Lecture
Это окончание невероятной информации про лобная акалькулия .
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who gives the task (operation) to the child sequentially, explaining it. It is good to give all this work a playful character, and it is better to work not individually with each child but with a group (2—3 children). It is useful to employ such methods as the method of competition, the method of one child helping another, the method of cross-checking (in which each participant checks his own work and the work of other members of the group). The method of the place-value grid is used to restore the understanding of the role of zero in a number and the understanding of its quantitative essence — zero denotes the absence of something (of some particular place). Prolonged work with the place-value grid, placing zero in different places with the same digit and with different digits, contributes to restoring the understanding of its place and role in a number. For younger children (older preschoolers and younger schoolchildren), it is good first to use another method — the method of translating a concrete quantity of objects into an abstract number by playing with objects and the numbers denoting them. For this, 2 matchboxes are given (later 3, etc.); in the first of them there are always 10 matches (or buttons, etc.), while in the other the number of matches varies — now one, now five, etc. On the first box a digit 1 is pasted, while on the other cards with different digits are placed each time. First the child must open the box, look at its contents, count the matches, feel them, and close the box. After this action the child already knows — what is in this box and how many (10 matches), and that we denote this quantity by the number 1. This means that here 1 = 10. To this box we add a second box, on which is written now 5, now 3, etc. units, and the child must name the numbers that result from adding the boxes together. At first the work proceeds jointly with the instructor, then jointly-and-reflectively, and finally reflectively and independently. After prolonged work using this method, one can move on to working with the place-value table, i.e., from the material form of work to one materialized in the form of diagrams. These methods form in the child the concept of number — its composition and place-value character, and the understanding of the dependence of a number on its place in the place-value grid (table).
Above we wrote that in lesions of the frontal lobes of the brain, computational operations are also impaired. This concerns the operations of subtraction and addition, multiplication and division, especially those of them in which a carrying-over through a ten is required to find the sum or difference of numbers, as well as other arithmetical operations that contain intermediate links (operations), which require being remembered and their place and role in the series (program) of operations to be taken into account, the performance of which is necessary for the final solution of the given arithmetical operations. These distinctions emerge most clearly in the study of counting under maximally dynamic conditions, when the minuend is constantly changing, i.e., when the final result of the preceding operation (subtraction or addition) each time becomes the minuend (100 - 7 = 93 - 7 = 86 - 7 = 79, etc.).
In this case, in order to restore computational operations, methods are needed that would facilitate the replacement of the impaired links in the structure of counting, as well as the restoration of the understanding of the significance and role of intermediate operations within the integral arithmetical action, and the retention of the intermediate result in working memory.
With patients with prefrontal syndrome it is necessary to work on restoring the process of understanding and making sense of the actions they perform. For this purpose, one must first disinhibit and restore the sphere of meanings and significations, both verbal and nonverbal, in order, on this basis and through it, to approach the restoration of the patients' understanding of numbers and operations with them. In patients with other variants of frontal syndromes, this kind of work contributes to the ordering and restoration of the dynamics of intellectual processes — in some cases it inhibits the patients' impulsive actions, while in others, on the contrary, it activates them, facilitating the processes of switching from one action (or element) to another, while overcoming perseverations in doing so. A number of well-known and well-established methods can be used.
I group of methods. The method of classification (its various forms) — directed and free classification on verbal and nonverbal (pictorial) material; the method of finding analogies — "the odd one out".
II group of methods. These methods relate to the restoration of the process of planning activity: the method of retelling picture stories and texts, the method of composing a plan for a retelling, the method of planning compositions (oral and written), the method of series of picture stories (arranging, telling, composing a plan), the method of composing a story according to a given plan and one's own plan, etc.
These and a number of other methods, described by us in detail in other works (FOOTNOTE: Tsvetkova L.S. Neuropsychological Rehabilitation of Patients. Moscow: Moscow University Press, 1986; Tsvetkova L.S. The Brain and the Intellect. Moscow: Prosveshchenie, 1995.), precede the beginning of the restoration of counting, and are then used in parallel with the work on restoring counting.
A smooth transition from this group of methods is the method of solving arithmetic word problems. In this method, first, the condition of the problem (its content) serves as a meaningful background for working with numbers. Second, the numbers in the problem are made concrete (object-related). This is good for restoring the understanding of concrete numbers and can serve as a transition toward restoring the ability to operate with symbols, with abstract numbers. This method should be used with a gradual increase in its complexity, since it makes it possible to restore the concept of number and the ability to operate with abstract numbers through the connection of number with meaningful context and with concrete objects (phenomena, objects). This method, like the preceding ones, is not recommended for prolonged use. It is possible and necessary to return to it in difficult cases, but working on number with its help for a long time is not beneficial, since the knowledge and understanding of concrete connections of number, of object-bound numbers, may become entrenched, which will hinder (or make impossible) the transition to restoring the concept of number and operations with it.
Work using the method of solving arithmetic word problems begins with one-step problems, later — two-step, then — three-step problems. For example, "A housewife bought 3 kg of apples and 7 kg of pears. How many kg of fruit did the housewife buy in all?", or "The USA launched one satellite and Russia two. How many satellites in all are flying in space?", etc. The concept "three kilograms" is more firmly established in the experience of patients with frontal syndrome than the number 3. The words "three kilograms" actualize certain everyday concepts of number. Therefore, no problems arise in solving such word problems and in operations with numbers.
From solving arithmetic word problems, one must gradually move on to solving arithmetic examples. For example, the word problem "3 kg of apples + 7 kg of pears = 10 kg of fruit" should be translated into the arithmetic example, dropping the words connected with the numbers: 3 + 7 = 10. After solving similar word problems and examples, one can move on to more complex problems. For example, "3 birds were sitting on a tree branch, 4 more birds flew in, and then 2 birds flew away. How many birds are left?" Recording of the condition: there were 3 b., 4 b. flew in, 2 b. flew away. Solution: 1) 3 b. + 4 b. = 7 b.; 2) 7 b. - 2 b. = 5 b. Arithmetic example: 3 + 4-2 = ?; 1)3 + 4 = 7; 2) 7-2 = 5.
The psychological essence of this method consists in the fact that in an arithmetic word problem, numbers are situated within a meaningful context, represent a quantitative characteristic of objects (objects, phenomena), and stand in an inseparable connection with the object. This kind of everyday experience is well established and unfolds at the involuntary level. The method of translating an arithmetic word problem into arithmetic operations (examples) constitutes a series of programs consisting of sequential operations. Work on the programs is at first performed by the patient in cooperation with the instructor, and later — independently.
Program No. 1
Instruction: You will solve the problem, but first read the program gradually, step by step, and carry out each task.
1. Read the problem.
2. Repeat it.
3. Say how many (apples) ... there were in the problem.
4. Say, and how many (pears) ... there were.
5. Say what must be found out.
6. Write down the condition of the problem — write out only the numbers (a model is given).
7. Solve the problem.
8. Explain why you solved it this way.
9. Check the correctness of the solution. Patient:
1. Repeats the problem.
71 2. Records the conditions in the notebook.
3. Finds the necessary number-cards.
4. Finds the necessary word-cards denoting numbers.
5. Draws up an oral plan of the solution.
6. Writes down the solution.
7. Repeats the solution with the cards (at first both the number-cards and the word-cards are used, and then they are gradually dropped).
Program No. 2
Instruction: Now you will solve the problem, but without naming the numbers. The problem is the same. To do this, perform the following operations.
1 . Repeat the problem.
2. Write out all the numbers from the condition of the problem. (Model: 3, 4, 2).
3. Solve the problem. To do this, perform all the necessary operations with the numbers:
a) say what must be found out?
b) perform the necessary operations with the numbers.
4. Check whether you solved the problem correctly?
5. Now once again put in the necessary arithmetic signs in the operations with the numbers. 3 and 2 = 5
6. Write down the entire solution of the problem:
a) write out the condition of the problem,
b) write its solution.
Model. Condition: 823 = 7
Solution: 1) 8+2=10 2) 10-3 = 7
By means of the gradual and sequential performance of this program for solving arithmetic examples, the understanding of number and of operations with numbers, rather than with objects, is restored.
To carry out these programs, methodological material is needed: a) digits and numbers written on separate cards, b) various naming words written on cards (kilogram, item, liter, apples, fruit, etc.). Program No. 1 is first carried out entirely by the instructor, then by the patient in cooperation with the instructor, then by the patient independently.
The psychological essence of this method and the programs consists in:
In this section we have formulated the tasks of restorative learning of counting in patients with frontal syndrome, its general direction being, on the one hand, toward the organization and restoration of behavior, personality, and motives of activity, and, on the other hand, toward the restoration of thought processes, of the understanding and making sense of operations with numbers, and toward the formation of a connection between thought and action. A number of specific methods have been described, the number of which can be increased, but all of them must be adequate to the mechanism of the impairment of counting in lesions of the frontal systems, and the entire activity of the patients in solving one task or another must be organized with the help of the method of programming activity with numbers.
In our view, frontal acalculia occupies an intermediate position between nonspecific and specific disorders of counting, since, as we saw above, lesions of the prefrontal convexital regions of the cortex of the left and right hemispheres also lead to primary acalculia, the main distinguishing feature of which is a primary (though through different mechanisms) impairment of the concept of number, its composition, and its place-value structure.
Часть 1 2.3. Frontal Acalculia: Diagnosis and Treatment
Часть 2 See also - 2.3. Frontal Acalculia: Diagnosis and Treatment
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