conics in basic school and what objects can be fed by them, even rescuing contents that have been forgotten over time and that allow a series of important articulations to understand these objects. As a consequence, we suggest changes in the school curriculum so that the teaching of conics is distributed throughout basic education and not to focus only on the 3rd year of high school. In addition, we built a Didactic Reference Model in which we develop Study and Research Activities for the 9th year of elementar school, presenting different ways to build a representation of conics in which the student can be impelled to conjecture, investigate and reflect, while using several mathematical properties. For the 1st year of high school we elaborated an activity about parabola that involves the transport of some elements of synthetic geometry to a cartesian reference, relating analytical geometry with taxi geometry, evidencing the difference between its metrics and elaborated another activity related to hyperbola to understand the location of a ship through electromagnetic waves in the LORAN-C system, relating synthetic geometry to analytical geometry. In the 2nd year of high school we developed an activity that relates the synthetic and analytical geometries in the study of parables and hyperbole in the construction of a reflector telescope and another, to treat the ellipse, in these same geometries, related to the celestial orbit of the planet earth, considering the positions of the aphelium and perihelium. In the 3rd year of high school we built an activity to study the ellipse through the coordinates of five points of a celestial orbit in which we relate the linear and analytical geometries and another activity, involving the synthetic, analytical and projective geometries to determine which conical represents the projected shadow of a lamp on a wall