Joint project-research activity of the instructor and students of IT directions in creating practice-oriented cases within the disciplines Mathematical analysis , Linear algebra and analytic geometry at the level of higher professional education

Abstract

The article examines a pedagogical model oriented toward overcoming the gap between the academic presentation of higher mathematics and the applied needs of students in IT directions through involving students in joint project-research work with the instructor to create practice-oriented cases for the disciplines Mathematical Analysis and Linear Algebra and Analytic Geometry . It is emphasized that constructing problems related to data analysis, machine learning, computer graphics, cryptography, and optimization positions the student as a co-author of educational content and compels them to mathematically formalize a professional problem, select an adequate apparatus, and interpret computational results, rather than reproducing algorithms by pattern. The organization of work over four semesters (2021-2023) with the participation of 248 students and 12 instructors is described, including division into control and experimental groups based on entry testing results, application of observation, questioning, analysis of activity products (cases and software code), competency diagnostic maps, and statistical verification of differences (Student's t-test, Pearson's chi-square test). It is shown that initially successful performance of standard operations did not ensure knowledge transfer to loss function optimization tasks or geometric transformations; inclusion of collaborative design was accompanied by significant growth in interdisciplinary synthesis indicators (abstraction, formalization correctness, interpretive validity) and reduction in result dispersion in the group. Expert evaluation of over 120 cases revealed maximum methodological and programmatic maturity of projects in the clusters of computer graphics and intelligent data analysis, as well as risks of excessive theorization in cryptographic tasks. A shift in the distribution of exam scores toward higher grades and a decrease in the share of unsatisfactory results were recorded, along with a pronounced increase in the professional significance of mathematics, intrinsic interest, and confidence at the same time as a decrease in academic anxiety. The conclusion is drawn about the replicability of the approach as a mechanism for updating the case fund and strengthening the applied meaning of fundamental training in a rapidly changing IT context.