Integration of Digital and Computer Technologies into Teaching Mathematical Analysis: Innovative Competence-Based Approaches and Prospects for Development

The study aimed to explore correlations between digital activity, student satisfaction, and assimilation of mathematical analysis content in Kyrgyzstan. The theoretical and empirical study was conducted between January and April 2025 at Kyrgyz State University named after I. Arabaev and Jalal-Abad State University named after B. Osmonov. The sample included 130 respondents, including 112 undergraduate and graduate students majoring in mathematics and computer science, and 18 teachers of relevant disciplines who participated in the survey before and after completing a digital module implemented using the GeoGebra, Desmos, Moodle, and Wolfram Mathematica platforms. A theoretical analysis of educational programmes and regulatory documents governing digital integration was also conducted. The results showed an increase in the proportion of highly motivated students from 30% to 60%, a decrease in the proportion of low-motivation students from 25% to 10%, and an increase in satisfaction with digital solutions to 62.5%. Statistical analysis confirmed a significant positive correlation (ρ=0.47) between the regularity of digital tool use and self-assessment of learning outcomes. Institutional differences in approaches were identified: at Kyrgyz State University named after I. Arabaev, the emphasis was on visualisation and methodological support, while at Jalal-Abad State University named after B. Osmonov, the emphasis was on functionality and analytical accuracy. The data obtained confirm the didactic significance of digital solutions for adapting course content to the specifics of training, increasing learning motivation, and developing functional mathematical literacy. The results can be used to update educational standards, develop digital training modules, and improve the quality of training for mathematics teachers in the context of digitalisation