DEVELOPMENT OF STUDENTS' RESEARCH COMPETENCE BY TEACHING THE EULER LINE AND EULER CIRCLE

Abstract

Today, the rapid development of society requires from the educational system not only the upbringing of 
specialists with academic training, but also individuals who are open to new ideas, capable of exploring complex problems, and thinking creatively and critically. The rapid growth of science and technology, the increase in information 
flows, and the integration of new technologies into our daily lives make it imperative that the student is not limited to 
being a mere recipient of ready-made information. On the contrary, the student must form as an individual capable of 
applying the acquired knowledge in practice, conducting analysis, forecasting, solving difficult problems, and drawing 
independent conclusions. 
Mathematical experiments and research play an important role in the mathematical preparation of students. It has 
been proven that their use increases efficiency in achieving a deeper and more complete assimilation of mathematical 
knowledge, forming in students qualities of creative thinking, skills of formulating hypotheses, conducting logical 
analysis, generalizing, and summarizing results. 
Therefore, the purpose of the article is to teach a geometry topic by organizing research while having students 
conduct mathematical experiments in the GeoGebra computer environment. 
The article considers a didactic development proposed for teaching the topic "The Euler Line and the Euler 
Circle" in classes with an in-depth study of geometry. In order for students to understand these two theorems to a degree 
that allows their application, they must prove them independently. Since the properties of many points are considered 
simultaneously here, to ensure independent mastery by students, complex theorems were divided into tasks (lemmas) 
while maintaining their sequence. 
In this methodical development, the teacher acts only as a guide, while the student takes on the role of a 
researcher of the properties of these remarkable points. 
It is recommended to use this system for 9th-grade students in elective classes, specialized classes, and 
Olympiad preparation sessions.