Designing and implementing digital educational models using the Mathematical Analysis discipline using Maple and Moodle

Abstract

In the context of the global digitalization of higher education, traditional approaches to teaching mathematical analysis face challenges, such as insufficient student engagement and the difficulty of mastering abstract concepts. This research is aimed at designing and implementing a digital educational model that integrates the Maple computer algebra system and the Moodle learning management platform in order to increase the effectiveness of mastering the discipline. The aim of the work is to develop an integrated methodological system that enriches the traditional process with interactive elements, visualization and adaptive knowledge control, which contributes to a deep understanding of the concepts of limits, derivatives and integrals. The research methodology includes the creation of an electronic course in Moodle based on a modular principle, where each module contains theoretical lectures with interactive Maple applets, practical tasks with reports in the Maple Worksheet format, and tests with calculated questions to generate unique options. The pedagogical experiment was conducted during the semester with the participation of an experimental group (52 students) who studied according to the new model, and a control group (50 students) who used traditional methods. The effectiveness was assessed through a comparative analysis of academic performance, time tracking for assignments, Moodle activity data, and questionnaires. Statistical processing included the calculation of averages, standard deviations, and the Student's t-test. The results showed a statistically significant increase in the average score in the experimental group (4.45 versus 3.78 in the control group) on key topics, with the greatest improvement in integral calculus (a difference of 0.68 points). The standard deviation decreased (0.68 versus 0.94), indicating a leveling-off in academic performance. The time for standard tasks was halved (5.40 hours versus 10.10), and the survey revealed a high level of satisfaction (4.72 versus 3.61 points). The Moodle activity data confirmed the increased engagement. The discussion of the results highlights that the integration of Maple and Moodle transforms learning by shifting the focus from routine computing to research activities, increasing motivation and inclusivity. The model has proven its effectiveness in overcoming traditional constraints, contributing to the formation of competencies for engineering specialties. The data obtained confirm the hypothesis about the synergetic effect of digital tools, opening up prospects for the modernization of mathematical education. In general, the study demonstrates the potential of such models to improve the quality of teaching fundamental subjects in higher education.