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 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 children preschool age …................................................................................................................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 about geometric shapes ah and the development of 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. Explore psychological features 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 on doing mathematics, and also 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 broad 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 various forms of education for 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. Hence, Active participation Moreover, the gain in the didactic game depends on how much the child has mastered the knowledge and skills that are dictated by its teaching task. This encourages children to be attentive, memorize, compare, classify, clarify their knowledge. Means, 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.
The concept of the form of an object appears through those real objects that surround us in reality. This is quite natural, since form is the main tactile and visual property of an object. It is the shape that will help the baby to distinguish one object from another.
How can you describe the shape of an object?
Therefore, people came up with a special system with which it would be possible to designate one form or another. It includes a system of geometric shapes, which also has separate groups of shapes. But the main forms that help to distinguish objects are flat and spatial figures. Also, the shape can be rounded or with pronounced corners.
- And when we learn to determine what is an object and what is not, we immediately turn our attention to what what are these objects - what color or shape they are.
In order for the child to be able to navigate the shapes of objects, you need to complete such a small but useful task. This picture shows 16 objects of different shapes.
And from the following reference forms, he must choose which figures from above represent which form of the object from below:
The correct answers in this case would be:
- The first picture is a cup, a mushroom, a hat and a month
- The second picture is a stroller, a chair, an armchair and boots
- The third picture is a pyramid, a carrot, a leaf and a Christmas tree
- The fourth picture is a nesting doll and a lamp, a pear and a snowman
Using the example of objects of flat figures, you can help the child understand the most common forms for designating objects. A flat figure is one that has a straight surface and two lengths - length, height or width.
All the information found on this topic had to be greatly reworked, simplified and shortened - a lot has been written, it is tricky, but essentially the same thing.
In development " geometric knowledge» There are several different levels in children:
- First level characterized by the fact that the figure is perceived by children as a whole, the child still does not know how to distinguish in it individual elements, does not notice the similarities and differences between the figures, perceives each of them separately.
- On the second level the child already distinguishes the elements in the figure and establishes relationships both between them and between individual figures, but does not yet realize the commonality between the figures.
- On the third level the child is able to establish connections between the properties and structure of figures, connections between the properties themselves. Children also learn the relationship between the number of sides, angles and the names of figures ("The triangle is called so because it has three corners"; "The rectangle is called so because it has all right angles"). Counting the angles, the children correctly name the shapes: “This is a hexagon, this is a pentagon, a polygon, because it has many angles - 3, 4, 5, 6, 8 and more, then it already looks like a circle.”
The transition from one level to another is not spontaneous, running parallel to the biological development of a person and depending on age. It proceeds under the influence of purposeful learning, which helps to accelerate the transition to more high level. Lack of training hinders development.
To determine the shape of an object, a person uses a generalization in the form of geometric shapes. For example, the Christmas tree is triangular (cone-shaped), the sun is spherical with striped rays, the book is rectangular, the mushroom consists of a hemisphere and a stick, etc.
Introducing children to geometric shapes and their properties should be seen as:
1) sensory perception (by sight, by touch, by taste, etc.);
2) knowledge of the forms of surrounding objects;
3) distinguishing the features of their structure, properties, main connections and patterns in their construction.
That is, when a child studies an object, it is necessary to name what shape, color, temperature it is, what materials it is made of, what geometric shapes can be distinguished in this object.
It is known that an infant recognizes the shape of the bottle as the one from which he drinks milk, and in the last months of the first year of life there is a clear tendency to separate some objects from others and to separate the figure from the background.
The outline of an object is that common beginning, which is the starting point for both visual and tactile perception.
To start learning the shape of an object, the child needs to start interacting with it. The form of an object, as such, is not perceived separately from the object, it is its integral feature.
Specific visual reactions of tracing the contour of an object appear at the end of the second year of life and begin to precede practical actions.
Actions of children with objects on different stages different. Toddlers tend, first of all, to grab the object with their hands and begin to manipulate it.
Children 2.5 years old, before acting, in some detail visually and tactile-motorly get acquainted with objects. There is a special interest in the perceptual perception of the form (perceptual actions - relationships with the environment).
However, the importance of practical action remains paramount. From this follows the conclusion about the need to direct the development of perceptual actions of two-year-old children. Depending on the pedagogical guidance, the nature of the perceptual actions of children gradually reaches a cognitive level. The child begins to be interested in various features of the object, including the shape. However, for a long time he cannot single out and generalize this or that feature, including the shape of various objects.
Sensory perception of the form of an object should be directed not only to seeing, recognizing the forms along with its other features, but also to be able, by abstracting the form from the thing, to see it in other things as well. This perception of the shape of objects and its generalization is facilitated by the knowledge of standards by children - geometric shapes.
When does a child begin to distinguish geometric shapes?
The experimental data of L. A. Wenger showed that children of 3-4 months have such an opportunity. Focusing on the new figure is evidence of this.
Already in the second year of life, children freely choose a figure according to the model from such pairs: a square and a semicircle, a rectangle and a triangle. But children can distinguish between a rectangle and a square, a square and a triangle only after 2.5 years. The selection on the basis of figures of a more complex shape is available approximately at the turn of 4-5 years, and reproduction complex figure carried out by individual children of the fifth and sixth year of life.
At first, children perceive geometric figures unknown to them as ordinary objects, calling them by the names of these objects: a cylinder - a glass, a column, an oval - a testicle, a triangle - a sail or a roof, a rectangle - a window, etc.
Under the teaching influence of adults, the perception of geometric shapes is gradually being rebuilt. Children no longer identify them with objects, but only compare them: a cylinder is like a glass, a triangle is like a roof, etc. Finally, children begin to perceive geometric shapes as standards that determine the shape of objects (a ball, an apple is a ball , a plate, a saucer, a wheel are round, and a scarf is square, etc.).
In order to better know an object, children tend to touch it with their hands, pick it up, turn it; moreover, viewing and feeling are different depending on the shape and design of the object being cognised. Therefore, the main role in the perception of the object and the determination of its form is played by the examination, followed by the designation of the word.
However, preschoolers have very low level examination of the shape of objects; most often they are limited to cursory visual perception and therefore do not distinguish figures that are close in similarity (an oval and a circle, a rectangle and a square, different triangles).
Gradually, the examination of the figures will not only provide a holistic perception of them, but will also allow you to feel their features (character, directions of lines and their combinations, angles and peaks formed, stability-instability, etc.), the child will learn to sensually distinguish the image as a whole in any figure and its parts, meaningfully analyze them.
Comparing three-dimensional and flat figures, children already find a commonality between them (“A cube has squares”, “A beam has rectangles, a cylinder has circles”, etc.).
Knowledge of geometric shapes, their properties and relationships expands the horizons of children, allows them to more accurately and versatilely perceive the shape of surrounding objects, which positively affects their productive activities (for example, drawing, modeling).
Of great importance in the development of geometric thinking and spatial representations are actions to transform figures (make a square from two triangles or add two triangles from five sticks).
All these types of exercises develop spatial representations and the initial skills of geometric thinking in children, form their ability to observe, analyze, generalize, highlight the main, essential, and at the same time bring up such personality traits as purposefulness and perseverance.
You already know that the main task of drawing is to learn to see objects in volumetric forms in order to practical work be able to convey volume by certain expressive means- line, stroke, tone. If you have correctly and expressively drawn an object, this means that its internal basis - the structure - is correctly built in the pencil image and the material properties (surface texture) are expressively conveyed. All this, it would seem, looks simple, but you have to work long and hard to learn how to perform such drawings. One should never rely only on certain abilities for the fine arts. A lot of painstaking work is needed, because knowledge, skills and abilities do not come by themselves, but are the result of huge and strenuous efforts.
There are no formless bodies in nature. If one could imagine such a thing, then apart from some kind of abstract (abstract) emptiness, nothing else turned out to be in consciousness. Therefore, one should believe in the form as an organization of certain parts, built expediently and in strict accordance. An object in the usual sense of the word is a product created by a person, what people need and performing a specific function. When studying a drawing, you must be guided by the form in your work. The well-known artist-teacher Dmitry Nikolaevich Kardovsky, in his book “Drawing Handbook” published in Moscow in 1938, wrote: “What is a form? This is a mass that has one or another character, like geometric bodies: a cube, a ball, a cylinder, etc. Living form of living natures, of course, is not a regular geometric form, but in the scheme it also approaches these geometric shapes and thus repeats the same laws of the arrangement of light along perspectively receding planes, which exist for geometric bodies.
The student's task is precisely to combine and coordinate the understanding of form with the techniques for depicting (constructing) on a plane with light ... surfaces that limit the form in space. When drawing a ball, they know what techniques should be used to depict the transitions of its surfaces in shadow and in the light, just as techniques are known when depicting a cube, pyramid, cylinder, or some more complex figure, etc. ... What characterizes, for example, the shape of a human body? This is a cylindrical shape. If the torso were a regular cylinder, then its image would be very simple, but there are bulges, depressions and other deviations in it that violate the simplicity of the cylinder. At the same time, these bulges and recesses are located in a large cylinder shape either on the side receiving direct light rays, or on the side not receiving them, or in transitional places. When drawing, these deviations must be maintained in tone, respectively: 1) light, 2) shadow and 3) penumbra. A sense of form, the ability to see and convey it must be developed by the student so that it, as they say, “transfers to the ends of the fingers” from consciousness, i.e. when depicting a form on a plane, the painter should feel it in the same way as a sculptor who sculpts a form from clay or cuts it out of stone ”(Kardovsky D.N. Drawing Handbook. M., 1938. P. 9).
People use the word "form" very often. Everyone correctly understands the meaning attached to this concept. Yes, indeed, the term "form" (from lat. forma) is translated as a concept that allows a person to comprehend the external outline, appearance, contours of an object. In any image, they always show, first of all, the shape of the object being drawn, i.e. true outline of it. When the artists say that the three-dimensional form is well conveyed in this drawing, they emphasize the veracity of the image. In fact, the concept of "volumetric form" essentially points to two words that are close in meaning, because the volume of an object also contains mass, configuration, inherent in the form. The volume itself should be regarded primarily as one of the quantitative characteristics of geometric bodies - capacity, which is expressed in the number of cubic units. Figures visual arts and architecture is understood by this word appearance space bounded by planes.
Thus, under the volumetric form of objects, one should consider the regularities of the structure, i.e. features of their design.
To depict a three-dimensional form, you need: the ability of the painter to see and understand the design features (structure) of objects and the transfer of three-dimensionality - length (or width), height and depth - the shape of these same objects on the two-dimensional plane of a sheet of paper.
Consequently, the representation of a form in any drawing from nature should be based on its construction, and not on drawing the external appearance of the object. Such a construction presupposes that the draftsman has a clear constructive approach to surrounding objects. Since you have a two-dimensional plane in front of you, but you need to draw three-dimensional volumes, imagine a sheet of paper as a certain (conditional) space and try, based on your knowledge of perspective drawing methods, to place the depicted shape in it. Remember what examples from the world of geometric bodies can be used to solve the problem of placing a form in sheet space using their combinations, visible in nature.
tone pattern
Drawing any object from life, you simultaneously solve several problems, one of which is the transfer of light and shade in the image.
To see the object being drawn, it must be lit either naturally (daylight) or artificially (electric light). physical phenomenon The distribution of light, thanks to which our vision distinguishes the surrounding reality, is called chiaroscuro in visual practice.
The perception of various forms becomes possible because reflected light rays enter the eye. Such emitted light allows you to visually perceive any object.
Illuminated objects located in space are distinguished by us as three-dimensional. The volumetric shape of an object, in accordance with its constructive structure, is determined by the play of light and shadow. The peculiarity here is that the shape of the object is made up of variously located surfaces located at different angles to the rays of light, due to which the illumination of this object turns out to be uneven: the light hits the areas that are perpendicular to the rays completely, and the others are distributed Weaker depending on from their position at a certain angle - as if “sliding”, but does not fall on others at all.
For the draftsman, the degree of illumination of the surface of the object is also important, which depends on the strength of the source and on the distance to it. The perception of the illumination of the drawn object is also affected by the distance between it and the person drawing. This is due to the light-air medium, which forms a “haze” (from the smallest particles of dust, droplets of moisture and other substances in suspension), which dissolves the sharp outlines of the boundaries of light and shadow, darkens the illuminated areas and brightens deep shadows.
So, the emission of light will give a luminous flux that propagates in one direction, reaches the object and reveals the lightness of its surface. Depending on the brightness of the light rays, the lightness of the object becomes contrasting. The word "lightness" should be understood as the reflective ability of the surface of an object. You know; that everything that we see and distinguish is connected with the physical nature of light, which, due to the reflectivity of material bodies, can give certain signals to our eye, which reacts to them with a remarkable property - color perception. It goes without saying that lightness is determined primarily by the feature of the surface of an object in the reflection of light. White, yellow, blue colors reflect more light than black, blue and brown.
Therefore, it is necessary to talk in more detail about chiaroscuro. Best of all, perhaps, a detailed description of all gradations of chiaroscuro is possible using the example of a spherical surface.
The shape of the ball is remarkable in that it is uniform on all sides, not distorted due to the peculiarities of perspective changes in the subject, and gives a complete understanding of the laws of chiaroscuro. Being in space, the ball in any position is equally illuminated by one light source and shaded with opposite side. This means that the rays of light fall on this geometric body, illuminating exactly half of its spherical surface in different ways. Why is it different? you might ask. After all, if half is illuminated, then the illumination is the same everywhere here. That's the thing, it's not the same. Only an inept draftsman can imagine an illuminated surface of the same tone, and even if he sees that this is not the case, he will nevertheless retain his conviction. Is it because in the drawings of the ball for people unfamiliar with the concept of chiaroscuro, half of the image is left untouched with a pencil, and the second is shaded evenly.
Let's look at the patterns of light distribution on the surface of the ball. Let the gypsum model of the ball be on a light gray plane at a distance of one of its magnitude from a white matte wall and illuminated by artificial light pouring from the left side from above at an angle of 45°. It will not be difficult to think correctly that the model is illuminated at this angle and that the brightest light on the surface of the geometric body will concentrate on the area that is perpendicular to the direction of the rays from the source. As you can see, we are talking about a direct hit of light rays on the surface and, therefore, about the right angle of the surface and the beam that fell on it. Part of the light rays hits the surface of the ball due to its structure at ever sharper angles, and than sharper angle, the less light hits the sphere. It turns out that the curved surface should gradually fade into shadow with decreasing light.
Finally, in the distribution of rays over the sphere, there comes a moment when the curved surface goes beyond the reach of light and plunges into shadow.
The most brightly illuminated spot on the surface of the ball is called a glare, which is very clearly visible on any shiny surface, such as glass. A light penumbra is visible around the glare, proving the rules for the distribution of light over a spherical surface. Artists call it a semitone. The semitone of the first stripe around the glare passes imperceptibly along its outer edge into the next one, which also imperceptibly merges with the now third one, and so on. All these transitions imperceptible to the eye merge with each other due to the spherical surface of the body, until the last of them just as smoothly leaves its edge into the shadow. Each new semitone is slightly darker than the previous one.
A shadow is a part of an object that got its name due to the absence of light, being outside its distribution. But everything that is in the shade also obeys its own laws, being influenced environment. You remember that the condition was set according to which the ball must be separated from the white wall at a distance of one of its magnitude. The word "white" is used in relation to the wall, and this is no accident. You begin to guess that the wall is illuminated by the same source, and therefore, reflecting the light, it must now make its own amendment to the light-and-shadow relations inside spatial environment. The light reflected from the wall at an angle of 45 °, but now from the right side, hits the shadow, and although it is much weaker than the direct one, nevertheless, its effect significantly affects the smooth highlighting of the shadow. On the surface of the ball, which is in the shade, due to the light reflected from the wall, a phenomenon called a reflex is formed. In that part of the ball that is connected with the surface of the table, a reflection from this surface is visible.
The shadow on the ball is called its own shadow. On the table from the ball in strict accordance with the direction of the light flux from the source lay another shadow, which is called a falling shadow.
The regularities of the distribution of light on the surface and around the visible object should be well known to every painter.
A person perceives the surrounding reality with all its phenomena, forms and volumes visually. IN visual perception the main role is played by his ability to see the world in color. If our primitive ancestor did not have this innate ability, who knows, humanity would exist as such. Distinguishing shades of color helped people of those distant centuries literally survive in the struggle against the harsh and merciless forces of nature. Could they survive if the world around them was absolutely colorless, what is called gray or black and white?
But why then, - you can rightfully ask, - black and white literate drawings are so truthful and attractive? We will wait a little while answering this question, but here we will come close to the concept with which we will have to associate the execution of images, taking into account the requirements of truthfulness, tone.
Before defining this concept, let us turn to the surrounding reality and name some examples related to visual activity.
The remarkable Russian landscape painters Alexei Kondratievich Savrasov, Ivan Ivanovich Shishkin and Fyodor Alexandrovich Vasiliev performed many completed pencil drawings of nature in their work. Each drawing not only impresses with its excellent craftsmanship, but also has a number of other advantages, which include correctly taken light and shade ratios. Indeed, how can one achieve differences in the tone of the crown of a tree and grass, foreground and background, shrubs and weeds? Masters achieved such a difference with brilliance, and a black-and-white pencil in their hands gave such tonal effects that it is just right to compare with picturesque ones.
With a simple graphite pencil, you can convey the brilliance of water and glass, velvet and satin fabric, tree bark and the most delicate form of a rose petal. And the point here is in the tone, and only in it.
The word "tone" (from the Greek tonos - tension) means the general chiaroscuro structure of the image (in painting, this concept corresponds to the color structure of the work).
So, the tone is called the chiaroscuro system of the image. Consequently, the artist who performs a long-term creative drawing of a landscape or everyday scene is faced with the task of conveying in his work the tonal relationships between all elements of the image, so that the drawing impresses the viewer not only with deep life content, but also with the expressiveness of form.
You already know that the whitest paper is much darker than the true highlight on a glossy surface, and the softest drawing material, not to mention the graphite pencil, which gives the blackest spot on paper, is still many times lighter than natural black space. Therefore, one must always remember that truthfulness in a light-tone (tone) pattern can be achieved only when the light-and-shadow ratios are proportional to nature.
For a preliminary acquaintance with the solution of the problems of tone drawing, let us turn to the analysis of a still life, composed in our imagination of three objects. Let it be a glass jar with cherry jam, a light yellow apple and a white tablecloth. All these objects pop up in your memory both at once and one by one. A shiny jar filled with dark jam with an abundance of berries looks wet black, and the apple is darker than the tablecloth, despite its light hue.
The still life is illuminated by daylight, and all its contrasting features are visible as well as possible. All reflexes are clearly visible on the jar, and the apple in front of the vessel with jam contrasts sharply with a part of the dark silhouette even in the shadow. The snow-white tablecloth beautifully emphasizes the voluminous forms of the fruit and the jar. Of course, such a still life rightfully claims to be a picturesque solution, since its color merits are obvious.
Is it possible to draw this still life, preserving in the image the first impression of this freshness and being able to subordinate the sharp contrasts between all objects to the general tone state of nature. Of course, you can draw such a still life if you have the necessary knowledge and skills of visual activity based on a holistic vision of nature.
In the process of graphic representation, it is completely pointless to try to convey the absolute ratios of the lightness of nature. You already know why this is not possible. It is only necessary to adhere to proportional ratios of brightness.
All the various tonal relationships can be conveyed by modest means of drawing.
Where to start? Since the establishment of the so-called tonal scale - the relationship between just white paper and the thickest layer of graphite substance deposited on its surface. Between these two extremes are in the appropriate relationship from light to dark all other gradations of tone.
So, in the presented still life, all the illuminated and shadowy places of objects are distinguished by a wide variety of different tonalities, which are revealed with a simple graphite pencil. Therefore, when working on any educational task, be sure to set the tonal scale. It can be depicted as a strip of several (according to the number of main spots of light and shadow observed in nature) rectangles shaded to convey the entire gamut of shades in the correct subordination. This will help a lot in your work, give you a great opportunity to “feel” the gradations and give you confidence.
It is very important to practice in developing the ability to subtly distinguish the gradations of lightness in natural productions. After a while, you will begin to catch even small tonal differences in nature.
But back to the imaginary still life. You set the tonal scale and it turned out that nine main spots of light and shadow are visible in nature. These are highlights on a glass jar and an apple, common spots of the tablecloth and background, as well as apples, two shadow spots of shadows from the jar and an apple, a common spot of the jar with its contents in the light and a common spot in the vessel's own shadow.
When modeling an image in tone, you would need to observe a proportional relationship between the luminosity of some spots in nature and their corresponding places in the picture. At the same time, in no case should you be carried away by the study of any particular part of the image, but only work with relationships all the time, constantly comparing the drawing with nature. The study of a separate place in a drawing without connection with others is fraught with complications associated with a violation of the integrity of the image. By doing such a study, you begin to compare a separate piece with the same in nature and, naturally, move away from a conscious decrease in the brightness or density of the shadow in the drawing.
All details in nature should never be conveyed in a drawing. This is impossible. In nature, all the details are connected with the general, obey it, but in the drawing it is hardly possible to link all this with the general. Thus, a tone drawing requires a developed sense of form, construction, skillful study of the form with chiaroscuro and final generalization so that the image looks collected and solid, and, most importantly, proportions in tone proportional to nature must be conveyed in it.
cube drawing
One of the outstanding artists of France, Ingres, once said well about drawing: “Drawing does not mean just making contours; A drawing is not just lines. Drawing is also expressiveness, inner form, plan, modeling” (Ingres on Art. Collection. M., 1962, p. 56).
When drawing from life plaster models of geometric bodies, you need to depict each body, modeling it by transferring light and shade ratios. You learned about the tone pattern in the previous paragraph.
Essentially, this is your first rather lengthy drawing, in which you will have to do difficult work related to the technique of pencil drawing. You are faced with the choice of technique - to draw in tone with shading or shading. Hatching is recommended, as it largely disciplines, teaches you to treat the drawing carefully and with concentration. The peculiarity of this technique is that the strokes must be placed according to the shape of the model, and if this requirement is not followed, very soon you can see that the strokes that covered the surface of the paper, applied at random, i.e. thoughtlessly, destroy the drawing, do not reveal the three-dimensional form.
The cube model should be illuminated with artificial light, the source of which should be placed from the top left. In this case, both the entire volume of the body and the chiaroscuro gradations are clearly visible from the point of view you have chosen. The cube is placed at an angle to the painter, slightly below eye level, so that the upper face is visible. The background should be light, and the model should be placed on a gray drapery, spread without folds on a stand for nature.
To get started, you need to remember the previous exercises on drawing from nature the wireframes of geometric bodies. Similar tasks you have to solve now. True, now the cube appears before you in the form in which it is truly perceived as voluminous. The frame made it possible to see through the cube, with all the faces and edges. Now some of them are not visible, but the eye must be able to "see" them, so that when building, taking into account perspective abbreviations, it will certainly be shown. Only then do they speak of the constructive structure of the form of a geometric body.
However, it is not possible to draw on paper without first placing the image. Only a few virtuosos of academic drawing could begin the image of this or that statue from any one point and, without lifting the pencil from the paper, draw a very precise contour of the antique sculpture on the sheet. You need to act much more simply and take the pencil away from the paper many times in order to look at the natural setting and at your sheet and draw on it the general shape of the cube, thus placing the drawing, and then refine it by comparing it with nature. The general shape of the cube on paper is applied so that the outline is not very large, but not small either. It is most expedient to represent a sheet of paper as a conditional space in which the cube model takes its rightful place. Of course, at first such an idea is given with difficulty, but in each new exercise it is necessary to include this kind of “mechanism” in order to eventually bring it to automatism.
The planned outline of the cube has taken its place on paper, and you can step back a little to see the layout of the picture from a distance and once again check whether the location of the image in the format is correct or incorrect in this case. Of course, further work largely depends on how you first placed the drawing.
Start refining values by visual comparison. Having chosen a certain height of the front vertical edge of the cube, subordinate the rest to it, but already taking into account the perspective changes in nature. First determine the location of this edge closest to you in the outlined image silhouette. Then mark the height of this edge, draw a vertical segment, and draw a strictly horizontal line at its lowest point, which will become auxiliary during construction. It will be necessary a little later to imagine a horizontal line perpendicular to the base of the edge in kind, in order to show, together with the one drawn on paper, the angle formed by the horizontal edge of the right side. For comparison, put a pencil or ruler at the base of the plaster model of the cube to see the angle in kind.
Further work on drawing a plaster model of the cube is carried out as a gradual revelation of the constructive basis of the object. Using the landmarks, build the lower face, trying to "see" its outlines from all sides, i.e. show the invisible edges, as was done when building the cube frame. At the same time, mark all the other vertical edges, constantly comparing their size with the edge closest to you.
Knowing the rules of perspective, associate visible changes in the shape of the cube with the construction. The two vanishing points of the conditional continuations of the edges, which are at an angle to you, remain guidelines for constructing all the remaining four upper ones.
After you have built the "skeleton" of the cube, compare the drawing with nature and think about what catches your eye first of all - the whole cube or the details of the shape. In this case, the inaccuracies will become visible. So far, it is easy to eliminate them, because when constructing the shape of a geometric body, we hope that you did not overdo it in drawing pencil marks on paper. Remember, when building the shape of the depicted object, all lines should be drawn easily and confidently.
Why did you see inaccuracies in the drawing? Our vision, as it became known thanks to the experimental data of psychologists, first grasps the general shape of the object, on a short time as if fixing it.
Having eliminated construction errors, check the image with nature again and make sure that the construction of the drawn cube corresponds to the visible model. Since the image of a cube on paper is carried out relatively quickly, when correct construction you should not outline the three-dimensional shape of a geometric body with light hatching, thus showing the shadow side of the object, because it suggested itself - it is known that we draw a semblance of an object, and what our eye sees in nature, he "wants" to see in the drawing.
Cut-off ratios in the drawing must also be built. We are talking in relation to visual activity different words, for example, "construction scale", "tone scale". In the first expression, one must keep in mind the definition in the drawing of the dimensions and ratios of the parts of the object in comparison with nature.
When drawing from life, you are rightfully trying to convey the image the way you perceive the subject. By shading or shading, you simulate the volume of an object, showing in the image the illuminated, transitional from light to shadow and shaded areas peeped in nature. You finish this work only after making sure that the light-and-shadow ratios are correctly conveyed in the drawing. By doing this, you have maintained the tone scale in the image, i.e. managed to find proportional ratios of the darkest and lightest tones.
Tone patterns are created by the skillful distribution of light, penumbra and shadow using line techniques.
Modeling the shape of a cube with a tone, in no case do not rush to immediately lay the shadow face of the geometric body. Firstly, this will not succeed, and secondly, as they do not draw, they do not apply the tone in parts. The point here is the difference between natural light and the whiteness of paper, the materiality of a natural object and the surface of a sheet of paper shaded with a pencil, etc.
To achieve the right (and not exactly the same) tone allows you to reasonably built in the figure proportionate to nature relations.
Therefore, we recommend you this approach to conveying light and shade relationships: choose the darkest hatching tone that you use in a certain place in the drawing and do not repeat it anywhere else, and all other gradations will vary from this dark to the tone of the paper itself.
Watch the general illumination of nature and convey this in the drawing.
Diversify the technique of working with a pencil, do not cover the drawing area with thoughtless, monotonous hatching that is “comfortable” for the hand. The texture of gypsum itself suggests to the thoughtful draftsman how to cover the paper with a layer of pencil.
At the end of the work, generalize the image, i.e. achieve the elimination of contrasts that hurt the eyes or a mechanical set of individual tones, and bring the drawing into a general subordination of all tones (Fig. 18). Learn to convey the correct tonal relationships that express form and material in a drawing.
Rice. 18
Cylinder drawing
The principle of lighting the next model for drawing from nature remains the same. This time you will perform a tone drawing of a cylinder - a geometric body formed by the rotation of a rectangular plane around a single axis.
The shape of the cylinder is peculiar. Unlike a cube, light is distributed over a cylindrical surface in many ways more complicated. The bases of the cylinder are round planes, and if they are at any angle (in perspective), they already look like ellipses.
You drew a wire model of this body and practically studied its constructive basis.
To build a vertical cylinder, start with layout general form body. In order not to make a mistake in placing the general shape (white silhouette) of the cylinder in the vertical format of a sheet of paper, draw a light vertical in the middle and visually determine the height of the depicted body, and then its width.
Further, the construction of the shape of a cylinder turns out to be an effective means of developing knowledge and practical skills in drawing, as it helps to master the rules of perspective and the constructive structure of objects well. Fulfilling this work, you must act confidently, freely hold the pencil.
Having built the frame of the cylinder, in which both bases are correctly depicted in perspective (the lower one is slightly wider, as it looked in nature), compare the image with nature and proceed to modeling the shape in tone. If in the tonal pattern of the cube there was a certain complexity caused by the transfer of proportional natures of light and shade relations, then in the tonal characteristic of the cylinder, additional efforts are needed to understand the degree of distribution of gradations of light and shadow over its specific surface.
Be sure to understand the gradations, because instead of conveying a three-dimensional form, the drawn image may look like it is wrinkled or flattened. To prevent this from happening, be extremely careful in modeling the surface of a cylinder built on paper.
The cut-off solution for the shape of the cylinder is subject to the knowledge of the painter. Everyone sees how the light propagating along the rounded surface of the cylinder clearly builds the shape of a geometric body. A small area looks most brightly on a cylindrical surface. This is a glare, and its phenomenon is caused by the fact that light rays fall strictly perpendicular to this part of the volume. Further, the light begins, as it were, to slide along the rounded surface and, of course, weakens the illumination of the object, until its effect is interrupted by an area that goes beyond the border between it and the shadow, which becomes the darkest spot. Consequently, the cylindrical surface gives a clear visual representation of the sequential distribution of light and shade gradations in approximately the following alternation: semitone, light, glare, light, semitone, shadow, reflex. Of course, the transitions between them are completely indistinguishable, and this is one of the difficulties of rendering a three-dimensional cylinder shape in a drawing. This means that you do not need to achieve an absolute similarity of the drawn cylinder with nature, but to monitor the correct transmission of the ratios of tone gradations proportional to it (Fig. 19).
The background in the tone pattern is an integral part of the spatial image. In addition, it affects the general state of illumination, being either neutral or actively influencing the perception of an object.
Rice. 19
ball drawing
The construction of such a geometric body as a ball is not particularly difficult, if we exclude the curved line, which is impeccable in terms of accuracy. However, it is needed only during construction, and in the completed tone pattern it will disappear, as if it did not exist at all. It has already been said that lines are not the boundaries of the form.
Rice. 20
A plaster model of a ball intended for drawing from life is placed in front of the painter at a distance that does not necessarily correspond to the triple value of the height of nature. Well-lit from the left and from above, nature is visible from a slightly greater distance.
You can build a circle with a vertical line that intersects it with a horizontal one and two inclined ones at an angle of 45 °. Having set aside identical radii everywhere from the center, easily draw a closed curve, which will become the boundary of the mass of the ball.
After the circle is outlined, refine its boundaries, remove auxiliary constructions and proceed to identify the spherical shape of the ball.
The sculptural term "modeling" is quite suitable here. Indeed, it is possible to achieve the transfer of the impression of a spherical shape (spherical volume) in the drawing only when correct definition tonal relations - as if "sculpting" the form.
The gradual change in the illumination of the ball is also expressed in the same gradations as in the cylinder, differing only in the characters of the surface. In the cylinder, all the imperceptible, brightening towards the highlight and gradually fading away when approaching the shadow, are distributed along a straight vertical line. The ball has its own, spherical, character of the surface, and chiaroscuro goes along it as in a circle.
Light rays incident perpendicular to spherical surface, form a highlight on the ball, around which an imperceptible darkening begins, spreading more and more along gradually increasing arcs, until, finally, it turns into a moon-shaped shadow in invisible outlines that does not reach the rounded edge of the body, because it is prevented by a reflex that itself gradually brightens when approaching to the falling shadow.
It is very difficult for an inexperienced draftsman to convey such a distribution of light and shade transitions. This requires diligence and culture of drawing, understanding of the task, thoughtfulness of each stage of work.
Please note that compliance with the rules of modeling the shape with a tone with a reasonable variety of hatching techniques inevitably gives positive results.
Correctly taken in the image, the light and shade transitions convey the illusion of the materiality of gypsum (Fig. 20).
Control questions. Practical tasks
1. Define the concept of chiaroscuro.
2. Explain the patterns of distribution of light in shape.
3. What is tone?
4. How to explain tonal relationships?
5. What are the main patterns of tonal relationships?
6. Perform several exercises aimed at mastering a variety of pencil techniques.
7. Do an exercise to gradually increase the tone.
8. Draw from nature any spherical object in tone.
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.
Dimensions that determine the length of the cylinders - constituent parts parts, 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?
