Tipos de prueba sobre el baricentro y circuncentro del triángulo que realizan estudiantes de 3er grado de secundaria cuando resuelven una secuencia didáctica con el uso del GeoGebra - Palomino Gomez, Haydee Lucia (2024)
This research aims to characterize the types of proofs about the barycenter and circumcenter of a triangle made by students of 3rd grade of secondary education when they solve a didactic sequence with the use of GeoGebra. The students' ages range between 15 and 16 years old, they are part of a private educational institution in Lima - Peru. The methodology used was qualitative and the method was a case study. The experimentation was carried out with two pairs of students who developed a didactic sequence made up of two activities, the first one, to test a conjecture about the relation of the segments of the median of a triangle, formed by the barycenter; the second activity is made up of two parts, one of them asks to test a proposition about the concurrence of the three medians of a triangle, and the second one, to test the concurrence of the circumcenter of a triangle with the center of a circumcircumscribed circumference to the same triangle. For the analysis of the results of our study, we took into account the Types of mathematical proofs of Balacheff (2000), which are classified into four types, organized into two categories: Pragmatic Proof and Intellectual Proof. The results show the types of proofs identified in the development of the activities, by the students and ranged from the type of proof “Naive Empiricism” to the type of “Generic Example” of intellectual proof category, in addition, there is evidence of little practice in conducting validation processes of conjectures, which can be addressed and enhanced with the use of GeoGebra tools, which allow greater analysis and precision of geometric properties.