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.