The article is devoted to the consideration of the methodological foundations of the organization and implementation of intensive training in higher educational institutions using the technology of modular training of structured and systematized educational elements. Description of the substantive structure of the subject in the form of systematized educational elements, as well as improvement of the modularly formulated teaching methodology on the topic of approximate calculation of the roots of a nonlinear equation by Newton's method, based on an object-oriented approach to goals. The components of the module are logically structured educational elements, interconnected in content and functionality, and their interconnected blocks are proposed to be presented in the form of a systemically structured logical graph diagram.