Abstract
<jats:p>Introduction. The integration of digital technologies into higher education is becoming more widespread every year, especially in disciplines that require complex conceptual understanding and dynamic visualization, such as mathematical analysis. Traditional methods of teaching differential calculus of functions of several variables often focus on formal-symbolic calculations, leaving out the geometric and conceptual essence of concepts. This leads to a significant gap between the learner's ability to perform algorithmic actions and their real understanding of mathematical objects in three-dimensional space. The lack of dynamic visualization hinders the formation of a holistic image of complex mathematical constructions. Purpose. To justify the expediency of using interactive models when studying the differential calculus of functions of several variables, describe the algorithms for developing such models in the GeoGebra 3D environment, and reveal the methodology of their use to ensure students' conceptual understanding of the essence of mathematical objects. Methods. A complex of scientific methods was used in the work: analysis of psychological, pedagogical, and methodical literature to clarify the state of the problem; modeling to create interactive applets in the GeoGebra 3D environment; methodical generalization to develop practical recommendations for their implementation in the educational process of higher education institutions. Results. The article describes in detail the methodology of working with four types of authors' interactive models. The first model, «Surface Scanning,» allows students to investigate level lines not as static formulas, but as a result of a surface section by planes and subsequent projection onto the Oxy plane. The second group of models is dedicated to the study of the function limit at a point. Thanks to dynamic trajectories, learners see that the limit exists only if they approach the same number regardless of the path. A case of «cognitive conflict» is described, where approaching along straight lines gives one result, and along a cubic parabola — another. The third model reveals the geometric meaning of partial derivatives through the visualization of surface sections by planes x=const and y=const. The fourth model demonstrates the study of local extrema with a parameter. It is emphasized that these models can be effectively applied during the study of other fundamental concepts of mathematical analysis. The proposed approach not only expands the teaching toolkit but also creates prerequisites for rethinking the ways of forming conceptual understanding of abstract concepts in learners. Originality. The scientific novelty lies in the development of specific algorithms for creating interactive 3D models focused on the systematic overcoming of epistemological obstacles in the study of mathematical analysis. Unlike existing approaches, the proposed methodology emphasizes the dynamic transformation of the model by the students themselves, which ensures the transition from procedural knowledge to a conceptual understanding of the essence of objects. Conclusion. It has been established that the use of interactive models in the GeoGebra 3D environment is an effective means of providing conceptual understanding of the differential calculus of functions of several variables. The proposed methodology allows overcoming formalism in knowledge by creating a cognitive bridge between the abstract symbol and geometric intuition. The described algorithms for constructing applets create conditions for implementing a research approach where the learner independently forms stable cognitive connections. The results of the study can serve as a basis for the further development of visualization technologies in teaching other sections of higher mathematics. It is recommended to implement dynamic modeling as a mandatory element of lectures and practical classes in higher education institutions.</jats:p>