Comprehensive impact of digital transformation of the university educational environment on improving the quality of student training in the disciplines Linear Algebra and Mathematical Analysis

Abstract

In the context of the accelerated development of information technology and the globalization of the educational space, higher education institutions are faced with the need to radically restructure traditional approaches to learning. Digital transformation is becoming a key factor in increasing the competitiveness of universities and the quality of specialist training, especially in fundamental disciplines such as Linear Algebra and Mathematical Analysis, which form the basis of engineering and technical education. These subjects are characterized by high abstraction and complexity, which often leads to a decrease in students' motivation and academic performance. The introduction of digital technologies, including interactive simulators, adaptive testing systems, and multimedia materials, opens up opportunities for individualizing learning and overcoming the barriers of the traditional system. The relevance of the research is due to the gap between the potential of digital solutions and their fragmented application in universities, which does not allow their didactic effect to be fully realized. The purpose of the work is a comprehensive assessment of the impact of the systemic digital transformation of the educational environment on the quality of student training, identification of key mechanisms and effectiveness factors for the development of recommendations for the modernization of the educational process. To achieve this goal, a pedagogical study was conducted at a technical university with the participation of 180 second-year students, divided into control (90 people, traditional education) and experimental (90 people, integrated digital environment) groups. The initial level of knowledge was leveled based on the results of the entrance test. The experimental group used an LMS platform with electronic notes, video lectures, simulators for visualizing matrix transformations, adaptive testing, and a forum for collaboration. The data was collected through final exams, cross-sectional tests, engagement analysis (LMS logs, questionnaires, attendance) and qualitative methods (focus groups). Statistical processing included Student's t-test and Pearson correlation analysis. The results showed a significant superiority of the experimental group: the average score in linear algebra was 76.82 versus 68.45 in the control group, in mathematical analysis – 74.38 versus 65.13; the percentage of successful completion was 93,3% and 90,0% versus 81,1% and 75,6%. The standard deviation in the experimental group is lower (8.54 and 9.17 versus 11.21 and 12.56), indicating a more uniform learning. The increase in knowledge was 42.14 and 43.29 points against 32.76 and 33.10. Engagement increased: time for independent work was 7,85 hours/week versus 4,25; access to materials was 14.7 versus 3.1; tests were 18.4 versus 2. The correlation with the final grade is high for simulators (r=0.68 in algebra) and testing (r=0.62–0.65). The discussion of the results confirms that the digital environment enhances motivation, personalization, and depth of understanding of abstract concepts through the synergy of tools. The decrease in the spread of grades indicates the support of lagging students. Correlation analysis highlights the priority of simulators for algebra and testing for both disciplines. The data obtained make it possible to recommend the systematic implementation of digital environments to improve the quality of mathematical training, taking into account the specifics of the disciplines. The study highlights the transition from fragmented technologies to a holistic paradigm that promotes the formation of competent specialists.