Pedagogical design of a digital environment based on Moodle and Mathcad for the organization of independent work of students and cadets studying within the framework of the discipline Mathematical Analysis

Abstract

The current stage of higher education development is closely connected with digitalization processes that affect all aspects of pedagogical activity. A particular importance is placed on organizing students' independent work, which has become a central component of learning, especially in fundamental disciplines such as Mathematical Analysis. The complexity and abstract nature of the material require deep understanding and practical application of knowledge. Traditional methods, based on lectures and paper-based resources, do not provide sufficient engagement and individualization, leading to decreased motivation. New models integrating digital technologies are needed. The Moodle system, as a platform for structuring materials and assessment, combined with Mathcad for visualization and calculations, allows the creation of an adaptive environment for active independent work. The purpose of the study is to develop and test such an environment to improve the quality of learning. The study was based on a pedagogical experiment conducted at a technical university over one semester. Fifty-four second-year students participated, divided into a control group (CG, 27 people) and an experimental group (EG, 27 people) with a comparable level of preparation. In the CG, traditional methods were used: lectures, practice sessions, written assignments. In the EG, a digital environment based on Moodle with Mathcad integration was implemented, including interactive modules, video tutorials, self-checking tests, a forum, and modeling assignments in Mathcad. Data collection methods: performance analysis (initial and final assessment), digital traces in Moodle (logins, time, activity), and questionnaires. Statistical analysis employed Student's t-test and Pearson's correlation. The results demonstrated a significant advantage for the EG: the average grade increased from 3.21 to 4.52 (growth of 1.31), while in the CG it rose from 3.15 to 3.68 (growth of 0.53). The standard deviation in the EG decreased, indicating a leveling of knowledge. Engagement in the EG was higher: 7.8 logins per week (versus 2.3), 4.5 hours of activity (versus 1.8), and 68,2% completion of optional tasks (versus 15,6%). Competence assessment: practical skills reached 4.65 in the EG (versus 3.44 in the CG), Mathcad skills 4.81 (versus 2.12). Correlation between working time and grade in EG was $r=0.76$ (strong), in CG $r=0.28$ (weak). The data confirm the hypothesis: integration of Moodle and Mathcad enhances motivation, develops deep competencies, and improves academic performance. The environment contributes to a transition towards research activities, relieving students of routine calculations. This catalyzes the educational process, ensuring productive effort. The model is scalable but requires teacher training. Future prospects include expansion into other disciplines with Al elements.