VISUALIZATION OF LINEAR ALGEBRA AS A TOOL OF APPLIED MATHEMATICS: EXPERIENCE OF IMPLEMENTING GEOGEBRA IN THE EDUCATION OF FUTURE SOFTWARE ENGINEERS - Marchuk, A. R.; Yaretska, N. O. (Systems and Technologies, 2026)
In modern technical education, dynamic computer environments play a key role in combining theoretical mathematical models with their practical application. The article shows the experience of systematic use of the GeoGebra environment in teaching the section “Linear Algebra and Analytical Geometry” of the discipline “Higher and Applied Mathematics” to future software engineers. Based on a review of scientific sources and an experiment, it is proven that visualization of abstract concepts of linear algebra and analytical geometry significantly enhances the understanding of the material by higher education students of the specified specialty. The approach used in our institution – the University of Economics and Entrepreneurship – where GeoGebra is integrated for conducting practical classes and independent work of higher and pre-higher education students is described. An educational experiment was conducted with two groups: experimental (group of 8 students) – worked with GeoGebra applets, control (group of 12 students) – worked according to the classical method of presenting the material of the discipline. A comparative analysis of the results of testing and questionnaires proves that higher education students from the experimental group not only improved their results and knowledge, but also demonstrated a deeper understanding of the geometric interpretation of vector operations, matrix transformations, and solving systems of linear algebraic equations. Visual interpretation and examples contributed to the formation of an instinctive vision of the structure of linear models used in software engineering. The obtained experimental results confirm the high efficiency of the dynamic computer environment GeoGebra as a tool for quick and visual demonstration, which significantly increases the level of motivation of students of technical specialties. Using GeoGebra allows higher education students not only to see the result, but also to explore it interactively by changing the parameters of the model. The article also presents practical recommendations for further scaling the approach to using GeoGebra – from creating author’s applets to implementing project-oriented tasks.