Methodological approaches to the use of Maple, Mathcad, and Mathematica computer mathematics systems in teaching linear algebra, mathematical analysis, and mathematical logic in technical, military, and law schools

Abstract

The current stage of higher education development is characterized by a deep digital transformation affecting the mathematical training of technical, military and legal specialists. Disciplines like linear algebra, mathematical analysis, and mathematical logic form abstract and systematic thinking, but traditional teaching methods based on manual calculations often reduce students' motivation and distract from understanding the essence of concepts. The relevance of the research is due to the need to integrate computational mathematics CCM systems – Maple, Mathcad and Mathematica – to intensify learning and increase its effectiveness. The aim of the work is to develop and analyze methodological approaches to the use of these systems in universities of various profiles, taking into account the specifics of disciplines and professional orientation, to improve academic performance, motivation and temporary effectiveness of the educational process. The study was conducted in the form of a multi-stage pedagogical experiment in the period 2020-2023 in Russian universities of technical, military and legal profiles with the participation of 680 students divided into control and experimental groups 340 people each. The control groups were trained using traditional methods, the experimental ones with the integration of SCM Maple for technical universities, Mathcad for military and Mathematica for law schools. Educational and methodological materials have been developed, including laboratory work and interactive assignments. The effectiveness was assessed through final tests, questionnaires for motivation and engagement analysis, time tracking for tasks, followed by statistical data processing in SPSS Statistics Student's t-test, correlation and variance analysis. The experimental results confirmed the hypothesis of a positive effect of SCM. In linear algebra, the average score in the experimental groups increased by 17,2–17,52 percent from 72,18 to 84,59 in technical universities and from 75,83 to 89,12 in the military, with a decrease in the standard deviation, indicating greater uniformity of learning. In mathematical analysis, the time for typical tasks was reduced by 83-94,21 percent for example, calculating the derivative – from 15,21 to 0,88 minutes. In mathematical logic, motivational indicators doubled perceived usefulness – from 4,23 to 8,15 points in law schools. Integral efficiency index for analysis 0,807, with an emphasis on time savings. The discussion of the results highlights that the effectiveness of the SCM depends on the discipline and profile of the university in technical and military – due to visualization and automation of calculations, in legal – due to motivation and applied logic. This allows you to shift the focus from routine to research activities, improving the quality of education. The conclusions recommend the differentiated implementation of SCM with methodological support, confirming their role in the modernization of mathematical education.