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EN
Active approach to the cognitive process provides the conditions of cognitive development, cognitive development of the abilities. The articleis dedicatedto theproblemof development of mathematical abilities of students of technical profile in the modern university. It is noted that detailed understanding of the mechanism of cognitive and metacognitive development of students’ abilities in the context of increasing mathematical and professional culture is on a par with the strategic components of modernization of the mathematical education in the three-stage system of higher education.The article explores the mechanisms of constructing cognitive and metacognitive space in accordance with modern views of modeling of the functional properties of neural networks.The obtained information will help to answer the question about the mechanisms of information storage and access in the processes of thinking. The approach to the analysis of complex mechanisms of thinking process, when a neural network is represented by a two-component structure, is grounded. Static image in the form of semantic relations of static images is stored in a static neural structure. Spatio-temporal images in the form of semantic networks of dynamic situations are stored in dynamic neural structure. The mechanism of the formation of static and dynamic semantic networks, in which images and situations in the process of thinking arise chaotically, is studied. The author believes that neural network with chaotic neurons triggers the appearance of chaotic images in the process of thinking. In this model, chaotic and not chaotic neurons have different parameters of interaction and “refractaire”. The role of chaotic neurons is reduced to the choice part of the semantic communications and to the merger with other semantic communication. The author concludes that such a process in dynamic semantic networks leads to unexpected spatio-temporal images. The process of the emergence of unexpected static images can be represented as the development of meta-skills; the emergence of the spatio-temporal situations can be linked to the mechanism of metacognition. The arguments point to the existence in thinking of the mechanism of metacognition, when the unexpected images, new algorithms for solving the problem, the strategy and the tactics of the behavior are formed. The emergence of thinking processes with elements of metacognition stimulates cognitive system of the individual to further development of skills and enhance mathematical and professional culture.
EN
The articleis dedicatedto the mechanisms of cognitive process from the viewpoint of neurodynamic concepts. The concept of neurodynamic processes is studying the modes of localization, synchronization, stabilization of metastable chaotic structures in the reticular formation neural network. Such dynamics characterizes the process of the formation of the models of the mental images in a neural network of the brain. The articleuses the assumption that the functional metastable structures in the phase space of the neural network are the model representations of mental images. Each metastable state corresponds to the certain mental image. It is noted that the relaxation process of the system triggers the process of reflection of the metastable structures of the model presentations of the mental images as the functional mod in the cognitive space. The metastable structure of the phase space of states is a model representation of the image. Cognitive space of the model representations of the images is defined as the phase space of the functional mod. The articleargues that functional regime forms the static manifold in the phase space as part of the cognitive space of the memory. The mechanism of the influence of the functional modes on the formation of the model representations is investigated. The articleidentifies the mechanism for creating of the model representations of the image of the chaotic nature of time variation of the parameters of the system. The author believes that the unpredictable mental images in the cognitive space should be interpreted as the elements of metacognition in the processes of students’ thinking. The detailed study of the mechanisms of formation and development of the cognitive space of the memory, as the subsets of the phase states, will give the new impulse in the understanding of approaches to the development of students’ thinking in the process of mathematical and professional training. The emergence of the elements of the metacognition in the processes of thinking stimulates cognitive system of the individual to further development, increasing mathematical and professional culture.
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