Categories of Intuitive Reasoning in the teaching of parabolas: A structured practice in Didactic Engineering

This work is the result of a pre-experiment carried out as part of a master’s course, dealing with the study of the parabola through different mathematical views. It aims to recognize possible didactic obstacles in its teaching, based on intuitive manifestations in the resolution of a didactic situation based on GeoGebra software. The methodology adopted was didactic engineering in its four phases, experimented with a teacher in initial training. The observation and data collection provided us with elements for a posteriori analysis and validation of the experiment in which we verified the need to discuss the parabola, articulating its geometric, algebraic, and analytical views.