Development of mathematical models of the project-vector space of educational environments

Abstract

Based on the analysis of scientific developments in the application of project management methodology for educational environment management, the application of the vector paradigm to the construction of project management methodology in academic environments is substantiated. The methodological concept of project management in the educational environment is proposed, and the conceptual basis of the methodology of project-vector management of educational environments is created. The theoretical foundations of project-vector management of educational environments are developed. A mathematical model for managing projects in educational environments has been developed, the originality of which is ensured by representing the entities of projects, products, tools and subjects of educational environments as the objects of project-vector space, moving from the starting point (project origination) to its completion. The notion of the potential movement of objects in the project-vector space (PVS) is introduced and used in the mathematical model. The definition of unforced resistance of PVS is given, the source of which is the regularity in the influence of a significant number of objects and subjects of the project-vector space on each other, which is present in most projects of educational environments and hinders their implementation. The proposed methodology creates a modern scientific and methodological basis for the construction of project management systems in educational organizations. The practical implementation of the results of the research creates a basis for improving the efficiency and quality of educational organizations due to a well-defined organization of management procedures.