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Active approach to the cognitive process provides conditions cognitive development, cognitive development of the student personality’s abilities. In the article the cognitive abilities, their procedural characteristics, parameters and factors interaction are explored. The information obtained will help to answer the questions about the structural components, the mechanisms and the directions of the formation and the development of the cognitive abilities of the students. In the article from the psychological-pedagogic positions the problem of defining the structural components of the mechanisms of the students’ abilities development in the system of continuous higher education is discussed, content, structure, energy potential of the factors that are able to improve the ability of the personality of the student are examined. In the article the main classes of cognitive abilities – intelligence, creativity and learning are discussed. The classes of cognitive skills: motivation, adaptation, activation and the goal of learning activities are defined. Content, structure, energy potential of the factors of the cognitive abilities forming are studied. Motivation is seen as the strategy and the tactics of the process of the achieving educational goals. Adaptation as the integrating optimization process forms the direction and the speed of the optimal occurrence in educational space of higher education institutions including the mechanisms of transition of the system “personality and educational environment” to the steady state. Activation is studied as the dynamic indicator which characterizes the possibility of the energy potential of the cognitive process. The highest possible power and the duration are the natural dominants of the personality. The purposefulness as the ability to build action sequences from the motive to the goal, is stimulated by the mechanisms of self-organization in the cognitive process. Understanding of the influence factors, principles and mechanisms of each component defines the direction and the level of the possible development of the cognitive abilities of the students. Acquired qualitative leap in the cognitive abilities of the students provides favorable conditions for the formation of mathematical and professional culture of the future specialists in a complex modern society. The development of the cognitive abilities of the students is one of the strategic components of the modernization of the mathematics preparation in the system of the multilevel higher education.
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