Regularities of the mental development of modern children and the age-related abilities of younger schoolchildren to assimilate theoretical knowledge
Describing the theory of developmental learning, Davydov wrote: "According to this theory, the content of developing primary education is theoretical knowledge (in the modern philosophical and logical understanding of them ), method - organization of joint educational activity of junior schoolchildren (and, first of all, organization of the decision of educational tasks for them), development product - main psychological neoplasms , inherent in younger school age (italics and the allocation of VV Davydov - VG).
The question arises: are junior schoolchildren ready to learn theoretical knowledge? After all, according to popular belief, a small child is very specific and he is not up to abstractions.
This doubt is connected with one extremely common in everyday life logical misunderstanding. People often identify the abstract with the theoretical, and the concrete with something directly perceived. In science (philosophy and logic), the relation between the abstract and the concrete is treated differently. Under the abstract is meant specially selected and considered separately properties of the object outside the connection with the conditions of its existence. And under the concrete - the properties of this object, reflecting the relationship with the conditions of its existence, ie. reflecting the essence of the position of this object among other objects. Therefore, an abstract characteristic may not reflect the essence of the object under study under specific conditions, i.e. the abstract is not identical with the theoretical. On the contrary, since in the theoretical characteristic the essence of the object is reflected, it is precisely this that can be an expression of the concreteity of the object, i.e. show its true difference from others.
Consider from this point of view several examples of thinking of young children. A girl of 5-6 years asks the mother: "Is that if the dog bites, then you need to make an injection?" Mom replies: "Yes, of course!" The girl continues to ask: "And if it bites twice, do you need two injections?" Mom absent-mindedly in response: "Yes, of course ..." And then the little one makes a conclusion: "If the dog bites a thousand times, you need to make a thousand punctures!"
Is it possible to consider that the child thinks specifically about the medical aspect of the problem? Of course not. The sphere of her thinking is turned into another. It abstracts from the phenomenon as such and considers the correspondence between the number of bites and sticks. In mathematical terms, the girl has made an inductive-type generalization on the basis of the notion of a unique correspondence between two discrete processes. Of course, this is not yet a theoretical generalization. As long as the child thinks abstractly , i.e. does not analyze and does not realize the framework of the conditions of these processes. But this is precisely the basis on which the child can develop theoretical thinking.
Another example. Kids jumping from the garage to the ground, imagining themselves at the airport. One kid jumped into the sand and shouted: "Soft landing!" The second jumped on the trampled earth: "Hard landing!" The third prepared to jump into the thickets of grass and shouted: "Tight landing!" And he froze with admiration. He no longer hopped. He needs to share with his friends his own discovery: "Guys, tight landing! Tight landing! In this case, the child identified in words a soft, taut, hard degree of elasticity of bodies. Of course, in a purely abstract way.
There are many abstractions in the world. Therefore, it is necessary to begin not with any abstraction, but with those that carry the essence of the objects under study and are simultaneously accessible to children. These are the so-called original content abstractions.
Consider from this point of view the concept of a real number - the central concept of mathematics, studied by children in school. By origin, it is, first of all, connected with the actions of measuring objects by their size. Let's consider, for example, how the number 3,52 could appear. Let's say the length of the bedroom was measured with a pole. It turned out that the pole was packed three times completely and a little more than its half. You can say a large room or a small room? No, because we argue abstractly. We do not have any information about the size of the pole, i.e. measures. But in our very action with the ratio of the size of the object to the magnitude of the measure is already very much meaningful. If we know that other rooms were measured with the same pole, then by numbers one can say exactly which room is longer in length and which is smaller. Let the length of the living room be 5.27. Obviously, the length of the living room is more than a bedroom. In this case, we proceeded from the abstract content of the ratio of quantities, but this was sufficient for certain conclusions. So, the ratio of one value to another is the initial meaningful abstraction for our understanding of the essence of actions with numbers.
Of course, we brought a somewhat exaggerated situation. The concept of number as a ratio of magnitude to another, a pre-determined value arose as a result of the diverse historical social productive activity of people. This experience as a way of people's thinking and actions is also fixed in various forms of the social life of people, for example, language, primarily in the figurative concept of words. In everyday life, he exists at the level of general ideas about abstractions which "rule the world". After all, there are no such concrete things that can be called the words more, less, equal. These words determine the result of comparing things (note any things) by their value, when other properties as if discarded from consideration, i.e. abstraction occurs from the rest of the properties of things other than the value. The concepts more or less than have their own logic, based on the laws of real relations between objects, but at the same time relatively independent of them. In this sense, abstractions rule the world & quot ;. So, if we know that one object is more than the second and the second is more than the third, then the first is always more than the third, regardless of whether we have the opportunity to compare these items directly or not. So to think is the natural ability of a person, which is extremely necessary for him.
We will not touch all the features of the ratio of quantities. Let's just note that for a child of 6-7 years old, when he has already begun to understand the relationship "more", "less", "equal", thinking with such abstractions is as natural as playing at preschool age. This is ensured by all previous development of the child's thinking and imagination. Children of this age are well aware that things can differ in size: some things are bigger than others, and so on. And they can even operate with relations of magnitudes in an imaginary plan. For example, they are quite capable of such a task: "Two identical towers were built from identical cubes. The first tower was put 3 more cubes, a cube for a cube. On the second tower put 2 of the same cube. Which tower is higher? Most children will correctly solve it: "The first tower has become higher". This means that the abstract ratio of the quantities expressed in words is greater, less than is not an empty sound for them.
Observations show a very peculiar way for children to solve this problem. Some children in the process of solving the problem draw two towers from the cubes: three cubes, a cube for a cube, and next two more cubes, a cube for a cube. However, they do not draw images of the original size of the towers. Apparently, they do not consider it necessary to draw them, since they are supposed to be equal in the mind. This is already the germ of theoretical thinking, from which developed forms of theoretical consciousness can grow in learning. This ability of children can be based on the educational process, the content of which is theoretical knowledge. At the same time, one must understand that the thinking capabilities of children are still limited.
Let the children who solved this problem successfully solve another, seemingly similar, but with substantially different conditions, for example: "There were two towers of cubes. The first tower was put only two cubes, a cube for a cube, and the second one is five, a cube for a cube. Can we say which tower is higher now? The majority will say: "The second became higher, because more cubes were placed on it." This decision is incorrect, since the initial ratio of the heights of the towers is unknown. Children solve the problem in the same way as the first, naively believing that both problems are the same. They take the external similarity of the conditions of tasks for the actual commonality of these tasks. In scientific language, this is called the "empirical generalization of experience" with respect to the external similarity of the features of objects. This is due to the fact that children do not know how to analyze the conditions of the problem. They do not realize (do not reflex) the mode of their action with imaginary relations of magnitudes. They can not plan their actions in such a way as to solve the problem in accordance with its essential characteristics. That is, they still do not have a general way of solving such problems. They have not yet developed theoretical thinking, the main components of which are analysis, reflection and planning.Empirical and theoretical is present in the minds of children in an undeveloped and undivided form. It is necessary to distinguish the actual theoretical component. To this end, in education, it is necessary to create a situation in which students can identify the initial abstraction (in our examples the ratio of magnitudes), fix it in a symbolic symbolic form, and analyze it as if in pure form. Then we must force them to reflect the way of this analysis and, in accordance with this method, plan their actions when solving all problems on the ratio of quantities. As a result, children should develop the foundations of theoretical thinking.
How is this possible in practice we will show in the next section, but for now we will try to evaluate the general pedagogical and social significance of this approach to assessing the age opportunities of younger schoolchildren. Many teachers often do not notice that a child can think theoretically. Thus they miss a favorable chance in its development. After all, a child can remain in captivity of his general, in fact, naive ideas, if he fails to rise to the level of a conscious attitude toward the reality of abstract relations. And it turns out to be defenseless, faced with the real practice of people designing houses, cars and ... financial pyramids. From this practice, and not from a simple account, there is a real understanding of the number as the ratio of the size of the object to the value of the pre-set measure. This relation is the initial abstraction from which all the variety of a number can appear. Working with such relationships develops the child's natural and necessary ability for people to understand the essence of things. As they say in theory, there is an ascent from the abstract to the concrete.
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