Digital educational ecosystem for teaching mathematical analysis and linear algebra in technical and military universities: pedagogical conditions for implementing a competence-based approach based on Moodle, WebTutor and Maple

Abstract

The current stage of higher education development in technical and military universities is characterized by the need to transition to a competency-based approach in teaching fundamental disciplines such as mathematical analysis and linear algebra. Traditional teaching methods often lead to superficial knowledge acquisition, low student motivation, and a disconnect between theory and practice. This creates a contradiction between the requirements for deep mathematical thinking in engineering and military specialties and the inefficiency of classical approaches. The aim of the study is to identify and substantiate the pedagogical conditions for implementing a digital educational ecosystem based on Moodle, WebTutor, and Maple, in order to realize a competency-based approach that ensures not only knowledge acquisition but also skills development and motivation for innovative activity. The research was conducted in two institutions (N. State Technical University and M. Military Academy of Communications) with a sample of 310 engineering students over four semesters. A control group (152 students, traditional teaching) and an experimental group (158 students, ecosystem-based learning) were formed. Methods included a pedagogical experiment (stating and formative stages), surveys, digital footprint analysis, Pearson correlation analysis, and Student's t-test. The ecosystem integrated Moodle for content structuring, Web Tutor for adaptive testing, and Maple for interactive research. The conditions tested included problem-based assignments, interdisciplinary integration, automated feedback, and material visualization. The results showed a statistically significant increase in academic performance in the experimental group: the average exam score was 79,81 compared to 67,21 in the control group (an improvement of 18,75%), Standard deviation decreased from 12,45 to 8,53, indicating more uniform student preparation levels. Engagement analysis revealed high activity: average session time in Maple was 48,75 minutes, and task completion exceeded 91%. Correlation analysis confirmed a strong relationship between time spent in Maple and final exam grade $(r=0.812, 0.001^{\prime}$. Teachers highly rated visualization (9.76 points) and personalization (8.87 points), but noted the high labor intensity of preparing materials (5.18 points). Discussion of the results highlights that the ecosystem's effectiveness is driven by a synergy of pedagogical conditions: emphasis on research activities in Maple promotes deeper understanding and motivation, while integration with WebTutor and Moodle provides monitoring and communication. The findings support the hypothesis that digitalization helps overcome contradictions of traditional teaching methods, particularly in technical and military universities where mathematical modeling is directly linked to professional tasks. However, scaling the system requires support for teachers in content development and digital competence enhancement. The study opens prospects for adapting the ecosystem to other disciplines, fostering a shift toward personalized education in the context of the sixth technological revolution.