Digital Twin Technology in Teaching Geometry: Didactic Potential and a Methodology for Visualizing the Concepts of Area and Diameter

Abstract

The article considers the possibilities of using digital resources and technologies of digital twins in the process of teaching geometry, in particular when forming ideas about the concepts of area and diameter. Digital twins are virtual models of real geometric objects that reproduce their properties, parameters and relationships in a dynamic mode. This approach allows students not only to observe the figure, but also to study its behavior when changing individual parameters, which contributes to a deeper understanding of mathematical patterns. The didactic potential of interactive learning tools, in particular GeoGebra, Desmos, PhET, is substantiated. Interactive Simulations and LearningApps, which can perform the functions of digital twins of geometric objects. Their use ensures the creation of a dynamic educational environment in which students have the opportunity to model circles, measure diameters, calculate areas, and also observe in real time the changes that occur when varying the radius or scale of a figure. It is shown that the technology of digital twins promotes interactive and research learning, activates the cognitive activity of students, develops spatial thinking and the ability to apply knowledge in practice. The article identifies methodological approaches to the implementation of digital twins in geometry teaching, including the creation of virtual laboratories, interactive experiments and tasks with parametric changes of figures. Special attention is paid to the role of digital twins as a tool for individualizing learning, which allows adapting the complexity of tasks and visualizing the process of forming geometric concepts at different levels of cognition. The use of such technologies meets the requirements of STEM education and the concept of the New Ukrainian School, where digital competence is considered a key component of modern mathematics education. Thus, the use of digital twins in teaching geometry not only expands the possibilities of visualizing the concepts of area and diameter, but also forms a new quality of the educational process – exploratory, interactive, and competency-oriented.