Form as a mathematical concept. Mastering the shape of objects and designating it with a word The meaning of the development of ideas in preschoolers

30.01.2022

Sensory education in the classroom is the basis for organizing the sensory experience of children. It is in the classroom that all conditions are created for the systematic management of the formation of sensations, perceptions and ideas of children.
The ability to consider, perceive objects and phenomena is formed successfully only when children clearly understand why it is necessary to consider this or that object, to listen to certain sounds. Therefore, teaching the perception of various objects and phenomena, it is necessary to clearly explain to children the meaning of their actions. This meaning becomes especially clear to children if they then use their ideas in practical activities; in this case, the perception of children becomes more conscious and purposeful: after all, if you do not accurately examine the object, then it is difficult to depict it or construct it. In the process of reproducing an object in a particular activity, the already formulated ideas of children are checked and refined. In this regard, the main task of sensory education is to form in children such skills to perceive and represent objects and phenomena that would contribute to the improvement of the processes of drawing, design, labor in nature, etc.
Thus, sensory education should be carried out in close connection with a variety of activities.
When teaching children to draw, sculpt, build, the teacher must at the same time pay special attention to the development of their perception, the ability to analyze, generalize, etc. Therefore, it is more useful to offer children to build not one or two beautiful houses, but a number of simple, but in a certain
system of increasingly complex houses. This will contribute to the formation of generalized ideas about houses, generalized skills to build houses in general, and not just one, even a very beautiful house. The same applies to visual activity.
Visual activity is closely related to sensory education. The formation of ideas about objects requires the assimilation of knowledge about their properties and qualities, shape, color, size, position in space.
Children define and name these properties, compare objects, find similarities and differences, that is, perform mental actions.
Mastering the content of this or that activity, children learn to depict more and more complex objects and phenomena in the drawing, to create more and more complex structures. Their knowledge and ideas about these subjects are expanding and deepening, new skills and abilities are being formed.
A child can create an image provided that he imagines the object that he wants to depict, that he owns such a set of movements that allow him to convey the shape of the object, its structure. These movements are made under the control of visual perception.
We call the specially organized perception of objects in order to use its results in one or another meaningful activity. Examination is the main method of sensory education of children. In the process, his children master the ability to perceive such properties of objects and phenomena as size, shape, color, etc. All these properties constitute the content of sensory education.
The content of sensory education must be consistent with the content of children's activities. This means that teaching children to perceive objects, the ability to analyze them, compare them should be consistent with the subsequent process of visual, constructive
or other activity. Otherwise, it is significantly reduced
the effect of learning and certain difficulties are created when children solve visual, constructive and other tasks.
A child in life is faced with a huge variety of shapes, colors and other properties of objects. It is still very difficult for him to understand all this diversity, and he needs the help of an educator (adult). The educator organizes the sensory experience of the child, using a certain social experience.
The task of the teacher is to bring the children to the realization of the need for preliminary detailed acquaintance with the subject, to organize an examination of this subject before the start of productive activity.
Different kinds of productive activity are connected in a special way with sensory processes. The main action in each of them is the execution of something: a construction (building), a drawing, a song, the pronunciation of words or a coherent text. In some cases - when singing, playing a musical instrument, reading a text by heart - the child's actions are preceded by the perception of a similar action, the perception of a sample. When they then act themselves, they listen to (perceive) their performance, and often the performance of other children.
In a similar way, designing, drawing, modeling can be carried out on the basis of the perception of the process of creating a building, drawing: children learn and repeat the actions of an adult and get a similar result.
During the classes, the children became convinced by experience that a preliminary examination of an object contributed to its correct reproduction in a drawing, facilitated construction, etc. The examination of an object began to act as a necessary link preceding the actual performing activity. Children developed the ability to divide the specific task of constructing an object or its image in a drawing into more specific tasks and establish their sequence.
Examination of objects should be carried out in different ways, depending on its purpose. So, for example, when examining an object before designing, the main attention is paid to its design, to the main fasteners. In this case, the object is considered from different angles, which is necessary for the correct perception of its three-dimensional form.
When examining an object in front of the image in the drawing, the main attention of children is drawn to the contour, its main parts. In this case, the object is considered only from one side.
Despite the differences in the examination of subjects, depending on the subsequent productive activity, it is possible to single out common main points that are characteristic of many types of examination:
1. Perception of the integral appearance of the object.
2. Isolation of the main parts of this subject and determination of their properties (shape, size, etc.).
3. Determination of the spatial relationships of the parts relative to each other (above, below, left, right).
4. Isolation of smaller parts of the object and the establishment of their spatial arrangement in relation to the main parts.
5. Repeated holistic perception of the subject.
This method of examination can be applied to the analysis of any form of a wide variety of objects, so it can be called generalized.
If we compare the methods of examination used in constructive and visual activity with the methods of examination in the labor process, it becomes clear that different methods of examination give different ideas about objects. This is determined by the very tasks of the activity: in constructive and visual activity, children must reproduce all the main parts of the object being examined and their spatial arrangement, and for this it is necessary to have a fairly complete idea of both the whole object and its parts.
Thus, the methods of examination used in sensory education are diverse and depend, firstly, on the properties being examined, and secondly, on the objectives of the examination. Survey training should be carried out taking into account the age differences of children.
Sensory education, aimed at the formation of a full-fledged perception of the surrounding reality, serves as the basis for cognition of the world, the first step of which is sensory experience. The success of mental, physical, aesthetic education largely depends on the level of sensory development of children, that is, on how perfectly the child hears, sees, and feels the environment.
The child at each age stage is the most sensitive to certain influences. In this regard, each age stage becomes favorable for further neuropsychic development and comprehensive education of a preschooler. The smaller the child, the more important sensory experience is in his life. At the stage of early childhood, familiarization with the properties of objects plays a decisive role. Professor N.M. Shchelovanov called early age the “golden time” of sensory education.
In the history of preschool pedagogy, at all stages of its development, this problem occupied one of the central places. Prominent representatives of preschool pedagogy (J. Comenius, F. Froebel, M. Montessori, O. Dekroli, E.I. Tikheeva and many others) developed a variety of didactic games and exercises to familiarize children with the properties and characteristics of objects. The main task of familiarizing kids with the properties of objects is to ensure the accumulation of ideas about the color, shape and size of objects.
An analysis of the didactic systems of the listed authors from the standpoint of the theory of sensory education leads to the conclusion that it is necessary to develop new content and methods for acquainting children with the properties and qualities of objects in the light of the latest psychological and pedagogical research. The proposed classes are part of the general system of sensory education developed by such scientists, teachers and psychologists (A. V. Zaporozhets, A. P. Usova, N. P. Sakulina, L. A. Venger, N. N. Poddyakov, etc.) on the basis of modern didactic principles. At each lesson, the solution of problems is successively focused on the actual level of sensory development of children and is promisingly aimed at mastering a comprehensive program of sensory education in preschool childhood. The first principle is based on the enrichment and deepening of the content of sensory education, which involves the formation in children from an early age of a broad orientation in the subject environment, that is, not only the traditional acquaintance with the color, shape and size of objects, but also the improvement of the sound analysis of speech, the formation of an ear for music, the development of a muscular sense, etc. Taking into account the important role that these processes play in the implementation of musical, visual activity, speech communication, the simplest labor operations, etc.
The second principle involves the combination of teaching sensory actions with various types of meaningful activities for children, which ensures the deepening and concretization of pedagogical work,
avoids formal didactic exercises. In the process of these activities, the child is guided by the properties and qualities of objects, taking into account their importance in solving important life problems. In most cases, they do not act on their own, but as signs of more important qualities that cannot be observed (the size and color of the fruits are signals of their maturity). Therefore, the improvement of sensory education should be aimed at clarifying the meaning of the properties of the objects themselves.
The third principle of the theory of sensory education predetermines the communication to children of generalized knowledge and skills related to orientation in the surrounding reality. The properties and qualities of objects and phenomena are so diverse that it is impossible to familiarize a child with all of them without limitation, as well as to communicate to him knowledge about each of them separately. The correct orientation of children in the environment can be achieved as a result of specific actions to examine the size, shape, and color of objects. special value
represent generalized methods for examining a certain kind of qualities that serve to solve a number of similar problems.
The fourth principle involves the formation of systematized ideas about the properties and qualities, which are the basis - the standards for examining any subject, that is, the child must correlate the information received with the knowledge and experience he already has. Very early, the child begins to use his knowledge as a means of perceiving and understanding a new subject.
In its centuries-old practice, humanity has identified a certain reference system of sizes, shapes, and color tones. Their endless variety has been reduced to a few basic varieties. Mastering this kind of system, the child receives, as it were, a set of standards, standards, with which he can compare any newly perceived quality and give it a proper definition. Assimilation of ideas about these varieties allows the child to optimally perceive the surrounding reality.
The implementation of the above principles is possible already at the stage of early and preschool childhood.
When, how and in what sequence do children begin to distinguish the properties of objects? Does the practical orientation in the qualities of objects depend on their verbal designation, primarily on the words-names of size, shape, color; on the nature of the child's activities with these objects?
When determining the content and methods of work on sensory education with young children, the principles of the theory of sensory education were the starting points. Based on them, it was found out what properties can and should be introduced to children, what color tones, shapes, sizes of objects should be used and, most importantly, how the process of teaching children to perceive the surrounding reality should be built.
Thus, the main task of familiarizing kids with the properties of objects is to ensure the accumulation of ideas about the color, shape, and size of objects.

Download:

Preview:

Integrated lesson for parents

Theme: Walk in the woods.

Software content.

To consolidate children's knowledge about the shapes of objects;
To teach children to find among the objects around them a circle, a square and a triangle;
Teach children to find objects of the desired shape and color them by color.
Learn to work in a team.

Material and equipment.

Bibabo dolls: hare, mouse, hedgehog;
Massage path, hoops;
Recorded CDs: Russian folk joke "Sly Cat", music by E. Tilicheeva "Bunnies", music by V. Volkova "Walk";
Set "Learn to count";
Buckets of three colors depicting geometric shapes: triangle, circle and square;
Workbooks by S. Gavrin, N. Kutyavin, I. Toporkov, S. Shcherbinin “Getting acquainted with simple figures”;
Colour pencils.

Preliminary work.

Didactic games: “Pick up a figure”, “Assemble a pyramid”, “Cover up holes”, “Where is a circle, and where is a square”;
Drawing geometric shapes.

Lesson progress

The teacher puts a bibabo hare doll on his hand and hides it behind his back.

Educator. - Guys, today we will go for a walk in the forest, (the music “Walk” sounded and the children make movements to the music), and the teacher shows the bunny she hid.

Bunny. - Hello guys, I'm very glad that you came to visit me. Educator. - Hello, bunny. Why aren't you funny?

Bunny. - I was walking through the forest and I stumbled and dropped the buckets, from which everything fell apart, and it got mixed up that now I can’t collect everything.

Educator. - Bunny, don't worry, my guys will help you.

The teacher put buckets of different colors on three chairs, where figures are depicted: a triangle, a circle and a square. She gave the children a task: "Find a house for each figure." (Children collect all the figures in buckets to the music).

Educator. Let's check if we've got it all right. I take a red bucket with a triangle on it, Katya, what figure did we put in it?

Katia. - Triangle.

Educator. - Right.

When all the buckets have been checked, the children go further to the music of "Bunnies".(Children, together with the teacher, overcome the obstacle: jump over hoops, walk along the massage path).

Bunny. - We ended up at the hedgehog's house, it's his birthday today, he loves pictures very much, let's make him a present.

The teacher sits the children at the tables, on which sheets with the image of balloons and colored pencils were laid out.

Educator. - The hedgehog loves round balls very much, let's see who is holding a round ball in the picture, a chicken or a frog?

Alyona. - Chick.

Educator. - Right. Let's pick up a pencil and color those balls that the chicken is holding..

(The teacher goes between the tables and helps those children who do not succeed).At the end, all the pictures were hung on an easel.

You and I did a good job, I think the hedgehog will like it.

(The teacher takes a hedgehog).

Hedgehog. - Hello. What beautiful pictures.

Educator. - Hedgehog, these are the children wishing you a happy birthday.

Hedgehog. - Thank you. Guys, can you help one of my mice.

Educator. What happened, hedgehog?

Hedgehog. - My dear mouse washed the handkerchiefs and hung them up to dry, but the cunning cat ruined all her handkerchiefs.

Educator. - The guys and I will help her, let's go to the mouse home.

The teacher and the children went to the table, where there were already prepared multi-colored triangular handkerchiefs, in which holes were cut.

(The teacher put a bibabo mouse doll on her hand).- Hello, mouse.

Mouse. - Hello. (Answered she is sad).

Educator. - Mouse, we know what happened to you, don't be upset, the guys will help you, they will find round peas and seal the holes in your handkerchiefs. Guys, we will look for round peas with you and close all the holes. (The children collected the circles that werescattered around the table and under the table, and helped close the holes).And now we have to be careful, somewhere nearby is a cat. Spin around, spin around and turn into mice. The mouse is small, walks quietly.

The teacher puts a cat toy on a chair, turns on the music "Sly cat",

(children walk on tiptoes

A sly cat sits in the corner,

Lurking as if sleeping

Mice, mice, that's the trouble

Run away, who goes where.

(when the teacher takes the cat toy, the children run away to their parents.)

Educator. - Guys, you are all great today. Look what the animals left us. (The teacher tries to open the box, but she fails). Look, here is the letter and it says:

You tell a poem and get a surprise. Which one of you wants to tell a poem?

Katia. - The hostess threw the bunny,

Bunny left in the rain

Wet to the skin,

I couldn't get off the bench.

The teacher opens the box, from which he takes out educational games and distributes them to the children.

Appendix

To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com

Slides captions:

Presentation on the topic: "Formation of the perception of the shape of objects in children of primary preschool age." Performed by the teacher of the II qualified category Rodkina Vera Nikolaevna

Introduce children to geometric shapes: circle, square and triangle; - to teach children to find and distinguish between round, triangular and square objects; - to consolidate children's knowledge about the forms of objects in games and in the classroom for fine arts. Target.

The circle is our helper and friend. You can easily recognize the circle. And everywhere you will find it: The circle looks like the sun, It looks like a plate, like a cutlet, And like a cherry berry, And like a wheel, of course... Dasha has round glasses, Buttons on Masha's jacket, Ball, watermelon, watch, badge And the pig has a piglet!

Look, guys! Here is a square. A square has all four sides of the same length.

The big square said: “I am the elder brother of the squares!” The second is small, but proud too: “I am at least smaller, but younger!”

We connect the points along the ruler on the leaflet Three - we get the Triangle. We easily recognize him: Triangles - ears At the kitten on top; The triangular "nose" of the rocket, The sail of the yacht, the roof of the house, the "Corner hat" from the newspaper And the flag in Roma's hands.

Form is a sign of an object, accessible to visual and muscular-tactile perception.

In the form of an object, more or less typical features are distinguished: roundness or elongation, stability or dissection, symmetry of parts or asymmetry.

The specific tasks of mental education when getting acquainted with the form are:

Formation of ideas and knowledge about form as a sign of an object and beauty;

Development of the ability to see, distinguish, compare, group objects according to their shape;

· Development of the ability to see the form in combination with other signs in life, in objects of art;

Development of vocabulary and coherent speech and teaching children to use the exact names of forms and their features, figurative, expressive words, generalized words-concepts;

Teaching children how to apply knowledge about the form in a variety of activities;

· Education of cognitive interests.

The ability of a child to perceive, to see the form in an object is not innate, but is formed in the process of education and training.

Familiarization of children with the form as a sign of an object and a generalizing concept has a certain sequence, repetition and complication from one age group to another.

Junior group.

The teacher teaches children to see and distinguish objects by their shape, introduces the basic geometric shapes - a ball and a cube - and names them himself. The teacher organizes visual and tactile-muscular perception, cognitive actions with objects, teaches how to examine objects, test them in games, in classes with building materials, with toys.

In classes with an individual child or with a small subgroup, the teacher shows the ball and says: “This is a ball” - and performs actions with it, emphasizing its shape.

Cognitive practical actions should be performed repeatedly. The period of practical testing should not be shortened. In repeated classes, in games, the teacher again calls the figure and its features.

In subsequent lessons, in games, the teacher asks the children to show, bring. Put the balls in the basket. According to the action performed, he checks whether the children have learned the name and whether they correlate the word with the object. In the future, he exercises the children in the name of the form of the object.

By organizing games with balls and other toys, the teacher exercises the children in distinguishing them by shape and at the same time includes a new one - color - into the familiar and teaches them to distinguish balls by color. In the next lessons, the teacher offers balls of different sizes - large and small, then calls the words "big - small" and uses the word to reinforce the difference.

A lot of game activities are organized by the educator with objects of a cubic shape - he encourages to inspect the cubes, rearrange, move. Visually-motor perceiving the cube, the child feels the edges and planes and practically learns the features of this figure.

The definition of shape and size can already be included in one lesson, since the previous mastery of the shape of the ball contributed to the development of children's attention, the ability to look and see. Both in subsequent lessons and in games, the teacher exercises the ability of children to choose large and small cubes from building material.

Then the teacher organizes a comparison of the ball and the cube as two different figures.

In the future, he reinforces the idea of a ball and a cube in various classes, in games ..

Thus, educator ml. gr. in accordance with the program, teaches children to distinguish between a ball and a cube in shape and call them the exact word, teaches them to apply the acquired ideas in various activities.

Middle group.

The teacher consolidates ideas about the ball and the cube and improves the methods of sensorimotor examination of objects based on visual and tactile-muscular perception. Introduces children to new shapes: rectangle, square, triangle, cylinder - and teaches to distinguish between straight, naked, square, triangular objects. With the expansion and complication of the content, the requirements for the mental activity of children expand and become more complicated, and new qualities of cognitive activity are formed. The educator teaches to see the same form in objects of different content.

And in the middle group, the educator first introduces objects in which various forms are expressed, and especially those with which children need to be introduced in accordance with the requirements of the program.

The teacher introduces children to new figures in the usual and already familiar way for children.

The new quality of form as a common feature of many surrounding objects should be revealed on the basis of content familiar to the child.

Mastering ideas about the basic forms of objects, the ability to group objects according to their forms does not occur only in the classroom, in didactic games, it requires “practice” in life.

Introduction...…………………………………………………………………………2-3

Chapter 1……………………………………………………………..

1.1 Shape as a mathematical concept……………………………………………4

1.2. Psychological features of the perception of forms by preschoolers ...... .4-7

1.3. Pedagogical aspects of the formation of ideas about the form………..7-9

Chapter 2. Tasks - puzzles, didactic games as a means of formations about the shape of objects……………………………………………………………………………….

2.1. The value of didactic games and exercises in the formation of preschoolers' ideas about the form…………………………………………………………..10-14

2.2. Classification characteristics of didactic games of geometric content…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

2.3. The specifics of conducting geometric games with preschool children .................................................................... ................................................. ...................15-18

2.4. Puzzle tasks in the formation of the geometric vision of preschoolers……………………………………………………………………..18-19

Chapter 3 Experimental confirmation of the effectiveness of the use of didactic games and exercises to consolidate knowledge of geometric shapes and develop geometric vision in children of primary preschool age………………………………………………………………………… …….20-24

Conclusion………………………………………………………………………..25

Literature………………………………………………………………………...26-27

Application………………………………………………………………………..28-35

Introduction

Relevance of course research such scientists as M. Montessori, A.A. Stolyar, E.I. Tikheeva, F. Froebel, E.I. Shcherbakova, Z.A. Mikhailova, L.S. Metlin.

The aim of the study is to study the influence of puzzle tasks, didactic games on the development of ideas about the form in children of middle preschool age

Research objectives:

1. To study and analyze the literature on the problem of the formation of children's ideas about the form.

2. To study the psychological characteristics of the perception of the shape of objects by children of preschool age.

3. Consider the methodology for developing ideas about the shape of objects in preschoolers

4. Consider the value of entertaining mathematical material as a means of developing ideas about the shape of objects

5. Develop a system of educational didactic games for the formation of elementary mathematical concepts in preschoolers

6. Reveal the possibilities of puzzle tasks, didactic games in the development of ideas about the shape of objects.

7. To reveal the effectiveness of the influence of the system of developing didactic games on the formation of elementary ideas about the form.

research problem the question was what is the influence of puzzle tasks on the development of ideas about the shape of objects in children of middle preschool age.

Object of study: the process of developing ideas about the shape of objects in children of middle preschool age.

Subject of study: developing didactic games as well as puzzle tasks as a means of forming elementary ideas in children about the form. Through tasks - puzzles, didactic games in mathematics classes, as well as in regime moments both with all children and in individual work with them

Research hypothesis- I suppose to check what kind of influence the subject of research actually has on the object. What is the level of development of ideas about the shape of objects in middle preschoolers

depends on various forms of use of entertaining mathematical material, namely

from the use of puzzle tasks and didactic games. If, when conducting mathematics classes for group children, a system of developing didactic games, puzzles is used, this will lead to an increase in the level of elementary mathematical ideas about the form.

Experimental base

Theoretical significance

Practical significance

Research novelty.

Chapter 1 Psychological and pedagogical foundations for the formation of ideas about form in preschoolers

The formation of children's initial knowledge about the shape of objects should be carried out in such a way that training would give not only an immediate practical result, but also a wide developmental effect. The currently used methods of teaching preschoolers do not realize all the possibilities inherent in mathematics. It is possible to resolve this contradiction by introducing new , more effective methods and diverse forms of teaching children. One of these forms is teaching children with the help of didactic games and puzzle tasks. Children in the game are attracted not by the learning task that is inherent in it, but by the opportunity to be active, perform game actions, achieve results, win. However, if the participant in the game does not master the knowledge, mental operations that are determined by the learning task, he will not be able to successfully perform game actions and achieve results. Consequently, active participation, especially winning in a didactic game, depends on how much the child has mastered the knowledge and skills that are dictated by her teaching task. This encourages children to be attentive, memorize, compare, classify, refine their knowledge. This means that the didactic game and puzzle games will help him learn something in an easy, relaxed way.

Shape as a mathematical concept

The concept of the form of an object appears through those real objects that surround us in reality. One of the properties of surrounding objects is their shape. The form of objects received a generalized reflection in geometric figures. Geometric figures are standards, using which a person determines the shape of objects and their parts. This is natural, since the form is the main visually and tactilely perceived property of an object, which helps to distinguish one object from another.

You already know the basic rules for sizing. Consider now, using the example of a drawing of an object - a support (Fig. 116) - some additional information about applying dimensions.

Rice. 116. Dimensioning

How to determine what dimensions and where to put on the drawing of an object? An analysis of the shape of the object will help us to find this out (see II).

The object shown in Figure 116. a can be mentally divided into a parallelepiped with a cubic hole and a cylinder (Fig. 116, b). Their dimensions are applied on the drawing: for a parallelepiped and a cubic hole - length, width and height; for a cylinder, base diameter and height.

Now the dimensions of each part are indicated. But are they enough to craft an item? No. It is also necessary to apply dimensions that determine the relative position of the parts of the object, i.e., coordinating dimensions: 16, 18, 5 and 6 mm.

Dimensions 16 and 18 mm determine the position of the cylinder relative to the parallelepiped, which is the base of the object. Dimensions 5 and 6 mm determine the position of the cube relative to the parallelepiped.

Note that the dimensions that determine the height of the cylinder and the cubic hole do not need to be applied in this case. The height of the cylinder is defined as the difference between the total height of the object (36 mm) and the thickness of the parallelepiped (14 mm) and is equal to 22 mm. The height of the cubic hole is determined by the height of the base, i.e. it is equal to 14 mm.

Each dimension in the drawing is indicated only once. For example, if in the main view (Fig. 116, a) the size of the base of the cylinder with a diameter of 20 is plotted, then it is not necessary to apply it in the top view.

At the same time, the drawing must contain all the dimensions necessary for the manufacture of the item. Very often, schoolchildren forget to apply dimensions such as 16, 18, 5 and 6 mm, without which it is impossible to determine the relative position of the parts of the object in the drawing.

Dimensions must be included on the drawings. Overall dimensions are those that determine the limiting (largest and smallest) values of the external (and internal) outlines of products. In figure 116, these are sizes 67, 32, 36.

You know that when applying dimensions, smaller dimensions are placed closer to the image, and larger ones are further away. So, size 14 in the main view (Fig. 116, a) is closer to the image, and 36 is further. By following this rule, it is possible to avoid unnecessary intersections of dimension and extension lines.

Thus, the overall dimensions, which are always larger than others, are located farther from the image than the others. Without overall dimensions, the drawing is not finished.

Figure I17, a and b shows two examples of applying the dimensions of a shaft-type part. In the first case, correct, in the second - unsuccessful, with errors. Errors are highlighted in color.

Rice. 117. Dimensioning

Dimensions must be applied in such a way that it is convenient to read the drawing and, in the manufacture of the part, not to find out anything by calculations. In the first drawing (Fig. 117, a), the length of the part -100 mm - is immediately visible. On the second (Fig. 117, b), it must be counted.

The dimensions that determine the length of the cylinders - the components of the part, in the first case, are applied taking into account the manufacture of the part. How will you make this part in the workshops? First machine a 40 mm diameter cylinder to a length of 45 mm, and then a 20 mm diameter cylinder to a length of 25 mm. The same on the other side. In the second case, this is not taken into account when applying dimensions.

Dimensions are applied, as a rule, outside the contour of the image and so that the dimension lines, if possible, do not intersect with each other. The numbers are written above the dimension lines, then the drawing is easy to read. In Figure 117, b, this is not consistent everywhere. Diameter sizes 30, 40, 20 (right) are located inside the outline of the image. Sizes with a diameter of 20 are marked below the dimension line. Dimension with a diameter of 50 is set far to the right, which led to the intersection of many extension lines and made it difficult to understand the drawing. In this case, it is more convenient to apply it, as in Figure 117, a.

Rice. 118. Applying chamfer dimensions

The axial (dash-dotted) line should go beyond the contour of the image by about 3 mm and not cross the dimension number. In Figure 1 17, b, this is not sustained. Extension lines are also unsuccessfully drawn, they do not go beyond the dimension lines or are drawn too far.

For parts that have the shape of bodies of revolution, often the end edges are cut into a cone. This element is called a chamfer. Its purpose is to facilitate the assembly of parts, protect the edges from damage, and the worker's hands from cuts.

The most common bevels at an angle of 45 °. Their dimensions are applied by writing, for example, 2X45 °, where 2 is the height of the chamfer (Fig. 118, a). If there are several identical chamfers, their size is applied once, indicating the quantity (Fig. 118, b).

The dimensions of the chamfers at other angles are indicated by linear and angular dimensions, and not by the inscription (Fig. 118, c).

How does the analysis of the shape of an object help determine the dimensions necessary for drawing a part on a drawing?
What dimensions are applied on the drawing of a cylinder, cone, rectangular parallelepiped?
Thanks to what signs can a cylinder and a cone be depicted in one projection? a prism with a square base?
What dimensions in Figure 116 determine the relative position of the parts of the part?
What are the overall dimensions? Do they need to be included in the drawing?
How are bevels measured at a 45° angle?

When considering an object as a whole, the eye perceives its geometric shape and structure. Almost all visible elements are limited on all sides by shells or planes of various shapes. This means that each element, each object has a certain spatial form. The primary elements of the spatial form of objects are geometric appearance, size, position in space, mass, texture, texture, decor, color and chiaroscuro.

Geometric view. This is a property (element) of the form as a whole and its parts, determined by the ratio of its dimensions in three coordinates of space, as well as the nature of its surface (straight or curvilinear, broken line). Depending on the predominance of one of the three dimensions, the following types of shape are distinguished: volumetric, planar and linear. The volume view is characterized by three sizes. A planar view is characterized by a sharp decrease in one of the dimensions. In a linear form, one dimension prevails over the other two, even though they are relatively small.

Form lines. It is human nature to relate emotionally to the phenomena and objects around him. The idea of peace and movement, light and heavy, passive and active, a person associates with various types of lines, their slope and character (Fig.).

The horizontal line, for example, is associated with the concept of rest, static, passivity. It contributes to the visual reduction of the figure vertically.

The vertical line - energetic and hot - expresses the desire to rise, visually lengthens the shape.

The sloping line is associated with instability, falling, and the closer it is to the horizontal, the more it is associated with confidence and calmness.

Otherwise, a diagonal line is perceived. It acts as a force that overcomes passivity, expresses movement, dynamics. Distinguish between right and left diagonals. They are perceived differently. The right one is the ascending diagonal, the left one is the falling diagonal. Diagonal is typical for asymmetrical clothing, soft and hard draperies, etc.

A wavy (smooth) line characterizes the uniformity of movement, softness, fluidity. Smooth lines are used in clothes of complex styles.

A broken line is associated with uneven movement, abrupt changes in events, with ups and downs.

The spiral is associated with the concept of rotation, and the arc is associated with overcoming some obstacles and subsequent take-off.

To create the shape of products, the designer uses geometric lines in a complex, i.e. in various compositional subordinations, combinations. In this case, one of the lines should play the role of the main, leading one, on the basis of which the whole composition is built.

Form size. This is the extent of the form and its elements along three coordinates. The size of the form is determined in relation to the size of a person, the size of products of other forms or individual elements of the same form. When comparing forms, their equality or inequality is seen. The size of the form can visually increase or decrease when comparing large and small. Small details in a large form emphasize its size, while large ones, on the contrary, reduce it.

position in space. This is a property of the form, determined by its location among other forms, as well as relative to the observer in the system of frontal, profile and horizontal planes. An object whose shape approaches a rectangular parallelepiped having two equal dimensions can occupy three typical positions with respect to the observer: frontal, profile and horizontal. A cube with all three dimensions equal has only one type position. The same can be said about objects whose shape approaches these figures.

The mutual arrangement of forms in space in relation to each other and the viewer can also be considered on another basis - according to the location relative to each other or the viewer is closer, further, higher, lower, left, right. In relation to the horizon line, forms can be located above, below or at its level.

Mass of the form. This is the visually perceived amount of material of the whole object or its parts, which can fill the space within the geometric shape. The mass of the mold depends on the size of the object. A larger form visually corresponds to a large mass. The perception of mass also changes depending on the geometrical form of the form. The largest visually perceived mass is possessed by forms approaching a cube and a ball, and all those whose dimensions in three coordinates are equal or close to equal. Forms approaching linear have a minimum mass, therefore narrow and long clothes always seem less massive than short and wide ones.

The perception of mass changes depending on the degree of filling of forms. As the degree of filling increases, objects appear more massive. The most massive objects in which there are no voids. The change in the visually perceived mass of the form depends, in addition, on the color, texture and texture of the material from which it is made, and on the size of the objects adjacent to it. The visually perceived mass of the form increases if there are smaller objects next to it. If their sizes increase, then the mass of this form visually decreases. All these illusory changes in the mass of forms are often used in product design.

Texture(lat. factum - processing, structure). Texture - the visible structure of the surface of the form. The texture is smooth, shiny and glossy, matte and rough, coarse or fine-grained, etc. Each material (metal, glass, fabric, paper, sand, stone, etc.) has its own texture. Its perception depends on the distance of the viewer to the surface under consideration, the nature of the lighting (if it is lateral, then the roughness is clearly visible).

The volume and mass of the shape of products depend on the texture of the material. Strengthening the texture of the surface increases the volume and mass of products. A smooth and shiny surface, on the contrary, gives lightness and visually reduces volume. The texture of the material can even influence the perception of the proportional relationship of the form.

Texture(lat. texturg - fabric, connection, structure). Texture - signs of internal structure visible on the surface of the material. For example, products made of wood, stone, and leather have an expressive texture. Various textures are used as a decorative tool that reveals the aesthetic originality of the material.

Color. This is the property of bodies to cause certain visual sensations in accordance with the spectral composition of the light reflected, transmitted or emitted by them. There are physical, physiological, emotional and psychological properties of color.

The physical properties of color include hue, brightness (lightness), and saturation. Hue is what makes it possible to distinguish one color from another: red, green, blue, etc.

Brightness, or lightness, is characterized by the amount of reflected or transmitted light. Each color has a certain lightness. Orange is lighter than red, blue is darker than blue, brown is darker than pink, etc.

All colors are divided into achromatic and chromatic. Achromatic - white, gray, black - do not have selective absorption and differ from each other in lightness. Chromatic - spectral and mixed - are distinguished by color tone, lightness and saturation.

Saturation is the percentage of a pure spectral color in a given color. It is defined as a percentage. The saturation of the corresponding spectral color is taken as 100%, and white or another achromatic color is taken as zero. Thus, spectral colors have saturation equal to one, while achromatic colors have zero saturation. The most saturated colors are the main spectral and magenta. They are called clean, open, intense. The colors located between the main spectral ones are intermediate (yellow-green, blue-violet, orange-yellow), less saturated, they are called complex, calm, restrained, soft. The saturation of any color decreases when white or black is added to it. Colors, the saturation of which is reduced by adding white, are called bleached (pink, lilac, etc.). Colors that have been reduced in saturation by adding black are called tinted.

The physiological properties of color are its ability to affect the human body, for example:

intense red color causes too much excitement, increases blood pressure;

green promotes the expansion of capillaries, lowers blood pressure, relieves visual fatigue, soothes; yellow stimulates brain activity;

blue and violet have a beneficial effect on the lungs and heart, increasing their endurance;

gray and black colors can cause an oppressed, depressed state.

The emotional and psychological properties of color are associated with physiological effects and all sorts of illusions and associations. So, according to the nature of perception, all colors are divided into warm and cold. Warm colors - red, orange, yellow, yellow-green - are associated with the sun, fire, warmth. They are bright, catchy, dynamic, increasing the size and volume. Cold colors - blue, blue, violet, green-blue - are associated with water, ice, cold. These colors are calmer, less prominent.

Distinguish colors light and heavy. All light and cold colors are classified as light, dark and warm colors are classified as heavy. Colors are divided into "protruding" - light and warm and "retreating" - dark and cold. The properties of color to bring closer or remove, to make objects lighter or heavier, to increase or decrease their volume are widely used in fine and decorative arts. In particular, the spatial properties of color make it possible to create a visible depth of the image on a flat canvas of the picture.

Due to the associative nature of perception, colors evoke different feelings and sensations in a person, special emotional moods, evoke some images:

red is perceived as exciting, hot, the most active and energetic, courageous, passionate, the color of valor, strength, power;

green - calm, moderate and refreshing - gives the impression of softness, pleasant and beneficial peace; a symbol of spring, fertility, youth, freshness, joy, hope, memories;

yellow - exciting, revitalizing, cheerful, cheerful, fussy, flirtatious, somewhat daring, the color of fun and jokes, a symbol of sunlight, warmth, happiness;

orange - hot, cheerful, cheerful, fiery, cheerful;

blue - light, fresh and transparent; white - light, cold and noble, a symbol of purity.

Color perception is influenced by a number of factors that can change the apparent color of bodies. The change in their color is often associated with the spectral composition of light sources. So, in the light of incandescent lamps, there are more yellow rays than in sunlight, so yellow colors become more saturated, reds brighten, the hue becomes yellow, blues darken, lilacs become yellow, and violets become red. The color of the material also depends on the texture of the surface. Colors on glossy shiny surfaces appear lighter, on matte surfaces they appear darker (satin and velvet).

The perception of color also depends on the phenomena of contrast. Distinguish between simultaneous and sequential contrasts. In turn, the simultaneous contrast can be a contrast in lightness and color, or chromatic. Simultaneous contrast in lightness is that colors located on or near a dark background lighten, and darken on a light background or next to it. White on a black background is especially bright, while black on white is a deep black. The same gray pieces of fabric on a black, white and gray background will look different. On a white background, the fabric seems darker, on black - lighter, on gray it will hardly change.

A variety of contrast in lightness is also due to the marginal, or borderline, contrast. On the border of light and dark, light becomes even brighter, and dark darkens, which creates the impression of unevenly colored areas. To destroy the edge contrast, the planes are separated by a contour line.

Simultaneous chromatic contrast is a change in color depending on another color surrounding it. The color always changes in the direction opposite (complementary) to the surrounding color. For each chromatic color, another chromatic can be found, which, when mixed with the first in certain proportions, gives an achromatic. These two chromatic colors are called complementary. On the color wheel, complementary colors are located at opposite ends of the diameters. Additional pairs of colors are: red and bluish-green, orange and cyan, yellow and blue, green and magenta, etc.

As a result of chromatic contrast, gray on different backgrounds acquires an unequal apparent color. So, on a red background, the gray pattern turns green, on green it turns red, on blue it turns yellow, etc.

Sequential contrast occurs when two colors are viewed not simultaneously, but alternately. The second color will appear to be a complementary color to the first.

Color is not only an element of form, but also an important means of unifying and harmonizing its other elements. The color of industrial products is chosen taking into account their functional purpose and methods of operation, design, material, composition.

Chiaroscuro. It is a consequence of the different angle of incidence of light rays from the light source onto the form and is characterized by the distribution of light and dark areas on its surface. The formation of light and shade effects depends on the shape of the object, the relief and texture of the material, the direction of incidence of rays from the light source. Chiaroscuro on clothes, for example, is largely due to the relief of the form. The relief is created by folds, overlays, seams, tails, drapery, etc. The abundance of details and draperies overloads the form with chiaroscuro effects and increases its volume. If chiaroscuro is formed by rare vertical lines, the volume of the form visually decreases: the effect of visual illusions operates.

Decor(fr. decor, lat. decoro - I decorate). This is an element of the form of products in the form of an ornament or pattern.

Ornament(Latin ornamentum - decoration) - a drawing (pattern) built from organized elements. There are two main types of ornament: geometric and pictorial.

The geometric ornament is built from abstract geometric shapes (squares, triangles, rhombuses, circles), as well as strokes, dots and lines, which, alternating in a certain order, allow you to get patterns from the simplest to the very complex. Geometric ornament is widely used to decorate modern products made of glass, ceramics, fabrics and other materials.

The pictorial ornament reproduces specific objects of the real world - plants, animals, things. Fabrics, knitwear, glass, ceramics, etc. are widely decorated with pictorial ornaments.