Abstract
<jats:p>The research aims to substantiate the necessity of developing and implementing new educational tools that enhance the fundamental nature of mathematical training in technical universities. In the context of modern technical education, the “fundamental nature” implies a learning process oriented toward preparing independently thinking individuals capable of self-determination regarding scientific and sociocultural development, possessing a capacity for self-improvement, systemic professional knowledge, and research experience. The theory of learning activities provides a framework for organically integrating the fundamentalization and professionalization of education. The article describes specific methods for organizing learning activities when working with mathematical propositions, following P. Ya. Galperin’s theory of stage-by-stage formation of mental actions as modified for mathematics instruction. The study substantiates the possibility of strengthening students’ fundamental mathematical preparation through a system of tasks designed to foster mental actions aligned with the knowledge required by a modern mathematics course. The scientific novelty of the study lies in the fact that, for the first time, a task system for organizing the learning activities of technical university students has been developed on this specific theoretical basis, with a focus on enhancing the fundamental nature of mathematical training. As a result, the authors propose a methodology for constructing tasks according to levels of assimilation, based on the following scheme: problem – inverse problem – extremal problem – modeling problem with various constraints.</jats:p>