The mental abilities and the intellectual faculties nature study is being conducted rather many years long ago, but this challenge, as before, is being left to be opened. The thinkers have been searching the answer this challenge at all the times (e.g. Platon, Confucius, J. Lokk, C.A. Gelvecius, Kant and the others). On the whole, they have based upon their own everyday observations, the speculative reasoning, the ordinary experience generalizations in their searches and the investigations. The detailed scientific research and the research study task of such subtle matter, as the human mind and the intellect, practically, it has not even been raised up, having considered, in principle, the quite unsolvable challenge, throughout many millenniums. Today, the mental and the intellectual abilities theme has once again been become the actual one, that is being conditioned by the economical - socially conditions, and the society state.

Nevertheless, the mental and the intellectual abilities development unified theory is not quite being existed, in spite of the psychologists´ rather considerable contribution (e.g. F. Galton, A. Bine, T. Simon, J. Piage, R. Sternberg, G. Aizenk, E.M. Sechenov, L.S. Vygotsky, S.L. Rubinstein, A.N. Leontjev, B.G. Ananjev, Ya.A. Ponomarev, P.Ya. Galperin, N.F. Talyzina, O.K. Tikhomirov, N.S. Leytes, V.N. Druzhinin, M.A. Kholodnaya, N.E. Chuprikova and the rest) in this challenge the experimental and the theoretical development. Generally, the testology has been engaged in the mental and the intellectual abilities study abroad. So, the «intellect» and «mental and intellectual abilities» terms have been considered the quite identical ones with each other, in the framework of this direction. Let us observe and follow the presentations formation logics on the intellect, as they, simultaneously, are being reflected, as well the mental and the intellectual abilities nature.

For the first time, F. Galton has begun to speak on the individual differences existence in the mental and the intellectual abilities. He, moreover, has supposed that the intellectual powers and the possibilities are naturally being conditioned by the human biological nature peculiarities and the special features, and they are, correspondingly, being situated in series, as his physical, well as his physiological characteristics. So, the sensory distinctive sensibility has been considered by him, as the common ones index - the intellectual abilities.

But A. Bine and T. Simon have the other intellectual abilities nature comprehension. So, they have recognized environmental influence upon the cognitive further development peculiarities and the special features, in the contrast to F. Galton, who has considered the intellect, as the inherent psychophysiological functions constellation. A. Bine gives the following definition: the intellect - this is the notion that is to say, which is named by the common sense, by the practical understanding, by the ability to be adopted oneself to the current circumstances. So, the intellect has been defined not so much, as the human ability to the cognition, rather than the mental and the psychical development achieved level, having revealed in the defined and the specified cognitive functions formation indices, and also in the knowledge mastering and the skills acquisition power indices in the context of the given approach. It is quite possible to be considered the first step to the intellect practical research the test challenges set creation by A. Bine and T. Simon for the mental and the intellectual development level assessment. Later, L. Termen qualified the Bine - Simon test, having used the intellect coefficient notion, which had been introduced much earlier by V. Shtern. This has been resulted in the following results: at the general consensus absence on the fact, what the intellect is, the psychologists have actively been studying its quantitative side; the relative constancy has been revealed, and also the direct dependence between the intellect coefficient indices and the school successes indices between the most prestige occupations and the mastering by them has been fixed it up; besides, it has been made the conclusion on its inherent conditionality during the investigations. Later on, the two conceptions have been appeared in the intellect nature study in the framework of the testological approach: the monofactor one and the multifactor one. The monofactor conception supporters (such as, Ch. Spirman, R. Cettel, A.R. Jensen, S. Bart, F. Vernon, L. Hamfrays, J. Raven and the rest) have been connected the intellect nature, as the ability with the one factor, which, in the different degree, has been presented at all the intellectual activity levels. The multifactor conception representatives (such as, L. Terstone, J. Hilford, H. Gardner, D. Feldman) have been considering the intellect nature, as the intellectual factors (e.g. abilities) multitude. So, the enumerated researches theoretical result has been the «general intelligence» or the «general mental and the intellectual ability» existence acknowledgement, that is some total foundation, with more or less specific weight, having presented in the intellectual activity different and the various types. So, the mental and the intellectual abilities are not only various and diverse, but and they are being in the defined and the specified correlation, that is the intellectual activity highest and the lowest levels have already been singled out. It, moreover, should be noted also the controlled influences presence idea in the intellectual components system, having had the different and the diverse generality level, that is the heredity and the environmental role is quite different in the mental and the intellectual abilities development.

Thus, the theories by J. Piage and A. Vallon are being occupied the special position in the foreign psychology. The cognitive structures operational characteristics of all the levels, including the conceptual one, have exhaustively been analyzed in them. So, J. Piage considers, that the developed intellect is being revealed in the universal adaptiveness, in the individual´s «equilibrium» achievement with the environment. And, consequently, the human behavior is the more «intellectually», the more complex and the more varied trajectories have been become, by which the subject influences on the objects are being passed, and, moreover, they are being carried on to the more progressive compositions. From the internal side the intellect, by J. Piage, these are the systems, having coordinated between each other of the reversible operations, which are being formed the ensemble: «The psychological reality is being consisted from the total operational systems, but not from the isolated operations, having comprehended, as the previous elements by these systems». So, the mental and the intellectual abilities nature is being borne the adaptive, and the active character in the framework of this approach.

At present, the cognitive approach in the mental and the intellectual abilities study is being developed in the foreign psychology. First of all, it has been based on the intellect comprehension, as the cognitive structure, the specific character of which is being defined by the individual´s experience. This direction´s representatives (such, as R. Gleiser, J. Carrol, N. Frost, A. Hunt, R. Sternberg, G.S. Halford, R.M. Clark) research the cognitive processes, the strategy and the approaches peculiarities and the special features, which are being provided the successful tasks solution to the individual. So, R. Sternberg, for the first time, has undertaken his attempt to give the definition to the «intellect» notion at the level of the ordinary behavior and the everyday conduct description. He has chosen the experts´ opinions and the specialists´ judgments factor analysis, as the definite and the specified method. So, the intellect, in his point of view, would be much better to be measured in those spheres and the areas, where the tasks for the individual are being the relatively new ones, and the cognitive skills and the habits are being at the automatization stage. According to the given model, the intellect - is the purposeful activity, having pursued the total three global targets achievement: the environmental adaptation, the environmental formation, and the environmental choice. So, the each one from them has the special, the peculiar and the specific realization in the people´s life. The diverse and the different contextual environments are quite able to be resulted in the further different mental and the various intellectual abilities development.

On the whole, the mental and the intellectual abilities nature has been turned into the ordinary and the everyday explanation, into the ecological bases and the cultural grounds. J. Carrol has already received the 24 intellect factors: the image data mental handling, the verbal fluency, the syllogistic mental decisions and the conclusions, the perceptibility to the contradiction and etc., having applied the factor analysis for his test data processing, but, at the same time, having based upon the cognitive psychology ideas (e.g. the decisive significance - is the information processing). So, the special direction is being developed, having connected with the central nervous system structures study, with the electrophysiological brain activity indices, having lain on the basis of the intellectual abilities (such, as G. Aizenk, R. Chalk, J. Artle), side by side with the above - considered directions in the foreign psychology.

Thus, it has been given much consideration to the mental and the intellectual abilities challenge abroad from the antiquity times and up to our days. The science and the practice growing interest is being observed to the quite different and the various work types with the personality´s mental and the intellectual abilities. So, this kind of work has been acquired, especially, the wide - ranging swing in the USA. The US economic and the social development contemporary level is being demanded the highest occupational level from the experts and the specialists of the every activity sphere and the area. In this connection, it has been directed the country´s attention to the gifted pupils´ needs, who are the every society development potential, according to the American scientists´ and the scholars´ convictions.

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The work was submitted to the international scientific conference «Fundamental research», (Israel, Tel Aviv), 10-17 April, 2010. Came to the editorial office on 23.03.2010.