New methods for mathematical simulation of the dynamics of competence formation in the education process

Abstract

Abstract.  Purpose. Existing educational technologies are aimed at developing the verbal component of thinking on the basis of  artificial logical schemes. In doing so, there is little, if any, purposeful development of intuitive image thinking, which i s based on  natural logic. This is due, first of all, to the lack of adequate mathematical models of the adaptive unconscious, which would reveal  the  genesis  of  implicit  inherent  knowledge.  The  aim  of  this  work  is  (1)  the  construction  of  a  mathematical  model  of  implicit  formation of “thin sections” (limiting sense) in discrimination problems (diagno sis, forecasting, management), (2) the formulation of  a new ecologic paradigm of education, and (3) the development of a methodology for cognitive simulator construction. Methodology.  The authors propose that the work of intuitive image component of an individual, including decision making, be simulated on the  basis of natural logic in the framework of a limiting generalization paradigm. Natural logic leads to the origination of rati onality as an  adaptive tool, which is not identical to the rules of formal  or fuzzy logic or to the rules of probability calculus.  Findings.  In any Zproblem of discrimination of the basis of a test bank (qualia bank), a cognitive categorization operator is defined, and, usi ng it, an  epistemological series is implicitly formed. Advancement along the series means a growth of Z-competence. The limit of the series is  a “thin section” containing invariants (“internal codes”), with the help of which images of the world are coded. A failure to  reach the limit results in cognitive deficiency. Originality. The limiting generalization paradigm made it possible to develop the system basics  of educational technologies that allow one to overcome cognitive deficiency and thus to educate expert-level specialists.  Practical value. The proposed model is a methodological basis for the development of ecologic educational techniques, which would develop, first of all, the intuitive image component of thinking. The model also suggests ways to develop broad -spectrum cognitive simulators.