Topic 1. FEATURES AND PROPERTIES OF OBJECTS

Absolutely all objects surrounding us have signs and properties. What is an attribute of an object?

An attribute of an object is a distinctive property of an object. For example: a green car: a car is an object, and green is a sign, a property that distinguishes it from other similar objects (for example, from a red car).

Items differ in color, shape, size, purpose, smell, material from which they are made and in other ways. To determine the attribute of an object, you can ask the question: what is it?

Let's try to highlight the essential (that is, the main) features of an ordinary notebook. Tell us what it is, a notebook: what material is it made of, what size, what thickness, what is it intended for? If you were able to talk about a notebook, then you were able to highlight the features by which it differs, for example, from a pencil. So, one of the main features of an object is color. Let's define the color like this:

And the first thing we need to repeat is the colors of the rainbow.

Now name as many things as you can:

a) red

b) green

c) black

d) blue.

Look carefully at the picture and say which vegetables and fruits are colored incorrectly. How would you color them?

Well, here we are convinced that you are well acquainted with such a sign of objects as color.

The next important attribute of an object is its shape. We define the form like this:

What shape are the objects? Round, square, what else?

Name as many things as you can:

a) round shape;

b) oval;

c) square;

d) rectangular.

Look closely at the table. Which of the fruits and vegetables lying on it is of such a shape as shown in the diagram: and this color:

The next important attribute of an object is its size. We will denote the size as follows:

And now correctly name the large and small object in pairs. For example, an elephant is a baby elephant.

Highlighting the signs of objects, for example, color - red, yellow; shape - round, square; size - large, small - we compare objects with each other.

Now try with notation
indicate the signs of such objects: a blue cube, a big red ball, a tall yellow house. It can be defined, for example, like this:

- Red Apple.

There are many more signs of objects. We have presented them for you in the table. With the help of this table, you can identify the features of many objects.

TABLE OF DESIGNATIONS OF OBJECT SIGNS

Show the objects that have a smell in the picture. Try to label them with a table.

We examined such important features of objects as color, shape, size, familiarized ourselves with the table of designations for attributes of objects, and tried to apply these designations. And now let's try to perform CONTROL WORK. With its help, we will check how you have learned the material.

Task 1. Look carefully at the picture and complete the task. And adults who help you answer test questions will enter your answers on a special answer sheet.

Task 2. Guess the riddles about what Nyusha bought at the market?

1 riddle

2 riddle

3 riddle

4. Make up your own riddle about what grows in the garden

Task 3.

Task 4.

Task 5.

Task 6.

Find the picture you want in each box.

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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 polymeric floor coverings and their disposal after the end of the operation process provide a recyclable property.

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 through questioning the opinions of merchandisers, hygienists and technologists working in the 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

	Property name
	Biosecurity
	Biological resistance
	Appearance
	wear resistance
	Odor intensity
	Incombustibility
	Non-contaminating and cleanable
	Heat impermeability
	Sound impenetrability
	Chemical resistance
	Service life (durability)
	Stability of operational properties (preservation)
	Resistance to mechanical stress
	electrified

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

Ranks in R ; . properties of PVC linoleums

Hygienists

Technologists

Commodity experts

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

	Name properties		Significance properties	gravity properties	Significance of properties, taking into account weightiness
	Durability (service life)
	biological security
	Non-contamination and cleanability
	Intensity
	Resistance to mechanical influences
	Heat impermeability
	Stability of operational properties
	Appearance

• 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.

One of the most important conditions for the effectiveness of the educational process is the prevention and overcoming of the difficulties that younger students experience in their studies.
Among the students of general education schools there are a significant number of children with insufficient mathematical training. Already by the time they enter school, students have different levels of school maturity due to individual characteristics of psychophysical development.

Mathematics, as a subject, requires the child to have certain abilities: the ability to analyze and generalize the material, the ability to think abstractly, in abstract categories.
It is these abilities, necessary for the successful mastery of mathematical knowledge, that some younger schoolchildren have not developed enough.

The heterogeneity of the composition of students in the primary general education school, different opportunities in the assimilation of mathematical knowledge requires a differentiated, individual approach to children in teaching them mathematics. It is necessary to search for effective didactic techniques to correct the difficulties experienced by students, taking into account the developmental characteristics of children and their assimilation of mathematical knowledge.
Comparison of two groups of objects causes significant difficulties for these children. They can determine the difference relations only in those cases when the objects in the groups are one-to-one (visually) correlated.
Reduced activity of perception is expressed in the fact that children do not always recognize familiar geometric shapes if they are presented in an unusual perspective, upside down.

Difficulties in teaching mathematics cannot but be affected by such features of these students as reduced cognitive activity, fluctuations in attention and working capacity, insufficient development of basic mental operations (analysis, synthesis, comparison, generalization, abstraction), and some underdevelopment of speech.
The content of the elementary school program involves comparing objects and groups of objects based on the knowledge of students about the color, shape and size that they receive in the preschool period. However, students with mental retardation come to grade 1 either with insufficient knowledge about color, shape and size, or they do not have this knowledge. There is a contradiction between the requirement for students' knowledge of color, shape and size and the insufficient formation of this knowledge among students with mental retardation. The problem is how to fill in the missing knowledge about color, shape and size, taking into account the peculiarities of perception of students with mental retardation in lessons and remedial classes in mathematics.

General properties of objects and their manifestations

The concept of "General property of objects"

Properties expresses the characteristic of an object, which determines its difference or commonality with other objects and reveals in its relation to them. Each item has many properties. The properties of objects include: mass, time, color, smell, shape, length, area, speed, hardness, strength, temperature, etc.
If we consider sets of elements of different nature, then we can see that the elements of each set have some common properties, if only because they are included in the same set: for example, a set of objects that have color, or a set of objects that have length. A common property is a property that is common to all items in a given set. A specific or individual manifestation of a common property in each element of the set is called the value of this property. After all, each object of one or another set, for example, has its own color or length, i.e. color or length value.

If color values ​​carry a qualitative characteristic, giving rise to the answer to the question "What color?" (green, red, blue, etc.), then the length value, in addition to the qualitative characteristic (long - short), carries a quantitative characteristic, giving rise to the answer to the question “How much?”, And they can be written in a certain way. And the answer to the question "How much?" suggests: "the same", "a lot" or "little", but compared to what?
For example, the area occupied by planted potatoes in a summer cottage occupies “the same amount” (relative to the area of ​​beets) as the area of ​​planted beets, “a lot” (relative to the area of ​​radishes) compared to the area of ​​planted radishes, but “small” (relatively area of ​​the dacha) compared to the area of ​​the entire dacha. Here we are talking about the external certainty of the subject, which can be expressed in quantity, if criteria for comparison are found.
Lengths of objects can be compared by an application, masses by weighing, capacity by capacity, time by the duration of an event, and so on. It should be noted that only homogeneous properties of objects are compared, i.e. those that characterize one real state of an object: either linear extension, or inertia, or three-dimensional extension, or the duration of an event, etc.

If, for example, the length of the Christmas tree occupies - on a straight line "the same" space as the wavelength, "a lot" of space compared to the length of the arrow, but "little" space compared to the length of the stick, then the value of the length of the Christmas tree can be expressed by the number of waves and is recorded in a certain way - (I) waves; number of arrows and recorded - (II) arrows; the number of sticks and is written - (I) sticks. In this case, the wavelength, the length of the arrow, the length of the stick are called units of the length of the Christmas tree
The comparison that “answers” ​​the question “Are the lengths of the herringbone and the wave equal?” Establishes an equal-size relation (the herringbone is equal in length to the wave). The equal-size relation is reflexive, symmetrical, transitive, i.e. is an equivalence relation, and therefore generates a partition of the set of objects into equivalence classes of objects equal in length.

A comparison that "answers" the questions: "How many times is the length of the Christmas tree greater than the length of the arrow?" and “How many times is the length of the Christmas tree less than the length of the stick?” sets the multiplicity ratio. Multiplicity relations are antisymmetric and transitive, i.e. is a relation of nonstrict order.
If you ask the question: “How much is the length of the Christmas tree more than the length of the arrow and less than the length of the stick?”, Then the answer will also be expressed in quantity and will be written in a certain way: on the arrows and on the Christmas tree. A comparison that "answers" the question: "How much longer is the length of the herringbone than the length of the arrow and less than the length of the stick?" Establishes a difference relation. The difference relation does not obey the property of transitivity, but it generates the relation "greater than" (or "less than"), which is a relation of strict linear order.

Thus, the length of the Christmas tree gives rise to answers to the questions: "What is the length of the Christmas tree compared to the wavelengths, arrows and sticks?" (equal, long or short), “How many waves, arrows and sticks fit along the length of the Christmas tree?” (wave, arrows and sticks) and is written in a certain way.
Properties of objects: mass, time, length, area, speed, temperature, etc. - are continuous if any adjacent parts of the object have the same value; their meanings give rise to answers to the questions "Which one?" (equal or relatively opposite) and "how much?" (relatively specific); and they can be written in a certain way. Such properties are called quantities.
Thus, the general properties of an object express the characteristic of the object, which determines its difference or commonality with other objects.

Characteristics of the properties of objects size, color, shape

Value

The emergence and initial development of the concepts of magnitude and its measurement were dictated by the tasks of natural science. In the process of life practice, it became necessary to consider sets of objects that are characterized by a common continuous property quantitatively (division into component parts) so that in its manifestation this property is different for each element of the corresponding set. This property is called magnitude.

It is historically known that the concept of magnitude arose as an abstraction of some properties of real objects and phenomena, the measurement of which led to the concept of number.

“A quantity is everything that can be more or less,” said ancient Greek mathematicians.
“A set of quantities is something to which the concepts of more and less are applied, but not exactly measurable” - the opinion of Academician A.N. Krylov (1863-1945).
“A value is everything that can increase and decrease,” is the definition of a corresponding member of the St. Petersburg Academy of Sciences G. Darboux (1842-1917).

From the foregoing, it is possible to formulate signs for determining the size of an object.
The value is a generalizing concept of continuous special properties of an object, is its abstraction. In other words, a quantity is an abstract concept that expresses qualitatively and quantitatively a continuous property of an object. Quality is determined by equality (same) or relative opposite (large - small, heavy - light, high - low, thick - thin, long - short, etc.), the quantity is determined relative to the chosen unit of magnitude. Thus, abstraction from the properties of an object gives rise to the concept of a quantity, the real essence of which is determined by the real properties of the object.

Therefore, from the point of view of reality, the magnitude of an object is understood as a property of an object, and from a formal point of view, a formal record of the magnitude (nominal number). With this approach to the concept of magnitude, one can find "points of contact" between all existing interpretations of the concept of magnitude.
A value is a common continuous property of a set of objects, the value of which is generated by answers to the questions “What?” (equal or relatively opposite and "how much?" (relatively specific) and they can be written in a certain way.
This definition of magnitude is built constructively: through the genus and specific difference. The generic concept of magnitude is “a common continuous property of the population”, the specific difference is “the values ​​​​of which generate answers to the questions“ Which one? (equal or relatively opposite) and "how much?" (relatively concrete) and they can be written in a certain way. The formulated definition can be used to recognize the size of an object.

Colour

Color is also a common continuous property of a set of objects, but its values ​​generate an answer only to the question: “What color of each of the set of objects is red? blue? green? or other?" (relatively not the opposite). Therefore, Color is not a quantity;

Blue color (blue) is a common continuous property of a collection of objects, and its values ​​generate an answer to the question: “What is the blue color of each of the collection of objects the same? Dark or light? (equal or relatively opposite). But to the question: "How many units are contained in the blue color of each of the totality of objects?" there is no answer, since the unit of blue color is not defined (not invented). Blue is not a value. Although, if you enter a unit of blue color intensity and build a notation scale for each blue value (measurement scale), then the blue color will become a value.
The magnitude of objects in the form of representations enter the life of a younger student when performing exercises, measuring work and solving word problems. The received ideas about the sizes of objects already in the basic and secondary school are replaced by strict definitions based on axioms. At the same time, the concept of magnitude and its measurement may remain beyond the understanding of schoolchildren. Therefore, already in elementary school, it is necessary to reveal the real and formal essence of the concept of magnitude and highlight the main features of its manifestation.

• The value of an object as an abstract concept expresses a continuous property of an object, since any adjacent parts of an object have the same value.
• The size of the object gives rise to the answer to the question "What?" (equal or relatively opposite: large - small, heavy - light, high - low, thick - thin, long - short, strong - weak, etc.) - a qualitative characteristic.
• The size of an object is determined by the quantity (characteristic of division into constituent parts) in a certain way.
• The magnitude of an item has a unit of magnitude that can be subdivided.
• The size of the object gives rise to the answer to the question "How much?" relatively concrete, and its value can be written in a certain way (formally) - a quantitative characteristic.
• The magnitude of an object can be compared with a homogeneous magnitude (comparability property). Comparison, which determines equal values ​​of a quantity, establishes the ratio of equal-sizedness on a set of objects for a given value. A comparison that determines how many times one value of a quantity is greater or less than another establishes a multiple ratio. A comparison that determines how much one value of a quantity is greater or less than another establishes a difference relation. A comparison that determines whether one value of the value of another is greater or less than establishes a relation of strict linear order.
• The value, setting the equal-size relation on the set of objects, generates a partition of this set into equivalence classes of equal-sized objects.

The form

By spatial representations we will understand sensory-visual images associated with the shape, size and relative position of geometric figures in space (on a plane), which are reproduced in consciousness without direct impact of objects on the senses.
Children are not interested in a stationary object, but in its change, movement, inclusion in new connections and relationships, the possibility of “interacting with it” through various forms of visual interpretation and constructive geometric activity. In addition, the world around the child is full of objects that have the geometric shape of a cube, parallelepiped, cone, cylinder, ball, but no segments, rays or straight lines.
From a philosophical point of view, any object of reality is a unity of content and form: “Content is the unity of all the constituent elements of an object, its properties, internal processes, connections, contradictions, tendencies. Form is a way of existence and expression of content. Form and content in each specific object are inseparable from each other. Form is the unity of external and internal. It is the structure of the object. The Great Soviet Encyclopedia gives several meanings for the term "form":

1. outline, appearance, contours of the subject;
2. external expression of any content;
3. a device for giving something a certain shape;
4. clothes uniform in color, cut according to other characteristics.

We will understand the form as the main component of spatial representations as the outline, appearance, contours of an object.
Thus, from the foregoing, we can conclude that the value is a common continuous property of a set of objects, the values ​​of which generate answers to the questions “What?” (equal or relatively opposite) and "How much?" (relatively concrete) and they can be written in a certain way.
Color is a common continuous property of a set of objects, its value generates an answer to the question “What color of each of the set of objects is red? blue? green? Or other?" Color is not a quantity.
Form is a property of the objects of the surrounding world, the unity of the external and internal. It is the structure of the object.

Violation in the perception of the properties of objects in junior schoolchildren with mental retardation

Even before school, children accumulate a large number of ideas about the shape and size of various objects. These representations are a necessary basis for the formation of important geometric representations in the future, and then concepts. Constructing various buildings from “cubes”, students pay attention to the comparative sizes of objects (expressing this with the words “more”, “less”, “wider”, “narrower”, “shorter”, “higher”, “lower”, etc. .).

In play and practical activities, there is also an acquaintance with the shape of objects and their individual parts. For example, children immediately notice that the ball (ball) has the property of rolling, but the box (parallelepiped) does not. Students intuitively associate these physical properties with the shape of bodies. But since the experience of students and the accumulation of terminology is random, an important task of teaching is to clarify the accumulated ideas and assimilate the corresponding terminology. To this end, it is necessary to systematically offer a variety of examples. The relationship between objects, expressed by the words “same”, “different”, “larger”, “smaller” and others, are established either on real objects (strips of paper, sticks, balls, etc.) or on their images (drawings, drawings). Each of the examples cited for this purpose should clearly identify the main feature by which these relationships are clarified. For example, when figuring out which of two shelves is "larger", it is important to ensure that both sticks are the same thickness (or the same length). In all cases, when comparing, it is necessary to select such items for which the "sign of comparison" is clearly visible, unambiguous and can be easily identified by the student.

For example, it is easy to compare two balls of different diameters and colors, but difficult (especially at first) - balls of different diameters and the same color. Students in this case often say: "The balls are the same" (meaning the color).
The result of the activity of students depends on the ability to determine the form. Therefore, the first exercises should be aimed at practical actions that require reliance on the shape of objects.
In the future, students determine the form visually using the method of trying on.
Only on the basis of long-term use of methods of trials and fitting in a variety of situations and on a variety of objects, students develop a full-fledged visual perception of the form, the ability to isolate it from an object and correlate it with the form of other objects.

The size as well as the form, students learn to distinguish practically. Acting with objects, they pay attention to the size, they begin to understand that the result of actions depends in many cases on the correct determination of the size of the object, i.e. the value becomes a significant feature for students.
In the process of action with objects, children gradually begin to highlight the value visually.
Based on the long-term use of samples and trying on, children develop a full-fledged visual perception of the value, the ability to isolate it, to correlate objects by size.
Thus, we see that the ways of developing the perception of size and the perception of form are the same. However, there are differences between them. Size is a relative concept. One and the same object in comparison with others can be perceived both large and small.

At the same time, the value has different parameters - height, length, width. Therefore, in addition to the general definition of “big-small”, there are private ones: “long-short”, “high-low”, wide-narrow”.
The perception of color differs from the perception of shape and size primarily in that this property cannot be distinguished practically, through trial and error. The color must be seen, i.e. when perceiving color, only visual, perceptual orientation can be used.
At first, when determining the color, trying on, matching by application, plays an important role. When two colors are closely adjacent to each other, students see their sameness or dissimilarities.
When students learn to identify colors by their direct contact, i.e. by superposition and application, it is possible to proceed to the selection by the sample, to the real perception of color.

It is known that not all students with mental retardation can correctly assemble an ordinary children's pyramid. If they collect, they very often make mistakes in the process of selecting rings, again and again they return to the beginning of work. This means that they do not notice “by eye” which ring is closer in size to the given one, they do not know the method of comparison by superposition, they do not know how to find the next ring, but they often pick up the first one that comes across. They do not have a stage of reflection, it is unusual for them to doubt the correctness of choosing the next ring. Comparison of a series of objects according to their size has a corrective value and requires special training. Only as a result of specially organized refinement, application of assessments in various situations under the guidance of a teacher, students with mental retardation will learn to notice and evaluate such features of objects as: volume, area, length, width, height.

It is difficult for a child with mental retardation to switch from a conclusion that has just been made to a new one. The main difficulty is that directly opposite judgments are made about the same subject. When comparing, first-graders cannot yet be distracted from the sizes of the objects that make up the aggregates. They consider the larger the set in which the objects are larger or it occupies a large area. Schoolchildren still do not know how to place them in a way convenient for themselves, to establish a certain order among them, to characterize the spatial relationship of these objects.
The perception of color differs from the perception of shape and size “in that this property cannot be distinguished practically, by trial and error. When perceiving color, you can use the visual perceptual orientation.
Based on this theory, the following disorders in the perception of the properties of objects in students with mental retardation can be distinguished:

• do not notice “by eye” which object is closer in size to the given one;
• do not know the method of comparison by superposition;
• when compiling a pyramid, they do not know how to find the next ring, they take the first one that comes across;
• they lack the stage of reflection;
• it is difficult for them to switch from the conclusion they have just made to another;
• cannot be distracted from the size of the objects that make up the aggregate;
• do not know how to place objects in a convenient way for themselves;
• do not know how to establish a certain order among them;
• do not know how to characterize the spatial relationships of these objects.

These violations must be corrected and corrected.

Appendix 1 "Collection of exercises aimed at forming ideas about the general properties of objects in students with mental retardation in mathematics lessons"

In science, such concepts as "property" and "attribute" are often used. What do they stand for?

What is a property?

From a scientific point of view, a property should be understood as some attribute of an object that regularly manifests itself. For example, if it is a steel spring, then this may mean that it has such a property as "springiness". Which, in turn, can consist of a large number of other, "local" properties - for example, elasticity, sharpness, durability, etc.

The concept under consideration can either predetermine completely unique characteristics of an object, or form certain criteria for combining the corresponding object into one group with some others - perhaps not similar in essence. Especially if their functionality is close.

For example, from the point of view of applicability in mechanical engineering, elastic springs can be considered as parts belonging to the same category with equally elastic tires. Structurally, they are completely different products. But in terms of elasticity and, as a result, functionality, they are very close.

The properties of certain objects largely depend on how they are used or studied. For example, elasticity is, first of all, a physical property of a spring. In turn, if it is made of stainless steel, then it will acquire a chemical property - resistance to oxidation. From the point of view of mechanical physics, a metal spring has, as we noted above, "springiness". But from the point of view of electrodynamics, it will have the property of conductivity - since it will be able to conduct electric current.

Properties in many cases are amenable to adjustment, that is, they are fundamentally changeable. For example, if a spring is placed in a container at a very low temperature, its elasticity may be significantly reduced and it will become brittle. From this point of view, the property of springiness can be considered in this case as a temporary attribute that is stable only under certain conditions.

What is a sign?

From the point of view of science, a sign should be understood as a certain condition (a set of conditions) for identifying an object or assigning it to a particular category. For example, a spring has such features as: helicity, the presence of a metal base, the presence of annular coils at both ends (which gives the spring stability).

An object can have many attributes, as well as properties. Among them, the main ones (for example, the spirality of the spring) and “local” (for example, the same diameter of the coils of the spring spiral) can be distinguished.

sign is a constant attribute of an object. Basically, it cannot be corrected. If it is significantly changed, then the object will become different, and it will legitimately be attributed to a different category. For example, if a spring is stretched under conditions of exposure to a very high temperature - as a result of which it ceases to be helical, then it will turn into a wire.

Comparison

The main difference between a property and a sign is that the first is an attribute that can be changed, and this or that object will not fundamentally change its purpose, and, most likely, its structure will not undergo significant adjustments. In turn, a sign is a key condition for identifying an object or its assignment to a certain category. If it changes, the object will become different.

Obviously, the properties of objects are complemented by various features, and vice versa. At the same time, the presence of certain properties in any object is largely determined by its features. And if the latter change, the former will also be corrected.

Having determined the difference between a property and a sign, we will reflect the conclusions in the table.

Item property is the hallmark of an object. It is necessary to teach the child to highlight as many properties as possible from one object. For example: the ball is red, has the shape of a ball, rubber, toy, etc .; apple - green, sweet, fruit, etc .; cube - gray, wooden, has the shape of a cube, a toy, etc.

Comparison makes it possible to detect common properties of objects, highlight similarities and differences.

The ability to highlight the properties of objects forms students' ability to capture patterns.

For the development of the creative abilities of children, it is useful that they independently come up with riddles about the properties of objects, make sequences and patterns, and guess the rules for the arrangement of objects and figures invented by other children. For example, you can offer them some sequence, intentionally breaking the rule. The task of children is to determine the rule and find where it is violated.

1. What do all items of the 1st row (2nd, 3rd row) have in common?

2. What item is located in the 2nd column and in the 3rd row? What colour is he?

3. Name each yellow item.

4. Circle all the yellow objects with a line.

5. How do the items in the 1st line differ from each other? (The shape, the material from which they are made, etc.)

6. What do all items in the 1st column have in common?

7. Guess the item. This is a green toy. What is it?

8. Guess the object. It is located in the 3rd column, but neither red nor green. What is this subject?

9. How many blue circles are drawn below the table? How many big ones, how many small ones? How many red and green? Blue and yellow? How many non-red circles? How many are not blue and not green?