Technology of designing applied educational cases as a tool for implementing the competency-based approach in teaching mathematical analysis, linear algebra, and analytic geometry to future information security specialists in the context of collaboration between the instructor and the student group

Abstract

The article examines the technology of collaborative design of applied educational cases in teaching mathematical analysis, linear algebra, and analytic geometry to future information security specialists as a means of bridging the gap between fundamental mathematical training and the demands of professional disciplines focused on cryptography, steganography, and modeling secure systems. It substantiates that the perception of mathematical apparatus as abstract and «external» to practice is supported by the dominance of reproductive forms of learning, whereas joint construction of problems positions the student as a co-author and initiates reflexive mechanisms necessary for transferring methods to new classes of threats. The paper describes the iterative organization of design that resolves the contradiction between the requirement of preliminary competence for creating a case and the educational function of the case itself: initial student models are refined through discussions, instructor moderation, and expert verification. It presents data from a comparative study on first- and second-year cohorts (control/experimental), employing pre- and post-test measurements of algorithmic literacy, mathematical modeling skills, and motivation, as well as analysis of examination results by difficulty levels; processing was conducted using mathematical statistics methods. The results show that against a moderate increase in procedural skills, the most pronounced effects are achieved in modeling and motivation, with gains in experimental groups being statistically significant. Expert evaluation of the developed task array reveals the synergistic advantage of collaborative cases: high mathematical correctness is combined with professional relevance, interdisciplinary connections, and manageable computational complexity, whereas «purely instructor» and «purely student» solutions demonstrate complementary deficiencies. A growing superiority of experimental groups in performing productive and creative examination tasks is recorded, interpreted as a restructuring of cognitive strategies from formal application of algorithms to functional use of mathematics as a language of professional description. The paper discusses requirements for the new role of the instructor as a scientific moderator and prospects for scaling the approach, including updatable case repositories and automation of initial model verification.