Outline of the lesson (mathematics) on the topic: Properties of objects. Various item properties

Let us ask ourselves the question: is a thing different from another thing, or is it the same? If a given thing for us is in no way different from any other, then it is impossible to speak of our knowledge of this thing. If we know what a given thing is, then, consequently, it is something for us, and if something, then something definite, and if something is definite, then, then, a certain set of certain properties. A vase is something made of glass. She is a flower fixture. And, as such, it has a certain color, shape, and also the texture of the material from which it is made. The totality of all these properties of a vase in their integrity is its quality. It is clear that if we do not perceive this thing as something integral, then we are not able to distinguish a vase, for example, from a rose, and a table from a chair. But we fully understand what a vase is, what its structure and purpose are. Therefore, if we really know something as a vase, then we, therefore, also have knowledge of its quality, that is, its certainty, its isolation from the surrounding background. The quality of a thing is an indication of the totality of its properties, its composition and construction, as well as its functional purpose both in interaction with other things and with the cognizing subject. In other words, the quality of a thing is something essential for its knowledge, for its practical application and production. It is that which makes it possible to distinguish one thing from another, and, consequently, to identify, contrast, compare, unite and separate, and generally construct things not only in being, in practice, but also in consciousness. By operating with the category of quality, we produce, as it were, an imposition of one object on another, which acts as a means of identifying an object with itself and makes it possible to know that this object is precisely this, and not something else. And here a previously unknown object appears as a known one: for example, in a flying object we recognize a bird, and not a bird in general, but a dove, and not just a dove, but a pigeon of this particular breed.

The quality of an object is thus revealed in the totality of its properties, which are somehow structurally ordered: it is, as it were, a "bundle" of properties. From epistemological

from the point of view, a property is a primary and further indecomposable formation, correlated with an equally elementary cognitive phenomenon - a sensation, and in complex cases - with a concept, if it is inaccessible to the sensing ability of the subject. Properties can be both perceptible by the senses or physically accessible to instrument indication, and non-sensory, related to the sphere of socio-spiritual reality, characterizing, for example, the positive or negative qualities of a person when we say: a sensitive conscience, a kind soul. Properties are learned through the interaction of objects with each other and with the subject. Property, so there is a way of showing a certain side of an object in relation to other objects with which it interacts. It is precisely that by means of which something manifests its specific being for another. Among the totality of properties, both essential (necessary) 1 and non-essential (random) for a given subject, as well as internal and external, general and specific, natural and artificial, are distinguished. In general, the totality, or system, of properties forms the qualitative certainty of an object, characterizing it from the side of its integrity and relative stability. Quality is a definite certainty, an expression of the stable unity of the elements and structure of an object. It gives a holistic description of the object in some of its relation and state.

Properties appear with varying degrees of intensity, which characterizes the state of the system. The state refers to the stable manifestation of a given property in its dynamics. We are talking about the physical, mental, moral state of a person and people, the state of the economy of a given state, as well as its political or military state. By its properties, the object is turned outward, and by its state, first of all, into itself. Properties, states, functions and relationships form the qualitative features of an object.

Now, on the basis of identifying what a property and state are, we can approach a more complete definition of the quality of an object. Quality represents a holistic description of the functional unity of the essential properties of the object, its internal and external certainty, relative stability.

The way the quality of a given object manifests itself when it acts on another object depends significantly on the quality.

1 The concept of quality is sometimes used in the sense of an essential property.

venous state of the latter. Thus, a spark that has fallen on a powder magazine is immeasurably more dangerous than the same spark that has fallen on damp earth; plant organs, having different properties, under the influence of the same environmental factor, say light, take different positions: the tops of the shoots bend towards the light, and the leaves are located perpendicular to the direction of the rays. But the method of manifestation of the quality of an object also depends on the conditions of interaction with another object. Take, for example, the interaction of water with the earth: at a certain temperature, it penetrates the earth in the form of rain, and when the temperature rises, water evaporates from the surface of the earth. Under the influence of conditions, the interacting objects themselves change their qualitative state. Properties not only appear, but can also be modified, and even formed in these relations.

Any property or quality of an object that interacts with other objects acts as a relative one: in relation to wood, steel is hard, and in relation to diamond it is soft. Any qualitative state of an object is relative. Under the influence of various conditions, one qualitative state may disappear, but it disappears only by transforming into another. An object, possessing a set of properties that make up its quality, depending on the context, shines, as it were, with different shades of it. For example, a person acts as his various qualitative facets for a doctor, lawyer, writer, sociologist, anatomist, psychologist. Just as matter is not reduced to the totality of its properties, so no object is dissolved in its properties, but it is their carrier, substratum. The higher the level of organization of matter an object is, the more qualities and properties it possesses.

The concept of quantity

Each collection of homogeneous objects is a certain set. If it is finite, then it can be counted. Suppose we have, for example, a herd of cows with 100 heads. In order to consider each cow as "one", it is necessary to abstract from all the qualitative features of each animal. The same number "100" is a quantitative characteristic of any set of 100 items, whether they are cows, books or diamonds. Qualitatively homogeneous things can be compared quantitatively, and qualitatively different in some respects, but similar in other respects: say, by weight, hardness, and also by dividing an object into parts. Therefore, this or that quantity is a set if it can be counted.

thief, and the magnitude, if it can be measured. Quantity expresses external, formal relationship of objects, their parts, properties, connections: number, size, volume, set, class, degree of manifestation of a particular property. The concepts of number, magnitude, figure, etc., are aspects or moments of the category of quantity.

In order to establish the quantitative certainty of an object, we compare its constituent elements - spatial dimensions, rate of change, degree of development - with a certain standard as a unit of calculation and measurement. The more complex the phenomenon, the more difficult it is to study it using quantitative methods. It is not easy to count and measure, for example, phenomena in the sphere of morality, politics, aesthetic perception of the world, etc. It is no coincidence that the process of knowing the real world, both historically and logically, takes place in such a way that knowledge of quality precedes knowledge of quantitative relations. . Knowledge of the quantitative side of the system is a step towards deepening the knowledge of the entire system. Before counting, a person must know what he is counting. Science is moving from general qualitative assessments and descriptions of phenomena to the establishment of precise quantitative patterns.

The basis of quantitative thinking is objective discreteness, dismemberment of things and processes. Quantity is expressed as a number that contains two main meanings: a measure of generality, one-order elements of discreteness when they are compared to each other and separateness (real or mental) of an object, its properties and relations into homogeneous elements, relatively independent of its quality. The number "5", expressing, for example, the number of 5 people, is not something mergedly inseparable, not just something one, but a specifically separate unity of qualitatively homogeneous five units. Any number is a relatively independent, integral collection of a certain set, or a separate unity of quantity. In this case, the number is not identical to the number; the same quantity as a quantity (for example, length when measuring length) can be expressed in different measurement scales (meters, centimeters), and therefore in different numbers. Number is a mental form of mastering the quantitative definiteness of an object.

Measure

Any quality is expressed in a system of quantitative characteristics specific to it. It is known that quantity and quality act as something separate only in abstraction, but in reality they are different characteristics of certain realities, there are

and gravitate towards each other, being in an indissoluble unity that forms their measure.

Augustine already argued that measure is the quantitative limit of a given quality; It is that which cannot be greater than or less than. The category of measure was one of the main ones for philosophers of antiquity, no matter what they talked about - about the cosmos, about things that exist, about man, about knowledge. Hesiod taught: observe the measure in everything and do your deeds on time. According to Democritus, if you go beyond the measure, then the most pleasant will become the most unpleasant. In the same spirit, Plato said: measure is the middle between excess and deficiency. Thales also believed that measure is the best. The idea of ​​measure has permeated the entire history of philosophy since antiquity.

The measure acts as a "third member", linking quality and quantity into a single whole. For example, labor productivity as a measure has two sides: the quality of labor and its productivity (the amount of product produced). If we compare labor productivity in the period of industrial development before the scientific and technological revolution and after, then the measure of the dependence of the quantitative characteristics of labor on the improvement of its quality will become clear. And on the other hand, it is known from physics that atoms of different chemical elements differ from each other only in that their nuclei contain a different number of protons. It is enough to change the number of protons in the nucleus, as one element will turn into another.

But it is not enough to say that measure is the unity of quality and quantity, and also that it is the boundary in which quality manifests itself in its certainty: Measure is deeply connected with essence, with law, regularity 1 . Let us pay attention to the fact that the meaning-forming root element of the word “regularity” is precisely the measure. Measure- this the zone within which this quality is modified varies due to changes in the quantity and individual non-essential properties, while maintaining its essential characteristics.

As was shown, the content of any concept consists of essential properties inherent in a certain class of objects. It is these properties that distinguish these objects from objects of other classes. Both the process of assimilation of concepts and the process of their subsequent use are connected with work with properties. This means that students, first of all, must learn to see properties, know the types of properties, and be able to distinguish them.

In order for students to come to an understanding of essential properties, it is first important to teach them to distinguish properties in objects in general. Of course, this should be done in elementary school. Usually, students of this age do not see that an object has many different properties. How to teach students to see these properties? To do this, it is necessary to reveal the content of the technique for highlighting properties in objects. The technique consists in comparing this object with other objects with different properties, as a result of which the student highlights those properties that were previously hidden to him.

Mastering the technique of comparison makes it possible to move on to highlighting common and distinctive properties in objects. Students, working with several objects (for example, cubes of different sizes, colors, materials from which they are made, etc.), highlight those properties by which these objects differ from each other (distinctive properties), and properties that are common to these objects (for example, the shape of a cube).

After teaching students to highlight common and distinctive properties in objects, they should be taught to distinguish essential, important properties in objects (from the point of view of a certain concept), from non-essential, secondary ones. To this end, you can introduce a technique that helps the student to establish which properties of these objects are essential and which are not.

The technique consists in successive variation of insignificant, secondary properties of a given object and stating that this does not lead to a change in the belonging of the object to a certain concept (class). So, a triangle remains a triangle, regardless of the size of its angles, sides, spatial arrangement of the triangle itself.

A change in the essential properties of the subject under consideration leads to the fact that this subject will already relate to another concept. For example, an increase in the number of sides of a triangle does not allow referring this figure to the concept of a triangle - it can be a quadrilateral, pentagon, etc.

It is advisable to work out the method of highlighting essential and non-essential properties on various subjects belonging to different fields of knowledge, so that students see the general nature of the method, its independence from specific material. So, using the concept of “deciduous trees” as an example, students can be shown that these trees can differ from each other in many properties: the color of the bark, the shape and color of the leaves, the thickness and length of the trunk, the number of branches, etc. However, one property remains unchanged for all these trees - the presence of leaves, which gives us the right to call them deciduous trees. If we change this essential property - we take trees not with leaves, but with needles, then we will not be able to call them deciduous trees: they will be coniferous trees.

Students tend to take any common property as essential, so it is important to show them that all essential properties are at the same time common to a given class of objects. So, the presence of a geometric figure - a triangle - of three sides, is both a common and essential feature of all triangles. At the same time, it is necessary to show students that not all common properties in objects are their essential properties. For example, all triangles studied in planimetry have in common that they are located on a plane. This property is a common but not essential property of these geometric figures (a triangle can be located in three-dimensional space as well).

The ability to differentiate the properties of objects into essential and non-essential allows students to understand such types of properties as necessary, sufficient, necessary and sufficient.

The necessary properties of a concept are those that are necessarily present in all objects related to a given concept, as well as in some objects related to an opposite concept of the same kind.

Sufficient properties of a concept are those that are inherent in some objects related to a given concept, and not inherent in any object related to an opposite concept of the same kind.

The necessary and sufficient properties of a concept are those that are necessarily present in all objects belonging to this concept, and not present in any object belonging to an opposite concept of the same kind.

The absence of one of the specified properties of the concept or all at once leads to the fact that the given object turns out to be not related to this concept. Thus, the property "part of a line" is a necessary property of any segment or ray. If a geometric object does not have this property, then it does not apply to the concept of "segment" (or "ray").

The property “has two boundary points” or “limited on both sides” is inherent only in the concept of “segment” and is not inherent in the concept of “ray”. Consequently, these properties are necessary and sufficient in relation to the concept of "segment".

Misunderstanding of the difference between necessary, sufficient, necessary and at the same time sufficient properties is a widespread phenomenon among students. Thus, seventh-grade students were offered special tasks, the fulfillment of which presupposes the possession of the ability to differentiate these types of properties. Here is one of these tasks: “There is a well-known theorem: “the diagonals of a rhombus are mutually perpendicular.” Explain which of the two formulations of this theorem is true: 1) if a quadrilateral is a rhombus, then its diagonals are mutually perpendicular; 2) if the diagonals are perpendicular, then the given quadrilateral is a rhombus.

The results of the assignment showed that 50% of the students coped with it (they chose the first definition as the correct one). 26% of students answered that both proposed statements are correct. Characteristically, these students did not see any difference in these provisions at all. They believed that both formulations meant the same thing, "only the words were rearranged." This means that they do not understand the difference between necessary properties and sufficient properties.

In the second statement, these properties are necessary for a rhombus, but they are not sufficient for its definition, since not only a rhombus, but also a deltoid satisfies these requirements.

Students make similar mistakes when working not only with mathematical, but also with other material. So, students of grades VIII-IX were offered the following task: "Prove which of these words - beauty, fireplace, big, nail - are adjectives, and which are not." One of the students quite correctly reproduced the definition of the adjective, but could not apply it correctly. Here is his answer: “We need to check on the question “what?”. If the word answers that question, then it is an adjective.” The teacher draws the student's attention to the fact that another property is indicated in the definition: adjectives denote the attributes of objects. The student was confused and refused to complete the task.

In this case, the situation is similar to the previous one: the student confuses the necessary and sufficient properties. What an adjective is a word that answers the questions “what?

(what?) ”is a necessary property: all adjectives answer this question. Any word that does not answer this question (does not have this property) is not an adjective. However, this property alone is not enough to highlight words that are adjectives. Indeed, to the question "what?" words that are participles also answer: blushing, going out, running, etc. That is why two properties must be taken into account in order to distinguish adjectives.

It is important to show that not every necessary feature is sufficient. Students' mistakes are often associated with the fact that they act with necessary features as if they were sufficient. For example, a quadrilateral that has at least two right angles is considered a rectangle. This is not true, since a rectangular trapezoid also has such properties. For both a rectangular trapezoid and a rectangle, this property is necessary, but it is not sufficient for either object. This means that not every necessary property is sufficient. Conversely, not every sufficient property is necessary.

“Where is it warmer: here, in the classroom, or in the yard?” - "In the room warmer."- "From what?" - “The stove is heated in the room, and the stove heats up.” - “And if you heat the stove in the yard, will it be warm in the yard?” - "No, the room is fenced with walls, ceiling and floor, which do not allow heat to escape." - "What is the stove made of, what are the walls made of?" - "Stove brick, stone; walls wooden".- “Why is the stove stone, and not wooden?” - “They make a fire in the stove, a wooden one would burn out.” - “Give me here the things that can burn down; name those that do not burn. So I put a chair to the stove: which is wider - a chair or a stove? - "Stove wider, the chair is narrower.- "What are our tables?" - "Our tables narrow And long."- "Why are they made like that?" - “It’s good for us to sit in the room in winter, because we won’t get cold.” - “What can we do in the room?” - “In the room we can write, sew, cut, plan and so on.” - “Can we do this in the dark? When it happens light, when it happens dark? Where is lighter: in a room or in a barn with closed doors? - “The room is lighter because there are windows. The windows in the room are pierced so that it is light. ”-“ Why are there frames in the windows? - “Frames in order to insert glasses into them that let in light, keeping the cold out of the yard.” - “Here I will insert a board into the window: is it visible through it or not?” - “You can’t see through the board: She not transparent and glass transparent." Why do we need transparent glass? Here is a glass, what is it? - “The glass is glass, transparent.” - “And what else? Light or heavy? Why do you need a glass to be light? Why is it difficult to drink straight from a bucket?” - “It is easier to lift a glass and bring it to your lips than a bucket.” - “Is it only easier to bring a glass to your mouth because it is light?” - “Also because it is small, the bucket is large, and it is difficult to put it to our lips” - “If you sit under the table top, can you stand up?” - "No." - "How are you standing in the room, not under the table top?" - “After all, the ceiling is also a cover.” - “The ceiling high, and the table top low".- "Why is it necessary that the table top be low?" - “We are sitting at the table, leaning on it with our elbows.” - “Is the bench higher or lower?” - “The bench is even lower.” - “Why?”

So the teacher continues to indicate not only the properties of the object, but also their purpose and, if possible, the reasons why the object has those and not other properties. This must be kept in mind when elucidating each property. General concepts about the material from which an object is made, about its color, size, shape, position, transparency, hardness, etc., do not yet constitute real knowledge about the object. In elucidating them, we do not leave the circle of abstract concepts. We only learn that things are made of stone, wood, round, flat, white, etc., and this is still not enough. In addition to the general concept of properties that are found in different things, it is also important to know which property in this or that thing is most necessary, which in it is accidental: what in one case can be essential and necessary, in another is accidental, and vice versa (white color in written paper, white color in paper, which is pasted over the box). Here we consider the properties of things in connection with their use and purpose, and this is always easy to point out in ordinary objects made by man. Thus, each feature is presented to the student much more clearly and visually, and he not only understands it, but is also aware of its connection with other features in the subject. (According to its purpose, the table should be of a certain height, have legs or a support and a smooth board on top; it is more convenient for the class if it is black so that it does not get too dirty.) In natural objects, such explanations require special knowledge that is not assigned to the first year, but even here you can touch on some differences that are well known to the student (what a cat needs claws for, a dog and a wolf need teeth and quick legs, wings for a bird, roots for a tree, etc.). However, in preliminary conversations it is enough to confine ourselves to subjects that are or can be found in the classroom. Let us now point out the properties of objects separately.

The material from which objects are made, and their other qualities. What is the chair, table, bench made of? What else is made of wood? What is the stove made of? What stone things do you know? (Slate board, lead, chimney, stone house, stone fence, stone millstone in the mill, stone whetstone). What is the damper in the furnace made of? Show me more iron things (a nail, a bolt, a key, a lock, a knife, a saw, an ax, a needle, etc.). What glass is this? What is it made of? What kind of glass things do you know? (Inkwell, bottle, glass, glasses, etc.) Why are a knife, an ax, a key made of iron and not of wood? Is it possible to make a stone axe, a stone knife? It would be difficult to sharpen a stone knife, because the stone is brittle, wears out, crumbles. Here I have an iron (steel) knife: I bent it a little, and it straightened up again. Iron bends; it is flexible and resilient. Does the stone bend? Is glass elastic? Is the tree resilient? Fresh, damp branches are elastic, dry breaking, reeds are always elastic. What can you say about glass? Glass is not elastic, brittle, can break into smithereens; it is transparent. Are stone, wood, iron transparent? Is the paper transparent? Thin paper and paper rubbed with oil are somewhat transparent. The slate board is light, and what things here are even lighter than the slate board? The chair is heavy, and what are the things that are even heavier than the chair? A small board is easy, but a big one? A small stone is light, but a large one? The knife is light, but the ax? Which is lighter: wood or stone, stone or iron? What is better in case of fire: a stone house or a wooden one? Why don't they build iron houses? Iron is expensive; in summer, in the sun, it gets very hot, and in winter, in the frost, it soon gets colder (iron houses are sometimes made in foreign lands). What is smoother: this log or a tree on the table? Name me things that are smooth and rough. What is liquid? What is soft? What is hard?

Assignment of items. What is the slate board used for? What other things do you need to write? What do they write on a blackboard, on a large blackboard, on paper? Is it possible to write with charcoal and on what? Why is it not so convenient to write with charcoal? What is a table, chair, bench for? What else can you sit on? Why not take a stump of wood instead of a bench, and a tub or box instead of a table. Is it possible to write without a table at all, only sitting on a bench or standing? Try it. What is the ceiling for? To shelter us from rain, cold, bad weather. Is one ceiling enough? Why is the floor needed? After all, it would be possible to walk in a room and on bare ground? Is it possible or not to get sick from dampness, from dirt? What are windows for? What are the frames and glass in the windows for? Which is better: a small or a large hut? In which hut is it easier to breathe when there are a lot of people? What is done with the walls of the hut to make it warmer? The walls are caulked with tow, sheathed with boards. In order not to blow from the floor and ceiling, what do they do? What windows should be in the hut? Is it good when there are very small windows in the hut? What happens to your eyes when you work in the dark? Eyes weaken and you can go completely blind. What else do you need for warmth? Are walls, ceiling and floor enough? What is a good oven? What kind of firewood gives more heat? Is it good when the stove smokes? Is it good to close the oven early? What is done from the frenzy? What's wrong with a chicken hut? What is the caftan, sheepskin coat and other clothes used for? Name the clothes that cover the head, chest, back and arms, stomach, hips and legs. In addition to heat and light, what else do we need? Is it good if you go around dirty, sit in a dirty room? Why is it harmful? You can get sick from dirt: you will completely lose weight, and all sorts of rashes, scabs will go on your body, nasty animals will start up ... what kind? How to keep cleanliness on the body, in clothes, in bed, in the room? What do you need a glass for? What other utensils do you need for eating and drinking? What would you do if you had no glass, no jug, no ladle, no fork, no knife, no plate? Would it be good? What is not good? Do you need cleanliness in the dishes?

Item color. In order for children to clearly distinguish colors, it is necessary to acquaint them in advance with the pure colors of the rainbow, since the colors on the surrounding objects are mostly mixed. To do this, the teacher brings to the class colored pieces of paper or balls made of colored wool (or simply skeins of wool), painted in pure colors: red, orange, yellow, green, blue, blue, purple. He, in addition, needs to have at least three, four pieces of good paint (carmine, red lead, gummigut, Prussian blue). He will then show how, from the combination of red with yellow, orange comes, yellow with blue or blue - green, blue with red - violet. Mixing all these colors, he will get black. In black, all colors are destroyed; because at night everything is dark or gray. On the contrary, white is a combination of all colors: the rays of the sun are white, and in the rainbow they break up into seven colors. If it is difficult for a teacher to get these things, then he can always have resin, sealing wax and several pieces of glass. With the sharp edge of the file, he will scrape the lines on the glass and, along these lines, will easily break off the glasses (especially not thick ones) into oblong plates about two and a half inches wide and about five inches long. You only need three of these pieces of glass; where there is a glazier, it costs nothing to carve them. He will fold these three identical pieces of glass with the edges into a triangle and tie them with threads so that they hold; then he glues them around the edges with sealing wax or resin and then removes the threads. He will put this triangular prism on the plank and also glue it to the plank from below. It is necessary to glue it well, especially from below, so that there is not the slightest hole, but also not to cover the glass too much with sealing wax. This will leave a triangular glass in which you can pour water. This prism or glass of water, choosing a sunny day, should be placed in the sun, on a window with clean, unfrozen glass (it is even better to do this in a dark room or in a barn, leaving one hole for sunlight). When the sun hits the prism, a bright rainbow will appear against it on the table, on the floor or on the wall. The teacher slightly rotates around and moves the cup until he gets rainbows; then in this place he will put white paper, so that the colors can be seen more clearly. On this rainbow, he will explain to the students the colors with their overflows. If he manages to find or break off a smooth, angular and clean piece of ice, then, holding it somewhat sideways in the sun, he will achieve! " but then such wide multi-colored stripes will not come out and it will be more difficult to consider colors. “Isn’t this a waste of time? - the reader will ask, accustomed to thinking that only a letter is needed for a public school, all this, perhaps, is good, but will there be time? That we are by no means sacrificing literacy for some other cause, the reader will see later, in our very exposition of how to practice literacy. But we would only like to ask: how much time is spent at school in fruitless, fragmentary conversations with completely undeveloped students? To take care from the very beginning, in order to give an orderly course of thought, to accustom one to ponder over objects, means at once to facilitate the study of all school science. Whoever does otherwise is like the owner who would build a house of only logs without a floor, without windows, without a door, without a stove, without everything that makes the house fit for habitation, and would leave, in case light is needed, to do windows, if robbed, make a door with a lock; if it gets cold, arrange a stove. Of course, he will spend ten times more time, money and labor to build a house than if he began to build thoroughly from the very beginning. Let's turn to our subject. Is it necessary for a child to be able to distinguish colors? If this is necessary, then why wait for an opportunity when it comes across in a book, each time interrupting reading and resuming interpretations that cannot firmly sit down in the head, because they are fragmentary and accidental? Having given an exact concept about colors at once, you will reduce the time for future explanations. This is the kind of abbreviation we had in mind when we somewhat expanded the volume of our conversations.

When the teacher sees that children distinguish colors from colored papers or from a rainbow of colors, he will draw their attention to the colors of surrounding objects and will ask questions: what color is the wall, brick, snow, shirt, caftan, grass, sky, what color do you know flowers ? At the same time, he will also indicate transitional, mixed colors: yellowish, sparkling yellow, bluish, flesh-colored, purple, dark red, brown, gray, greenish-gray, and so on. What kind of hair does Petya, Vanya, Masha have? Whose hair is lighter, darker, yellower? Tell me some things you have seen that are red, orange, yellow, green, blue, indigo, purple. For more exercise, the teacher will try to bring different colored objects to the class (different beads, beads, some berries, beets, etc.).

The position of the items. Vasya, where are you looking now: back or forward? You look straight ahead. Turn your head to the right, turn to the left, stand up, turn back. Fedya, do the same. Nastya, Senya, Masha, do together at once what I will say: head up, head down, look straight, turn your head to the left, right, stand up, turn around. We will do this all together: raise one right hand, lower the right hand, raise the left, stand up - everyone turn their heads to the left, right, stand on one right foot and raise their left hand, stand on one left foot and raise their right hand, raise both hands up, lower down, stretch forward, fold back, bend over to the right side, bend over to the left side, tilt the whole body forward, tilt back, hit the floor with one right foot, one left. The teacher makes sure that everyone does it correctly, and those who do not understand, make them especially do it. What do you see in front of you? Say tg, Kolya. What wall is in front? Which one is right? Tgh, Senya. Which one is to the left? You are Natasha. Which one is behind? You Misha. What is right in front of you? You Vanya. What's wrong with you? What's up? What's below? What's next to the stove?

So I put two books: which one is the front one from you, which one is the back one? And from me, which is the front, which is the back? From you, this front wall, this back, this left, this right. Turn back: what then will be your front wall, which back, right, left? From me, if I stand like this, how will the walls be? And if so? And if so? Where is your ceiling? Where is the floor? Here I am holding a board in one hand, and a book in the other: what am I holding, what is lower? Tell me what is closer to you, what is further. Here's a stick for all of you. Raise the sticks up, up, down, hold straight in front of you, closer, further, move to the right, to the left, point the stick sideways to the left, sideways to the right, back, up, down. Take slate boards. Put the stick along the board, across, at an angle, on top of the board, from below, from the right side, from the left side, hold the stick above the board, under the board, stand upright, hold the stick in front of the board, behind the board, stick through the board, put the board, turn the board vice versa. Here is a piece of chintz: where is the face, where is the inside? Where is your face on the dress, where is the inside?

Shape of objects. Take slate boards: specify how the board will be in length, in width, in thickness? Where is the table length, width, height, thickness? Here is a sheet of paper: how do I show now? In length. Now how? In width. Show with a stick how the wall will be in height? How long? Where is the length in this room, where is the width? How big is the room: long or wide? Here is my box: so what will happen? Length. So? Width. So? Height. But I will put it on the short side - like this: now what is the length? Vyshina. When a person lies down, how will he be from head to toe? In length. And when is it worth it? Up above. What is the ribbon? The ribbon is narrow and long. What is a tablecloth? Wide. When the jacket is only to the waist, how do they say about it? The jacket is said to be short. And what are the floors of the caftan? Long. What about the vest, if it's too tight? Narrow. And the trees? High. And the bushes? Low. And the knife, when to sharpen it? Spicy. And if you cut them a lot, what will it become? Dumb. Show and name things for me here: high and low, wide, narrow, long and short, sharp and blunt (children themselves can make such things from sticks and paper). Here I cut out three pieces of paper of the same length (the teacher cuts out three pieces of paper: the first is narrower, the second is wider, the third is even wider); look first at these two pieces of paper (the teacher takes the first and second): how do they differ? One narrower, the other wider. Which one is wide: this one or that one? The one in the right hand is wider. Good; this first piece of paper is narrow, the second is wide, but I will take the third one: what is it like? The third is even wider. If I put the second one next to the first, what will it be like? Wide. And if next to the third? Then the second piece of paper will be narrow. This means that the same piece of paper can be both wide, compared to one, and narrow, compared to another piece of paper. The same dress can be wide for one and narrow for another. In the same way, the teacher places three sticks side by side: one is low, the other is higher, the third is even higher and indicates that the middle stick is high in comparison with the first, and low in comparison with the third. The kitten is small, but compared to the cockroach, the kitten is a big animal. The river is narrow, but in comparison with the stream it is quite wide. The hour is long, but short compared to the whole day. The road through the whole village is long, but compared to the road to another village, it is short. The moon is bright, but pale in comparison to the sun.

So I ran my hand over the table: it is even, flat; this paper is also flat, but if I bend it like this (the teacher bends the paper in a vault), will it be flat? No, it will be convex, round. Indicate which things are flat, which are convex or round. Is the head flat? What wall? What apple? What is the glass in the window? What kind of baked bread? The board is flat; count how many corners it has: one, two, three, four. This board is square. What else is quadrangular here? (Rack, floor, ceiling, etc.) What kind of paper is this? Quadruple. But I'll fold it like this: how many corners are there in it now? Three; now the paper is triangular. Krgsha in a house with a ceiling, what will it be? triangular. (The teacher makes a kind of roof with a ceiling out of paper.) What can we find in every thing? Here is a box: this is one side or face, this is the other; between the sides where they converge - an edge or an edge; on each side where the ribs meet, an angle is visible, and between the sides at the ribs there are also angles. Here is the corner between the sides on the outside, but if I open the box, the corner is visible inside. So, in the box there are sides and edges: the corners are visible between the sides - at the edges, and on the sides - between the edges. Indicate the sides, or faces, edges and corners in a room, in a stove, in a board, in a stone, in a book, in a piece of wood.

When reviewing all these signs, one can take into account their relationship to our five senses. With our eyes we recognize color, with our eyes and together with our hands (touch) we recognize position, shape, material. Vision also includes signs: light, bright, dark, foggy, gloomy, etc.; to hearing: quiet, loud, sonorous, deaf (knocking), etc.; to touch: warm, cold, hard, soft, smooth, heavy, light, dry, wet, etc.; to taste: sweet, bitter, salty.

Parts of the subject. Here I have a piece of paper: I will tear off a piece of it. This piece, is it all the paper I've been holding? No, this is part of it: I have to attach a piece to the sheet from which I tore off so that all the paper comes out. So I will tear the paper to pieces and give it to you: what have I done? I divided the paper into parts. Look, I hold the key in my fist: do you see the whole key? No, we only see part of it. Here is a knife: what do you see in it? We see one petiole, but we do not see the blade; we see only part of the knife. If you take a leg from a table, is it the whole table? No, it will be part of the table. What other part of the table do you know? The other part of the table will be the top, or top board. Show me the parts in the room, in the stove, in the human body, in the head, in the cart, in the window, in the book. Why do carts need wheels and sledges need runners? Why don't they ride on skids in summer and on wheels in winter? Why does a stove need a pipe? And what do the ears, eyes, nose and mouth serve on the head? What about arms and legs? What is the binding for in the book? What is the petiole in the knife for? And so on.

action and state. Place, time and mode of action - to the questions: where, when, how? This includes all questions about the position of the object and, in general, all explanations for the action according to the above signs: put above, turn right, break across; high house - the house rises high, a narrow piece of paper - a piece of paper is cut out narrowly, smooth board - board scraped smooth and so on. Let's take a look at some of the actions.

Status and location change: lies, stands, is, rises, spreads, stretches; put, turn, move, take out, put in, etc.

Actions in relation to the material: make, cook, cut down, put together, hew, cut out, knock out, forge, pour (from metal), line up, lay out (with a stone), smear (with lime, clay), blind, cut, carve, sew, tie, dump.

Color: to paint, to bleach, to blacken, to cover with paint, to paint over.

Vision actions: to see, look, watch, observe, notice; shine, shine, shine, sparkle, flicker, fade, darken, grow dim, turn white, blacken, turn yellow, turn green, blush, shine through, be reflected (in water, in a mirror). The fence turns, the paper folds over, the top spins, spins, the yard goes around, the house moves forward, the corner protrudes, the corner protrudes between the walls.

Hearing actions: to hear, to listen, to heed, to listen; whisper, make noise, buzz, whistle, rattle, crackle, rattle, ring, tinkle, rustle, rustle, rustle, hiss, rumble, knock, shout, shout, groan, howl, respond, respond. This also includes various voices of animals.

Actions in relation to touch, smell and taste: feel, touch, feel, smell, try; harden, become soft, liquid, melt, melt, get wet, damp, smooth, smooth, prick (needle pricks), burn, get cold; warm, dull, sharpen, smell, fragrant, rancid, sour, salt, sweeten.

Partitioning: divide, disassemble, separate, saw, cut, cut, crack, break, scatter, spill.

Describing an item and comparing it with another item. Description of a large blackboard by position, by shape, by color, by the substance from which it is made, by other qualities and by its purpose. The chalkboard stands opposite us against the wall; it is quadrangular, black, wooden, hard, large, heavy; they write on it with chalk, showing the lesson to the whole class. similarity her with a slate board: both are quadrangular, both are black, they write on both. Difference from the slate board: the blackboard is large, the slate is small; the blackboard is heavy, the slate is light; classy-wooden, slate - stone; on the classroom they write with chalk, on the slate - with a lead; classroom - one for the whole class, each student has a slate. Here the teacher is still beginning to teach comparisons; he makes only a few comparisons and descriptions in order to deal with this with the students a little when grouping objects. So, he can still give a description and comparison: a lead and a pencil, a window and a door, a table and a chair or a bench. Let's take another example of a window description. The window is in the room, in the wall, which is to the left from us; it consists of a frame and glass (or two frames that open together); the glass is smaller than the frame, there are several glasses in the frame; both glass and frame are quadrangular; the frame is white, painted with white paint, wooden, transparent glass; The window was made to bring light into the room. Resemblance to a door: both the window and the door are in the wall, both things serve as an opening in the house, both are quadrangular, both have wood, both are solid. Difference: the window is in the middle of the wall, the door reaches the floor; the window serves for light, the door for entry; glass in the window, they are not in the door; there is a frame in the window, solid boards in the door; a lock is attached to the door to enter from the outside, in the window only from the inside there is a hook or a bolt.

Despite the variety that the teacher can give to all these conversations, they would tire the students if they were carried out all the time, throughout the lesson.

The teacher can allocate time in the following way:

• 1. The first 20 minutes - visual conversation.
• 2. The next 10 minutes is a repetition of what was covered in the conversation.
• 3. The next 5 or 10 minutes are gymnastic movements.
• 4. The rest of the time: showing pictures, combined with a story, or consciously learning songs. Sufficient material for this can be found in my "Russian alphabet" and "Book for initial reading", as well as in the "Native word" by Ushinsky, in the "Book for reading" by Rezener and Volkov, and so on. The teacher chooses the shortest and easiest stories for this and tells them orally, without the help of a book.

Live speech is what is needed here. For children, the development of imagination, fantasy, the development of moral feelings and the exercise in a coherent presentation of thoughts are especially important here. Stories should be directed towards this.

Grouping of items. The above exercises can be completed by the time the students begin to read the easy stories in ABC. In our alphabet (“Russian alphabet”), the first conversation serves to briefly repeat what was learned in these initial conversations. In further conversations of our alphabet, the teacher will find a grouping of objects in the following order:

A. Objects of nature: 1) Animals that can be found in the yard. Pets: chicken, goose, duck; goat, pig; dog and cat; horse and cow. 2) Wild animals. Wild four-legged animals: wolf, bear, fox, squirrel and hare. wild birds: large predatory, marsh, songbirds; migratory birds. Their comparison with home. 3) Insects: grasshopper, dragonfly, butterfly, bee, mosquito, cockroach, fly. Items animate and inanimate. Field and forest, vegetable garden and cornfield. Flowers growing in the field; trees growing in the forest; vegetables, cereal plants. 4) Spring, summer, autumn And winter. The sun And month. Wind.

5) Stones: cobblestone, flint, limestone, asp. Sand, clay, chalk, lime. Lands: sandy, clayey, black earth. Metals: iron, copper, tin, silver, gold. Copper and silver coins. 6) Fire And water. The manifestation of fire, various waters. Lake, swamp, stream, river, sea. concept about nature. Natural And artificial items.

B. Man and his properties. one) Parts of the human body: head, chest and back, stomach, arms, legs. Head parts: eyes, ears, nose, tongue, teeth. Five senses: sight, touch, hearing, smell and taste. Mind and speech. 2) Like a person uses his powers to your advantage? Dwelling and its device. food with vegetable gardens, fields and from animals. Cloth from field plants, from domestic and wild animals. Tools for various works. Tools used in some crafts. Household and agricultural implements. Items made from clay and iron. Tableware from wood, clay, glass, cast iron, iron and copper. Items used for driving. 3) skill And ineptitude in business. The science, teaching. Moral human qualities: virtues and vices.

Before each department, we have in the alphabet small stories, proverbs, riddles, poems, etc., which introduce the circle of subjects about which the conversation should go.

These articles are rather light in content and can be read without much explanation before the conversation to which each series of them is adapted. The first row of exercises and most of the articles in the second and third rows have a similar meaning in the "Book for Initial Reading". Where the "Native Word" is introduced, there you can also use the grouping of objects presented in this book, only slightly changing it according to the purpose that we will now indicate. In our ABC, from the very presentation of the talks, it is already clear where they should be directed, and here we will give only some explanations. First, do not think that we assigned each conversation in the ABC to one lesson. Just as not everything that precedes the conversation can be read in one lesson, so the teacher can divide the conversation itself into two or three lessons: in our division, we only wanted to indicate the categories on which we should sequentially stop. Secondly, we must remember that here only a grouping is already objects known to children not a detailed explanation. Here you teach children almost nothing new, but only bring to consciousness and put in order what they have already learned from direct observation. Consequently, the range of subjects should be as limited as possible (which we did), and in their very choice one should be guided by the instructions of the students: each time you ask what they know in this or that range of phenomena, and beyond what they know, you don't go in, because the first time your goal is to establish children's concepts, not to enrich with new information. Of course, where there is time, the teacher will also point to objects that are less familiar or completely unfamiliar, in connection with those that are known to children (in the villages - to the urban environment, in the cities - to village tools and work, presenting models, drawings and etc.), but here we are talking only about the main goal of the conversation.

We believe that this goal is already quite clear from our presentation; but some may still doubt: why teach children to what they know? Why, for example, ask them what is made of stone, what is made of wood, to get them to answer that a chicken has wings, and a horse has four legs, when you still don’t mean any new knowledge? Such questions are usually asked by persons who, consciously or unconsciously, according to ancient custom, with the word teach connect the concept of memorization. We warn teachers who have not completely rid themselves of this custom that by turning both the preliminary conversations and the studies indicated here into teaching of this kind, they completely destroy all their significance. Here the children freely express their observations and knowledge, and the teacher is only their interlocutor, who knows how to put questions in such a way that their knowledge is expressed in a more varied and complete manner. As for new knowledge, in the first year (we remind you that we are talking about the conversations of the first year), children already quite acquire them in the lessons of writing, reading, and arithmetic. This is their main occupation; we assign only four lessons per week for talks. On them, you give the children a chance to clarify the information that they already have. You will thus know the extent of their development and together lay a solid foundation for their further success. Firstly, it cannot be said that the simple concepts included in these conversations are already quite clearly learned by children outside the school: you will always have to add something new here to what is known. However, having children who are more developed, a reasonable teacher, of course, will speed up these studies, focus on more difficult questions, for example, take more time comparing and describing objects. In any case, he will have to practice a lot in the language, but not in the sense of developing children's eloquence, but in teaching the exact use of words. Children may know a word and not know with precision the concept it signifies, as is often the case with words learned by hearsay, from memory; they may know the subject and not know the word, or at least not firmly remember it; finally, they may know both the object and the word, but it is wrong to connect them, it is not clear to represent their relationship. It is a matter of first importance that in all these cases, while exercising in the language, the children should talk about objects that are close and familiar to them. Secondly, the logical setting of concepts is no less important. Children, of course, judge logically, but their judgments are fragmentary and incoherent, and generally such that it is still impossible to build any solid knowledge on these judgments. To leave them to themselves in this (that is, rather to teach them to read and write and then let them themselves acquire the necessary information from books) means to make them self-taught, that is, to allow chance and arbitrariness, and even the most talented person does not always go on the right path. Without a doubt, a rural boy can sometimes know more about animals, birds and other natural phenomena close to him than his teacher, even who has completed a full course of natural sciences at the university; but what of it? His knowledge, however, remains fruitless and does not in the least rid him of even the grossest superstitions. This means that it is not the amount of knowledge that is important here, but their internal connection is important, and all power lies in the way, in the method, by which we assimilate them and put them in order. In all knowledge we distinguish two sides: observation And output. For the completeness and accuracy of observation, it is necessary to know those aspects around which various properties of objects (material, shape, purpose, etc.) are grouped, and is it possible? to distinguish in these properties the essential from the accidental. For the conclusion, it is necessary to compare objects according to their characteristics, in order to reach a certain generalizing thought through the coincidence of these characteristics. (A hen, a goose, a hawk, a swallow have wings: this birds. In houses, sheds, barns, the walls and floor are quadrangular; buckets, glasses, bottles, plates, round pots. Therefore, in buildings we usually find the form quadrangular And triangular in a dish - form round.) Doing this properly, the teacher, so to speak, again walks with the children the path by which they originally acquired knowledge, but now this path is illuminated with a new light and leads to a common, definite goal. What is new here lies in the logical thread that links the scattered grains of concepts, in the assimilation of the first logical steps along which concepts ascend from the particular to the general. This is the beginning of the method, without which knowledge is completely fruitless. A consistent method of ascending from the particular to the general, from observation to conclusion, must be carried out in all subjects of elementary education. It is important not only because it contributes to a thorough assimilation of knowledge, but also in itself. Let us even assume that in another way the children would have learned arithmetic, arithmetic, and so on more quickly. But it's not about speed at all. Learning Consistently, Kids imperceptibly assimilate the very method of study, and this is the first, most important, most necessary of all the knowledge they acquire.

Let us now turn to the system of grouping objects that we have outlined and note the following about it. After the children have practiced on the objects in the room, we take them out into the yard, indicate what can be found in the yard. At the same time, we do not at all believe that in such a purely external way it is possible to expand the range of concepts: objects found in the yard, in the field, in the forest, can be more understandable children (especially rural children, who spend most of their time outdoors) than objects in the room: it all depends on which sides you pay attention to, and a conversation about dishes, about clothes, about parts of the house can be much more difficult are conversations about domestic animals, about the field and the forest, about the weather, and so on. What is close to the child should not be understood only in the sense of material closeness, but as close to his concepts (the chair on which the child sits every day is very close to him, but explaining the shape and structure of the chair is no easier than, for example, explaining that if you crush a stone, sand will come out, that a tree has a root, a trunk and leaves, etc.). We take the child out into the yard to start grouping objects with domestic animals. Where he will observe them, of course, is all the same: the point is that he knows them. The teacher asks which of the animals that are at the house are familiar to him and also how they differ. The student points out the few differences known to him in the form of these animals, in their habits, in the food they use, in the benefits they bring. For example, when asked how a chicken and a duck, a goat and a cow are different from each other, it is completely enough if he says: “The chicken rakes the rubbish and looks for grains, and the duck swims in the water and eats what it finds in the water; the duck has such a thick nose; the goat is small and the cow is big; cow mooing: moo, and the goat: be-e; cow gives milk. Perhaps, with some reminder from the teacher, he will say more; the teacher, gradually accustoming to observation, will perhaps give the class such a lesson in advance: “Look at such and such animals at home and think about how one is similar to the other and how one differs from the other; We'll see which one of you notices more." Recall that everything here must be known from visual observations. Objects that children have not seen should be shown to them in nature or, in extreme cases, in a picture (falcon, crane, heron); about those subjects that they know well, also recall from the pictures. Otherwise, it is better not to talk about the subject. But fuller and more comprehensive observations under the direction of the teacher are assigned for the next course; here it is enough to use the knowledge already acquired before school. The teacher here, only on occasion, will single out permanent, essential features from random ones. For example, if a child says: “Our cow is black,” then he will pay attention to the fact that not all cows are black, but, for example, all have a tail, four legs, horns. Here the teacher, where necessary, applies to the case previously learned concepts about the properties of objects, paying attention to their shape, position, color, purpose, and so on. There are few signs to be noted, but they are quite characteristic and with possible accuracy. Conversations about domestic animals make it possible to distinguish quadrupeds from birds; while the teacher will point to the third category - fish which the child, of course, happened to see. There are only a few differences here: the four-legged walks the earth, gives birth to live cubs; A fish swims in water but cannot live on land. Further, we will not set out in detail what to pay attention to: from these explanations, the teacher could understand the essence of conversations of this kind. Following that, in a few features, domestic animals are compared with wild ones (wild animals live in forests, run away from a person, harm him, but there is also a benefit from them ... what? - we get skin and fur from them). The difference between the wild ones is brief: the wolf is terrible with its teeth, the bear with its paws, the bear is larger and stronger than the wolf, and so on. Between wild birds, we distinguished predatory, marsh, songbirds, because these differences are quite sharp and can be familiar to a child without any special explanation (the difference between animals in teeth, in the arrangement of beak and paws belongs to the second course). We meet wild animals in the forest, in the field, and a brief conversation about the field naturally follows. Here we, firstly, end the grouping of animals, mentioning insects and, for the sake of completeness of the system, amphibians (frog), crayfish and spiders. The difference between insects is revealed by the fact that they are very small, with a body dissected into segments, and have six legs; crayfish lives much more in water, but is not similar to either a fish or a frog, which jumps on the ground and has four legs in total, and not ten legs, like a crayfish (a crayfish has five pairs of legs, the front pair with ticks); The spider differs from insects especially in that it has eight legs and arranges a web for catching flies. However, if these details can be confusing, then we will limit ourselves to mentioning the frog and insects. Further in the conversation, we move from animals to plants, which is why it is necessary to find out what an inanimate object is. When referring to various fruits, the teacher may dwell on the difference between a kitchen garden, a plowed field, a hayfield, a garden, an orchard, and a wild forest. Children find out the difference between grasses and trees briefly. The grass is small, the tree is big; the grass has a weak stem, the tree has a strong trunk; grass is fed to livestock, a hut is built from wood. Spruce and pine have needles; spruce branches are shorter at the top, longer at the bottom; birch has a white trunk, roundish, sharp leaves with serrations towards the end, and so on. It would be nice if the children learned here to distinguish trees by the shape of the leaves: having stocked up on dried leaves, the teacher in the drawing lesson could give them an outline of the leaf, putting it on paper. Children distinguish flowers by color and partly by shape, vegetables by size, shape and partly by taste, cereal plants by the type of grains and ears (the teacher can bring samples of grains and dry ears to the class). The child knows that plants bloom in spring and wither again by winter: insects also disappear in winter in the fields and appear with spring. These changes stand out so clearly that, by the natural connection of phenomena, we have to talk about the seasons. At the same time, the teacher has the opportunity to find out the measure of time, to give the concept of an hour, a day, a week, a year. He teaches children to use the clock as well. The idea of ​​the sun and the wind (strong and weak wind, warm and cold) are inseparably connected with the idea of ​​the seasons. Next, in the order of objects, we will talk about the fossil kingdom: about stones and metals. It is also convenient to show these objects in the classroom, so that for the first time the children, at least by color, brilliance and hardness, find out for themselves their difference. It would be nice to have sharp pieces of stones and metals, so that children, scratching one over another, can find out what is harder: if one thing scratches another, then it is harder. (Here you can compare other things: which is harder, bone or wood? Flint or iron? Wood or paper? Slate or glass? When scribbling, you don’t need to press hard: if you rub hard, then, perhaps, a tree can leave a mark on the iron. ) Of the stones, it is enough to show: cobblestone (granite), flint, clay stone (slate, dark gray, layered), limestone (whitish), sandstone (in grindstones), slate, marble (if any). If an opportunity presents itself, you can also show precious stones: otherwise it is better not to talk about them. Instead, let the students examine a piece of coal, sulfur, potash, etc. The student will say a little about the lands: sandy earth is dry, loose; clayey - viscous; everything grows poorly on clay or sand alone, the black earth is fertile. When talking about metals, the teacher also introduces coins. In connection with the discourses on fossil objects, there is the following discourse: on fire and water. In the stories preceding this and that conversation, mention is made of some works where fire and water are involved. These natural phenomena constitute a series of conversations about nature. Here we briefly explain the concept of nature and the difference between natural and artificial objects. Next, we move on to the person and to the grouping of all objects related to the person. First of all, it is most natural to talk about the parts of the human body (the teacher indicates the shape, position and purpose of these parts) and the five senses (their use). In addition to the articles of the alphabet, proverbs and riddles placed in the “Book for Initial Reading” (the second and third row of exercises) can serve here. In connection with other human abilities, language and speech are mentioned. After a conversation about a person's abilities, it is natural to talk about how a person thought of in order to arrange a dwelling for himself, find all kinds of food, and prepare clothes. The grouping of these objects in the place indicated by us is of particular importance, because we are talking about the mind and art and about the work of a person. Thus, the advantages of his nature are revealed and it becomes possible to point out his highest moral purpose. Since the previous conversations are already preparing for the present, here it is possible to enter into some details regarding the use that a person makes from various objects of nature (what is bast for? what is flax, hemp for? what does a sheep give for clothing? where is the skin for boots ?). In connection with these or other works, the concept of tools is also clarified. Finally, among the important conveniences of life is the use of various utensils and various means of transportation. We have separated the interpretation of dishes from the discussion of food, because here we are mainly dealing with the use of objects of the fossil kingdom (iron, copper, clay, sand for glass, etc.). We intentionally did not give at the beginning a grouping of objects from household life, because at the beginning it would be unsystematic and incoherent or would require more difficult conversations about human abilities in general. But household items: furniture, dishes, etc., are very convenient for explaining various properties in objects; in preliminary conversations, they are grouped according to various properties: by color, by shape, by material, by purpose, and so on. The student, of course, brings to consciousness much of what we have just mentioned; but all the same, there is still no grouping according to which household items would be included in a certain circle of phenomena.

Further conversations lead to finding out how to get down to business with the ability and how skill is given by science and, finally, the main moral qualities of a person. The connection with previous conversations is clear here: having the ability to turn all the objects of nature to his advantage, a person, for his happiness, must sensibly and conscientiously take up every business and act together in such a way that it would be good for others to live in the world. Moral qualities, however, are clarified not only here, but on occasion in all previous conversations, which is given by the proverbs, stories, and poems we have placed. Finally, the elucidation of moral principles belongs to religion as a special subject of teaching, which will be discussed later.

Here the conversations serve as a repetition of what was previously read and provide a variety of material that serves both for mental exercises and for developing a sense of beauty. Therefore, the whole lesson can be devoted to conversation with only a short break for gymnastic exercises. The teacher should not rush into these conversations, giving in each lesson what the students can learn according to their abilities. An approximate distribution of classes can be as follows.

• 1. For the first 20 minutes, the teacher recalls what has been read and explained before about this or that subject, preparing for grouping. At the same time, he points to real objects and pictures, clarifying the similarity and difference of objects in the main features (these indications, made before when reading, are repeated here in greater connection).
• 2. Follows 5 minutes of gymnastic exercises.
• 3. For the next 20 or 25 minutes, objects are grouped indicating their main differences, and the teacher makes the children repeat the definitions made with accuracy (cow, horse, dogs - four-legged animals; chicken, duck, goose, swallow - birds; perch, pike, ruff - fish) and also asks randomly (swallow - what animal? Pike - what? Put the following items in order: goose, dog, perch, cat, duck, pike, etc.) or, having said a few signs, he makes you guess the name (rakes litter - who? Digging with his muzzle - who? Viet with his hind legs - who?).
• 4. He will use the last 10 minutes to repeat or and sing one of the learned poems ...

In conclusion, we consider it necessary to note that we do not consider the distribution of time in the lessons indicated here, as in other cases, to be immutable and unchanged. Here we did not at all want to impose on the teacher any dead system, but only wanted to demonstrate clearly that some kind of order is necessary for classes in the classroom, which, of course, can, of course, be changed many times as required by practice.

Target: To consolidate the ability to identify and compare the properties of objects, to find a common property of a group of objects.

To form the ability to correlate flat geometric shapes with spatial bodies. Develop logical thinking. Continue to teach to express your opinion and give examples. Cultivate motivation for learning

Organization of the lesson:

part 1 - sitting on chairs

Part 2 - standing in a circle (physical education minute)

part 3 - sitting on chairs

Part 4 - standing in a semicircle

part 5 - sitting on chairs

Materials for the lesson:

Demo- pictures with the image of a Pencil (series "Funny little men"), a landscape sheet of paper, pictures with the image of vegetables.

Dispensing- colored pencils (red, orange, yellow, green, blue, blue, purple), pieces of paper, sets of figures: 5 circles - red, yellow, green, orange and blue, 5 ovals, 5 squares, 5 triangles and 5 rectangles of those same flowers.

Lesson progress:

I Properties of objects - color. Colors of rainbow.

The teacher inserts colored pencils of all colors of the rainbow into the glass. The same cups with colored pencils are on the tables of children. The teacher shows a picture of a Pencil:

Educator:- Guys, our Cheerful Pencil told me an amazing story! It turns out that pencils can talk and even brag. This pencil said (picks up a red pencil): "I can be poppy, fire, flag!"

The teacher draws a red line on a landscape sheet of paper attached to the board, and the children draw a red line on their pieces of paper. Then the teacher asks them to tell what the rest of the pencils boasted about.

Educator:- Guess what these pencils said?

Children voluntarily go to the board, choose a pencil and leave their own on a sheet attached to the board. The rest of the children draw lines in the same colors on their sheets. Sample responses from children:

Children:- Orange: "I'm an orange, a carrot!"

Children:- Yellow: "I am chicken, sun, turnip!"

Children:- Green: "I am the grass, the foliage, the whole forest!"

Children:- Blue: "I'm forget-me-not, sky, ice!"

Children:- Blue: "I am the ink, the sea, the cornflower!"

Children:- Violet: "I am plum, lilac, twilight, bluebell!"

The teacher thanks the children for their help and makes a riddle.

Educator:- Cheerful Pencil whispered one word to me. Guess what.

Through the fields, through the meadows

There was an elegant arc.

Children: Rainbow

Educator: Who knows the colors of the rainbow?

Children name: red, orange, yellow, green, blue, blue, purple. You can invite them to make a rainbow from strips of colored paper.

IIPhysical education "Guess whose voice?"

Children stand in a circle, in the center of which stands the driver blindfolded, hold hands and, walking in a circle, say in unison:

We all stood together in a circle,

They suddenly turned around

(everyone turns 180 degrees and goes in the opposite direction)

And how do we say: "Jump, jump, jump!" -

One of the children, at the direction of the teacher, repeats the last line, and the driver guesses who it is. If he did not guess, then he continues to be the driver, and if he guessed it, then the one who cast the voice becomes the driver. The game is repeated 2-3 times.

The role of the leader in the 2nd and 3rd rounds of the game is best entrusted to one of the children.

IIIComparison of objects on the basis of similarities and differences (color, shape, size, material, purpose, etc.).

1) Educator:- Consider pictures. What is in the first picture?

Children:- Doll and bears.

Educator:- Compare a doll and a bear: what do they have in common and how do they differ?

The teacher, if necessary, can start a comparison: the common purpose of the doll and the bear is toys; the same size; the common thing is that both the doll and the bear have ribbons, but they differ in that ... And the children name the signs of difference on their own.

Educator:-Compare the balloon on which Dunno flies and the ball: what do they have in common and how do they differ?

Children:-They have the same shape: both the ball and the balloon are shaped like a ball. And they differ in color: the ball is yellow and blue, and the balloon is yellow and red. They also differ in size: the ball is small, and the balloon is large. Their purpose is also different: the ball is a toy, and the balloon is an aircraft.

Educator:- Compare hedgehog and Christmas tree.

Children:-Spruce looks like a hedgehog: a hedgehog is in needles, a Christmas tree is also, and they “live” in the forest. They differ in size: the hedgehog is small, the tree is larger than the hedgehog. They are also of different colors: the hedgehog is gray, and the Christmas tree is green. The hedgehog is an animal, the tree is a plant.

In more prepared groups, work can be organized as follows: each child chooses one of the pictures at will and talks about it, and the rest of the children complete it.

2) Educator:- Look at the picture. Why do you think a fox and a carrot are connected with a thread?

Children:- They're both orange.

Educator:- Well done! Now take your “magic” pencils and connect objects of the same color with “magic strings”.

Children within 1 - 2 minutes draw lines on their own. Then they discuss aloud who completed the task.

Educator:- Tell me, what pictures did you connect? Why?

Sample responses from children:

Children:- Carrot and fox are orange.

Children:- I connected the chicken and the moon because they are yellow.

Children:- The tomato and the ladybug are red.

Children:- The frog and the apple are green.

The teacher helps the children correct their mistakes. In conclusion, it is important to praise those who tried: “Aizat did a great job - he drew all the lines correctly! Leah is also great - she found and corrected her mistake!

3) Children complete the task on their own.

Educator:- And now you have to find signs of difference and correct the mistakes of the Dunno artist.

Independent work can be carried out in the form of a competition game: who will find distinctive features faster and more. The winners receive prizes.

IV. Physical education "Look at both!"

Children line up no more than 7 - 10 people). The driver is chosen with the help of a counter or by appointment. He is invited to remember the order in which the children are. After the driver turns away, the children rebuild. The driver must determine what has changed and restore the broken order. The arrangement can be linear, circular, chaotic - depending on the level of complexity that the teacher wants to offer.

V. Strengthening the ability to highlight the properties of objects.

1)Conversation vegetables. Solving riddles.

Educator:- What vegetables do you know?

Educator: What is growing in your garden? for example, at the cottage)?

Educator: What vegetables are they talking about? How did you guess?

a) The red nose has grown into the ground,

And the green tail is outside.

We don't need a green tail

All you need is a red nose.

Children: Carrot

b) In the summer in the garden -

fresh, green,

And in winter in a barrel -

Yellow, salty.

Children: cucumbers

c) Round side, yellow side,

Sits on the garden bed.

He is rooted firmly into the ground.

What is this?

Children: turnip

d) He is big, like a soccer ball,

If ripe, everyone is happy.

It tastes so good!

What ball is this?

Children: Watermelon

Children explain by what signs they guessed what they were talking about: by color, shape, size, taste, etc. Guessing pictures depicting vegetables are displayed on the flannelograph. You can arrange a "confusion": expose pictures with errors, and then parse them.

2) The game "What does it look like?".

On the flannelgraph - pictures of vegetables.

Educator:- Well done! You are very good at solving riddles. Now look carefully at the pictures and choose geometric shapes that resemble these vegetables.

Sample responses from children:

Children:- Carrots are orange, shaped like a triangle, - I will put orange (Red) triangle.

Children:- The turnip is yellow and round. I choose the yellow circle. Etc.

Educator:- What did you like? What seemed difficult?

Educator:- Look: Dunno began to draw a pattern on the page below. Try to finish it at home.

Numerous properties of things (consumer items) that have certain qualitative and quantitative structures in the process of consumption are manifested in many ways. These manifestations realize quality through the multilateral relationship of objects and specific consumers in the appropriate social and climatic environment.

To establish the actual structure of the properties of consumer goods, it is necessary to know not only the function of things (materials), but also the specific features of the conditions for their functioning at the stages of consumption.

So, for example, synthetic floor coverings can be used both in the premises of the first, second, third floors, residential buildings, and in the halls and classrooms of schools, in corridors, in workshops, etc. Traffic intensity, traffic direction, operational loads are largely degrees will determine not only the values, but also the general structure of consumer properties.

In commodity science, as a rule, the functioning of clothing and footwear products is considered without separating the functional properties into an independent group, although in reality their functional properties are outlined quite clearly.

When materials and various consumer goods are consumed, their exploitation takes place, during which the utilitarian or operational properties of the product are manifested, as well as its appearance (aesthetic properties). The accepted division of properties is explained by the peculiarity of objects and their manifestation in the surrounding physical and social environment. Therefore, consumer properties of products can be conditionally divided into operational and aesthetic. Performance properties combine functional and ergonomic properties, safety and durability of commodities.

In turn, the structure of functional properties is determined for a specific consumer item, based on the specifics of its function. So, for a vacuum cleaner, the main functional property will be the dust-collecting ability, and for a household refrigerator, the ability to preserve food products. For a number of products and materials, the functional properties will be determined by their resistance to external factors (acid resistance, abrasion resistance, water resistance, etc.), as well as impermeability to heat, water, etc. Due to the significant specifics of the functioning of many consumer goods, this feature for specific objects of study.

On fig. 1.2 shows a block diagram of the distribution of groups of consumer properties of polymer (synthetic) floor coverings (PVC - linoleum, tufted roll materials). It can be seen from the figure that the selected groups of safety and durability properties, functional and ergonomic properties are assigned to operational properties, and the appearance property is manifested through the pattern and relief of materials.

As the research results show, the functional properties of polymeric synthetic materials for floors are manifested through the properties of resistance to external factors and impermeability (Fig. 1.3). The resistance property of flooring materials combines three main groups of properties that are manifested through external influences, namely: abrasion, deformability and destructibility. Abrasion is evaluated through the resistance (resistance) of the coating to abrasion by reducing the mass of the sample

Rice. 1.2.

polymer coatings for the floor or the thickness of its front layer. The deformability is determined by the elasticity, elasticity, recoverability and hardness of the material, and its destructibility - by the strength and stability of linear-volume dimensions.

The chemical resistance of floor materials is manifested as acid resistance, alkali resistance, grease resistance, water resistance, fuel resistance (Fig. 1.3). The determination of the degree of exposure to chemicals is recorded as the change in the resistance of samples to abrasion before and after exposure to the test substance.

The biological stability of polymer materials for floors is determined by their resistance to the action of molds (fungi), other microorganisms, and moths. It is very important to establish the degree of moth resistance of fibrous substrates, which are made using mixtures of fibers. Their moth resistance will determine the stability of the biological resistance functional property.

The heat and sound insulation properties of materials for floors will be determined by their heat and sound conductivity and heat and sound absorption, which depend on the presence and type of the substrate (base), the porosity of the polymer layers and their number, on the density, elasticity and elasticity of the material, and some other factors (see Fig. 1.3) . These properties are evaluated by the corresponding coefficients or absolute parameters.

Ergonomic properties (Fig. 1.4) of flooring materials combine hygiene and ease of use.

The hygiene of flooring materials is determined by the presence and duration of the smell, as well as electrification. The determination of the presence and duration of the smell is most realistically controlled by the organoleptic method, using experts for this purpose, and electrification with the help of a number of devices. Ease of use is determined by the cleanability and spreadability of the material under study. The cleanability of materials depends on many operating factors, the type of cleaning and is characterized by non-contamination and porosity of the material, and

Rice. 1.3. The block diagram of the functional properties of its spreading is determined by the ease of cutting, fit and ease of connection of the coating sheets (glues, high-frequency currents, welding or thermal soldering).

Rice. 1.4.

The safety of polymeric (synthetic) materials is characterized by their potential impact on humans and the environment and is manifested through environmental, biological, mechanical and fire safety (Fig. 1.5).

The biological safety of materials is determined by sweating and volatile substances released from the polymer layer, which are characterized by toxicity, carcinogenicity, mutagenicity and embryogenicity. The degree of impact of volatile substances released from materials on the human body and the environment will depend on the quantitative and qualitative composition of the released components (gas chromatography, gas-liquid chromatography or chromatography-mass spectrometry method).

Rice. 1.5.

The mechanical and fire safety of flooring materials combines the properties of incombustibility and non-slip properties. The incombustibility of materials is related to their flammability and self-extinguishing and is characterized by the corresponding temperature. The slipperiness of materials is estimated by the slip coefficient of the pair: floor material - shoe sole material.

Environmental safety is assessed by the possibility of reusing both technological production waste and polyvinyl chloride materials that are out of service. Waste-free production of polymer floor coverings and their disposal after the completion of the operation process provide the property of recyclability.

The durability property is characterized by the wear resistance of materials and their resistance to aggressive environments during operation, as well as the safety of materials (Fig. 1.6).

Rice. 1.6.

The wear resistance of the material will depend on the composition of the polymer layer and the type of wear (abrasive and fatigue), the specifics of moisture (with CMC), and other factors that appear during operation. The persistence of polymeric materials for floors is evaluated by the stability of functional and ergonomic properties (see Fig. 1.6). The indicator of storage is the coefficient of aging of the material, which characterizes the degree of reduction of specific values ​​of the most important functional properties over a certain period of time.

The structure of consumer properties of most consumer goods combines 14 groups of properties of the third level. Therefore, for an experimental study of quality, it is necessary to identify the most significant properties of consumer goods. The definition of significant properties will allow for rational studies of the quality of commodities.

We have studied the structure of consumer properties on the example of PVC linoleums by questioning the opinions of merchandisers, hygienists and technologists working in the field of production and consumption of these materials. The questionnaire sheets included the following properties of PVC linoleums, which manifest themselves during operation (Table 1.3).

Table 1.3

List of consumer properties and their codes

The list of consumer properties of PVC linoleums was compiled taking into account the opinions of experts. When filling out the questionnaire, specialists determined the place of each of the properties according to the principle of preference in a paired comparison of the selected 14 properties. The results of an expert assessment performed by three groups of specialists were processed by the rank correlation method.

The transformation of the matrix of ranks according to personal data was carried out taking into account the principle of the sum of ranks in each line, which should correspond to the value L(lLtl) = 105. The matrix we obtained is shown in Table. 1.4.

Consumer properties ranking results

Based on the summarized data in Table. 1.4 calculated the coefficient of concordance (W) :

where m = 3 (number of teams of specialists); n = 14 (number of variables);

The actual value of the concordance coefficient differs markedly from zero (W = 0.866), therefore, it is believed that the opinions of specialists regarding the significance of properties are in significant connection. It should be noted that experts rank “facts” with some difference, since the found value of W differs markedly from unity. In this regard, it became necessary to check the significance of the concordance coefficient according to the X 2 criterion:

The tabular value of X 2 for the 5% significance level is Xk P = 22.362; and its calculated value is 33.774. Thus, the results obtained confirm that the degree of agreement of opinions is quite high.

Based on the calculation data, we built an average a priori significance diagram for the estimated properties. The diagram of the importance of properties is placed on fig. 1.7.

Rice. 1.7. Diagram of the significance of consumer properties As can be seen from the diagram, the significance of consumer properties is most emphasized by experts for the properties of durability, biological safety, non-polluting and cleanability. The parameters of significance for the properties of odor intensity, resistance to mechanical stress, heat impermeability, stability of operational properties and appearance are very close. Properties that have a total score

Weight for significant consumer properties was established by an expert method according to the principle of a fixed sum. The results of assessing the weight of the most significant properties are presented in Table. 1.5, commodity experts, hygienists and technologists acted as experts.

Table 1.5

Summary data on expert evaluation of consumer properties

• Applied statistics. Fundamentals of econometrics: Textbook for universities. In 2 vols. 2nd ed., corrected. Vol. 1: Ayvazyan S. A., Mkhitaryan V. S. Probability theory and applied statistics. M., 2001. S. 301-306, 442-503.