Reliability and Quality of Complex Systems - K.V. Bukhenskiy; T.L. Lvova; V.V. Mironov (Надежность и качество сложных систем)
Background. The purpose of the article is to familiarize the Russian scientific and pedagogical community with the new scientometric method of qualitative analysis of knowledge among students and schoolchildren according to the Unified State Exam, to demonstrate its characteristic properties and application experience. Materials and methods. The idea is based on the authors' early articles on the creation of new scientometric indexes and at the same time contains significantly new elements. Real-time data collection, statistical analysis and averaging of data, clustering of data based on fuzzy logic, field testing of methods, analysis of results and conclusions take place. The averaging of subjective data makes it possible to give conclusions a stable, objective character. Results. New scientometric characteristics of a scientific event are being introduced: 1) a local index of knowledge of student groups according to the Unified State Exam and a measure of confidence in this parameter; 2) based on local indexes, an index of knowledge among students at the university as a whole is introduced. An indistinct ranking of the level of knowledge was carried out, both for groups and for the university as a whole. Based on the data on the knowledge index, the most knowledgeable students are determined, the core, tail and basement of knowledge in the university are created, and based on them, the scientometric M-index of university knowledge is calculated – a qualitative analogue of the author's generalization of the "statistical" Hirsch h-index. According to the M data, within the framework of fuzzy set theory, the university is ranked in qualitative categories.: "high knowledge", "good knowledge", "satisfactory knowledge", "weak knowledge". Conclusions. An algorithm has been created and based on it, the ZNANIE – SILA software package, which receives data on the Unified State Exam from students in real time, processes this data in real time and outputs numerical values of knowledge indices for individual groups of participants and for the university as a whole. A new method of objective analysis of mathematical knowledge of groups of students has been created. The method has been tested, aroused interest and approval in the scientific and pedagogical community, and received proposals for its announcement and dissemination.