Modeling the learning process of Mathematical Analysis in a technical university: approaches and prospects for optimization

Abstract

The article is devoted to modeling the learning process of the discipline "Mathematical analysis" in a technical university. The relevance of the topic is due to the need to improve the effectiveness of teaching fundamental mathematical disciplines in the context of digitalization of education. The purpose of the research is to develop and test a comprehensive mathematical analysis teaching model that takes into account the specifics of engineering education and modern educational trends. The tasks include a conceptual analysis of the literature, systematization of modeling approaches, development of the author's model, and its empirical verification. The methodology is based on system-activity, competence-based and technological approaches. The empirical base is represented by a sample of 120 students of 1-2 courses of technical training. The results showed a statistically significant increase in academic performance (t=3.84; p<0.01), motivation (r=0.62; p<0.05), and engagement (χ2=11.41; p<0.01) in the experimental groups. The proposed model demonstrates theoretical validity and practical effectiveness, opening up prospects for optimizing mathematical training of engineers. The directions of further research on the expansion of methodological tools and the adaptation of the model to the specifics of individual universities are outlined.