Exploring Additivity in Triangle Areas: Methodological Insights for Mathematics Education

Background/purpose. In modern mathematical education, it is important to develop students' ability to understand the fundamental properties of geometric objects deeply. This makes it relevant to study the additivity of the area of triangles as a property inherent in various kinds of quantities and ways of representing it methodologically in the process of teaching mathematics. This article aims to define the theoretical basis and form methodological approaches to the study of the additivity of the area of triangles.

Materials/methods. In the course of the study, literature sources were synthesized to form the theoretical foundations of the additivity of triangle areas, a comparative analysis was carried out to compare different digital platforms for visualizing educational materials in mathematics education, and a pedagogical experiment was conducted to determine the effectiveness of the methodological approach in teaching the additivity of triangle areas to students of mathematical specialities.

Results. In the control group, the average value of the final grades was Mean= 8.091, while in the experimental group the average score was Mean = 9.455; therefore, students who studied according to the improved methodology have a relatively higher level compared to traditional methods, which confirms the expediency of using digital tools in the educational process, which contributes to better learning and reduces the variance of student performance.

Conclusion. The use of interactive methods contributes to a more systematic mastery of the concept of additivity in the area of triangles, which has further application in the study of the principles of geometric additivity and related topics.

Keywords: Educational process, additivity of areas, analogy, centroid, orthocenter, incentre, euler's line, visualization technologies, digital platforms

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