Lecture
Counting and counting operations are one type of intellectual activity, in particular of thinking. "If the study of the problem of the cerebral organization of speech has a century-long history, then it can be said with full justification that the study of the problem of the cerebral organization of thinking has no history at all" (FOOTNOTE: A. R. Luria. Osnovy neiropsikhologii [Foundations of Neuropsychology]. Moscow: Moscow University Press, 1973. P. 307.).
In Russia, work on the question of the structure of intellectual activity (IA) and thinking has been carried out, and continues to be carried out, on the basis of the general concept of the structure of active mental activity formulated in the works of outstanding psychologists — L. S. Vygotsky, A. N. Leontiev, A. R. Luria, P. Ya. Galperin, and others. In these studies, thinking was regarded as a specific but complex mental activity, having its own structure and functions, which manifest themselves equally in both the visual-active and the verbal-logical forms of the thought act.
At present, in Russian psychology, the study of IA, of thinking, and of their pathology arising from brain lesions is carried out within the framework of the theory of activity developed by L. S. Vygotsky and A. N. Leontiev, within which thinking came to be regarded as a special kind of cognitive activity. Leontiev defines activity as a set of processes united by their common orientation toward the achievement of a particular result, which is at the same time the objective motivator of the activity, that is, that in which one or another need of the subject is concretized. Motive is one of the most important structural units of activity. In real life we are always dealing with a person's concrete activity, which is characterized by the object of the activity, the motive, and a structure consisting of actions and operations. An action has an intentional character (that is, it answers what needs to be done), while operations answer the question of — how to do it. We regard intellectual activity above all as an activity.
Our own research has given grounds for defining IA in a new way: in our view, it is not the sum of the separate mental processes that realize IA, but a complex totality of them, that is, it represents a different, qualitatively new formation that forms on the basis of HMF. Just as a word made up of separate morphemes — is not simply their sum, but a qualitatively different, new phenomenon of a higher order, so too IA — is a totality of HMF of a qualitatively different order, unfolding at the highest level, carrying out the highest syntheses.
It is precisely within the framework of this theory of activity that we studied the impairment of mental processes — writing, reading, and counting — and their restoration. IA has not only complex psychological content but also a no less complex structure, and as a process it consists of a chain of interconnected actions.
The psychological structure and the process of carrying out an intellectual act include, first of all, the motive that makes the task relevant and its solution necessary, and an understanding of the problem (the task). After the stage of formulating the task and understanding it, an orienting-investigative activity follows. This is an important stage of any intellectual act, since the subject solving an intellectual task, before beginning to carry it out, must first actively analyze the conditions of the task, compare these conditions with the sought-for element, and reformulate the task on the basis of the data obtained, which in turn leads to a deeper understanding of the problem being solved. The next stage is the choice of a path (strategy) for solving the task (the strategy stage), after which the appropriate means and operations adequate to the task being solved are selected (the tactics stage). Unlike the first stage, this stage is no longer so much creative as executive. The following stage is devoted to actually solving the task, or finding the answer. To this end, on the basis of the information obtained, the subject draws up a plan, which he implements by means of the operations corresponding to the solution algorithm found for the task. Throughout the entire process of solving any psychological task, the subject monitors his actions by comparing the results with the initial data.
Thus, a person's IA is an active process directed toward a particular goal; it takes into account the conditions under which the goal is given, proceeds by way of selecting adequate selective connections, and relies on a system of operations without which the attainment of the goal set is impossible. Being a self-regulating form of mental Activity, IA also presupposes the presence of a process of self-monitoring, thanks to which the correction of incorrect moves that may arise in the course of solving one or another intellectual task is carried out. It is the strict coordination in the operation of all these components of IA that ensures a person's goal-directed behavior in the situation of solving any tasks, and their correct solution.
It is known that IA is made up of a unified system of separate actions and operations, or a chain of actions (following A. N. Leontiev), which stand in complex relationships with one another; these operations involve singling out adequate connections and discarding inadequate, extraneous ones. A person solving an intellectual task must constantly evaluate each operation not in isolation, but within the system of given logical relationships, monitor each step of the solution, and correct errors. This is precisely what constitutes the process of the continual regulation of IA in solving any task — in our case, in carrying out written tasks, in reading texts, in solving arithmetic tasks, and in understanding number and its composition.
The structure of IA described above manifests itself in all its forms — both in the solving of visual-active tasks (for example, constructional ones) and in theoretical actions unfolding in the verbal plane, in counting and counting operations. This extremely abbreviated form of already-formed and automatized IA, which is characteristic of a healthy person, is difficult to subject to analysis from the standpoint of studying the structure of the intellectual process. The objective study of the structure of intellectual processes, and the identification of the factors that make it possible to carry out complex mental activity, constitutes a task in which the genetic method plays an essential role. It is now known that all forms of IA, at the early stages of their development, pass in their genesis through a series of stages that progressively refine the mental action. Mental activity is formed from an extended, materialized (or material) form of action to an abbreviated action, carried out first by means of overt speech and then "in the mind". At the level of a developed intellectual action in the adult subject, such "compressed", rapidly proceeding operations form the basis of thought processes (Galperin, 1959).
A significant role in studying the structure of HMF and of intellectual activity, their psychological content, and their interaction is played by a relatively new method of research — the neuropsychological method (see Introduction). The principal subject of study of this method is focal lesions of the brain. Using it, one can investigate various disturbances of thought processes caused by the dropping-out of various components of mental activity, directly brought about by a focal lesion of the brain. It is precisely for this reason that neuropsychology is highly effective in studying the structure of higher mental processes, in particular of IA, as well as in studying the ways, possibilities, and methods of restoring impaired HMF.
As the clinical picture of brain lesions shows, the normal intellectual process can be disrupted by various focal lesions of the brain, with the type of disturbance depending on the topography of the lesion. Using the neuropsychological method, it has been possible to identify the factors underlying the disturbance of IA, and to establish that different focal brain lesions lead to disturbances of IA that differ in their mechanisms and structure.
Counting and counting operations, representing one of the greatest difficulties in teaching children at school, meet all the characteristics of IA, being one of its forms, one that is highly complex both in its genesis, its structure, and its course. In brain lesions in adults and children, and in symptoms of its underdevelopment or delays in maturation, this form of IA is disrupted (or fails to form) most often and most severely.
Considering the history of the development of number and counting, as well as data on its formation in ontogenesis, it is not difficult to understand that such a complex mental process has a no less complex psychophysiological structure and brain mechanisms that ensure its realization. Studies have shown that the joint activity of these analyzer systems constitutes a functional system that forms the basis for the formation and realization of the function of counting. In the formation of the concept of number, afferentation comes from various analyzer systems — the optical analyzer, the spatial, the somato-spatial, the speech-motor, and others. The brain foundations of counting are, correspondingly, the joint work of the occipital, parietal, and frontal systems of the brain. As for the psychological content of counting, it can be said that number, the concept of number, is formed at the junction of several mental processes, their interaction and mutual influence: visuospatial and somato-spatial perception, on the basis of which the representation and sensations of the body schema are formed; the sensation and understanding of "left" and "right"; speech, in its organizing, regulating, and nominative functions; and thinking — in its visual-figurative and verbal-logical forms. Each mental process contributes its own specific element to this form of IA.
Counting, as a mental process, consists of a series of interconnected links forming a hierarchical system. The psychological complexity of this form of activity is due primarily to the fact that in the process of counting a person operates with abstract concepts, reflecting the relationships between things in objective reality.
Thus, our brief analysis of the history of the development of number has shown that the modern conception and notion of number and counting operations went through a long path of development, and the basis of its formation was human object-related activity, the development of societal and social relationships, and development from concrete object content to an abstract model of number. At the same time, despite the differing views of various researchers on the concept of number and counting, most of them single out the positional and cardinal principles governing the interaction of number, as well as its spatial perception.
The complexity of the concept of number is directly reflected in its formation in children during arithmetic instruction, and has to some extent given rise to debate regarding teaching methods. The search for optimal methods, and for their adequacy to the psychological essence of number and counting operations, has led many researchers to the conclusion that arithmetic must be taught by the method of operating with numbers.
Next, we will examine the neuropsychological method of analyzing counting and its disturbances. Neuropsychology makes it possible to study the internal structure of any mental process and of various forms of IA, including counting, counting operations, the psychological content of the concept of number, and so on, thanks to which it is possible to find the mechanisms of disturbance or of difficulties in the formation of counting, and consequently to develop the most optimal methods for restoring counting or for its formation in children.
Here it is important to understand that the psychophysiological basis of any HMF, including counting, is a functional system that is localized in the cerebral cortex according to a dynamic and systemic principle, so that the brain basis of any HMF is not a single area of the brain, as was thought earlier (the school of psychomorphologism, or narrow localizationism), but the interaction of a number of brain zones in which one or another HMF is localized as a system. These conceptions, together with a number of others, form the basis of the scientific approach to restoration, to its restorative and formative types of teaching of counting. They make it possible to find the mechanism, nature, and structure of a defect in counting in adults and of its non-formation in children, and to arrive at a differentiated diagnosis.
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