The concept of form and geometric shape, features of perception by preschoolers

  • 11. The ratio of specialized learning, joint and independent activities in the organization of mathematical development of preschoolers.
  • 12. Requirements for organizing classes in different age groups.
  • 2. Gnostic skills
  • 15. Concepts of the development of quantitative representations.
  • 16. Features of perception by preschoolers of quantitative representations in different age groups.
  • Comparison of sets by establishing mutual compliance between them (using the applix and applications)
  • Reception machines.
  • 18. Methods of learning a quantitative account in different age groups: stages, receptions and account skills.
  • 19. Improving the account skills by learning counting from more sample and by the named number in different age groups.
  • 20. Improving the account skills through account training with the participation of various analyzers (the score of sounds, movements, tanging) in different age groups.
  • 21. Formation of the concept of the number as a quantitative characteristic of sets. Types of work on overcoming phenomenon Piaget.
  • 22. Relations and relations between the numbers of a natural series. Methods of learning comparing adjacent numbers.
  • 23. Methods of teaching a sequence account on average and senior preschool age.
  • 24. Methods of familiarization with the quantitative composition of the number from individual units in the senior preschool age.
  • 25. The method of familiarization with the composition of the number of two smaller numbers and the decomposition of the number into two smaller.
  • 26. The methodology for familiarization with the division of a whole to equal parts, establishing the relationship "whole" and "part".
  • 27. Methods of familiarization with numbers and arithmetic signs.
  • 28. Methods of familiarization with coins.
  • 2. Practical part
  • 3. Conclusion.
  • 29. Methods of learning to solve and drafting arithmetic problems: types, stages of work, various approaches to the method of learning to solve and drafting arithmetic tasks.
  • 31. Properties of magnitude, features of perception by preschoolers.
  • 32. Methods of comparison in size: immediate mediated, with the help of an eyeball.
  • 33. Methods of learning comparing 2 items largest in the younger and preschool age.
  • 34. Methods of learning compared from 2 to 5 items on average and 10 items in senior preschool age, ordering (seriation) in ascending order and descending.
  • Tasks give a gaming character using the game:
  • 35. Methods for learning measurement of lengths, volume of liquid and bulk bodies conditional standards and generally accepted measures in the senior and preparatory preschool age.
  • 36. The concept of form and geometric shape, peculiarities of perception by preschoolers.
  • 37. Software tasks and receptions of familiarization with geometric shapes in the younger, middle and senior preschool age.
  • 38. Methods for the formation of generalized concepts quadrilateral and polygon.
  • 39. The use of various types of material in the formation of ideas about form and geometric shapes.
  • 40. Orientation in space. Features of spatial representations from preschoolers.
  • 41. The system of work on the formation of spatial representations from preschoolers.
  • 42. Methods of forming orientation in space in different age groups.
  • 44. Software objectives and methods of work on the development of temporary representations in different age groups.
  • 45. Acquaintance with the calendar as a system of time measures.
  • 46. \u200b\u200bDevelopment of a sense of time from preschoolers.
  • Stage 1.
  • Stage 2.
  • 3 stage.
  • 4 stage.
  • 48. Features of the organization of work in different age groups.
  • 50. Features of working with gifted children.
  • 51. Communication of pre-school institution and family on the mathematical development of the child.
  • 52. The continuity of the pre-school institution and 1 class school on the mathematical development of children: forms and content.
  • 53. Indicators of the child's mathematical readiness for school.
  • 37. Software tasks and receptions of familiarization with geometric shapes in the younger, middle and senior preschool age.

    Goals to familiarize children with the form of objects and geometric figures They are to organize the survey of objects of different shapes, manipulation them. Children should accustom to perform actions related to finding items that are the same in shape; It is necessary to create conditions for comparing items in form.

    As didactic tasks The following are formulated:

    Distinguish and call geometric shapes;

    Group figures for different features (volumetric, flat, having angles and rounded);

    Compare items in form, understand the dependence of the form from other qualities, signs;

    Call and show elements of geometric shapes (sides, angles, vertices, bases, side surface);

    Recreate and transform shapes (draw, draw, lay out, divide into two or four parts, etc.);

    Know the features of geometric pieces as standards when determining the shape of objects;

    To own different ways to compare items in shape, finding general and different;

    Develop eyemeter.

    The implementation of the program depends on the age characteristics of children.

    So, in the first junior group Children get acquainted with a ball and cube in the process of practical actions with them (raise, bring, rolling).

    In the second younger group Kids can be familiar with the square, circle, bar, consolidate their knowledge about Cuba and a bowl. The main content is to train the surveillance of the figure by contacting motor and visual. Children compare the same in shape, but different in color and magnitude familiar figures: circles, cubes, squares, triangles, balls, bars.

    In the middle group Knowledge of children are enshrined about already familiar figures, as well as they get acquainted with a rectangle and cylinder.

    IN senior group The formation of knowledge of geometric figures continues. Children can be familiar with the rhombus, pyramid, oval. Based on the existing knowledge in children, the concept of a quadrangle is formed.

    In the preparatory group Children are offered only one new figure - cone. However, children exercise in distinguishing and building polygons (five-, six-, sevenfones).

    In tab. The content of children's knowledge is presented (the program of raising children in kindergarten. Kiev, 2000.)

    Early age

    (1st Junior Group)

    Perform actions related to finding items are the same in shape. Exercise the child's hand in examination of the subjects; establish the similarity and difference of objects in form; Group, respectively, sample

    4th year of life

    (2nd Junior Group)

    Compare items in the form using a geometric shape as a reference. Select and call geometric shapes: cube, circle, ball, square, triangle. Learn to examine geometric shapes with a visual connate motor

    5th year of life

    (middle group)

    Acquaint with the title and signs of geometric shapes (circle, square, triangle, ball, cube, cylinder)

    6th year of life

    (senior group)

    Sharing familiar geometric shapes into groups: flat (circle, square, rectangle, triangle, quadrilateral) and volumetric (ball, cube, cylinder) compare items in shape using geometric shapes as standards

    7th year of life (preparatory for school group)

    Expand knowledge of polygons: triangle, quadrangle, five, hexagons. Call and show elements of geometric shapes (sides, angles, vertices). Share geometric shapes, two, three, four objects, etc. Parts

    From age to age, there is not only an increase in the number of geometric shapes and expansion of knowledge, but also the deepening of them, the ability to freely use them in different activities.

    Methods of formation of ideas and concepts about form

    Acquaintance of children with the form of objects the best way occurs with a combination various methods and teaching techniques.

    Are used visual methods and techniques: "Look and find the same figure," "What is like a figure", etc.

    Wide use in training find practical methods and techniques: "Find, bring, show ... Lay out, draw, make a pattern," et al.

    Along with visual and practical used verbal methods and techniques: "What is called, what is different than similar; Describe, tell me "...

    N. A. Sakulina suggested methodological model of children's learning examination of objects, defining the form as their main sign. This model stands out five components:

    1. Complete perception of the subject;

    2. Analysis of the subject - the decaying of the characteristic essential features, the definition of the shape of individual parts of the subject (round, square, triangular, long, spinning ...), the likeness of this part of the geometric shape, closest in shape;

    3. Evigious and tactile feeling of shape - loving motions with simultaneous pronaling, i.e., the survey of the subject;

    4. Again the holistic perception of the subject;

    5. Constructing a model from specified forms or parts.

    Based on this scheme of teaching children was developed specific method - sequence in the formation of knowledge about geometric figures (3. E. Lebedeva, L. A. Wenger, L. I. Sysuva, V. V. Kolezko, R. L. Nepomnyaznaya):

    1. Demonstration of the geometric shape and calling it.

    2. Examination of the geometric shape through concrete practical actions.

    3. Show a few of the same geometric figures, but different in color and magnitude. Comparison of geometric shapes. At the same time drawn the attention of children to the independence of the shape from the size and color of the figure.

    4. Comparison of geometric shapes with objects close in shape; Finding among the surrounding items of such that are close in their form with this figure.

    5. Comparison of items in the form of each other using a geometric shape as a standard.

    6. Comparison of familiar geometric shapes, determination of common qualities and differences (oval and circle, square and rectangle, etc.).

    7. Fastening the properties of geometric shapes by measuring, modeling, drawing, laying, construction, etc.

    Children must learn the basic actions to survey the form of objects.

    Survey Geometric shape is carried out by concrete practical actions (loving by contour). An important element Surveys is comparison of figures, different in form and magnitude. After the children have learned to compare geometric shapes with objects close to form, it is necessary to provide them with the ability to fix the properties of geometric shapes in drawing, modeling, appliqués, design.

    Children follow teach correctly showing elements of geometric shapes (corners, side, base, etc.).

    - when recalcifying the corners The child should indicate only to the top of the corner. The educator does not explain what a vertex is, but shows the point where the two sides are connected.

    - showing parties, the child must fingers along the whole segment - From one vertex angle to another.

    - Corner itselfas part of the plane is shown at the same time with two fingers - Large and index.

    IN volumetric figures Children stand out and called side sides and basis.

    In each age group, the method of familiarization with geometric figures it has its own features.

    In the second younger group Children learn to distinguish ball and cube; Circle and squareUsing receiving a pair comparison: Ball and Cube, Cube and Bar - Brick; Circle and square; ball and circle; cube and square. In this case, the subject should be kept in the left hand, and index finger right hand to circle him along the contour. To demonstrate the geometric figures, it is necessary to use different in size and color of the figure.

    Children look at and compare the ball and cube, Find a common and different in these subjects (figures). Turning to the question of children, the educator attracts their attention to the features of the figures: "What is it?", "What color balls?", "Which one is less?"

    On the instructions of the teacher, one child takes a small ball in his hands, and the other is big. Children pass balls in a circle: a little ball is catching up big Shar. Then the direction of movement changes. In the course of such games, children specify the features of the ball - is he round, he has no corners, you can ride it. Children compare balls different colors and sizes. Thus, the educator brings them to the conclusion that the form does not depend on the color and size of the item.

    Similarly, clarified children about Cuba are specified and summarized.. Children take a cube in hand, trying to roll it. He does not roll. Cuba has corners and sides (face), it is steadily standing on the table, the floor. From the cubes you can build houses, columns, setting one cube to another.

    The most important point When familiarizing children with the form is spectator and tactive-motor perception, a variety of practical actions, developing its sensory abilities.

    In organizing work to familiarize children with the form of the subject significant place is occupied by showing (demonstration) the Figure itself, as well as ways to examine it. The educator teaches children when examining the subject to keep the subject in the left hand, the index finger right hand Cut it along the contour.

    For development in children, the skills of the subject of the subject and accumulation of relevant submissions Different are organized didactic Games and Exercise. So, in order to assimilate the name and clarification of the main features of individual geometric shapes, the educator organizes the games: "call a geometric shape", "magic bag", "Domino figures", etc.

    In the game "Magic Bag" The teacher teaches children to choose the shapes to the touch, find along the sample. On the table there are geometric figures familiar children, and the bag is the same. At first, attention is drawn to geometric shapes placed on the table. Children call them. Then, by instructions, the child finds such that stands on the table, and shows it. If the child cannot fulfill the task, the teacher once again resembles the ways of examination of the figure: the right hand slowly drives along the edge (contour) (you can help with your left hand). When re-conducting the game, the number of geometric shapes increases.

    In the game "Find the subject of the same form", "What lies in the bag?", "Geometric lotto" children exercise in finding items on geometric samples. Such tasks are difficult, but generally affordable for children. They develop their ability to analyze the surrounding environment, abstract when perceiving the form of objects. The child, perceiving the Estamp, which hangs on the wall in front of him, is distracted by the plot of the picture, and it allocates the shape of the frame (square).

    In his free time, the children of this age group are very likely to love games with cutting pictures, mosaic, building material.

    In the learning methodology Children of the middle group distinctive is an a more detailed examination of geometric shapes. With new geometric figures of children introduced, comparing their models with already familiar or each other: a rectangle with a square, a cylinder with a cube or a ball.

    From the immediate comparison of items with geometric samples Children go to the verbal description of their shape, to generalization.

    Procedure for viewing and comparing figures Maybe such: what is it? What colour? What size (values)? What made? What is the difference? What are like?

    The main techniques may be:

    Practical actions with objects (ride, put);

    Imposing and applying;

    Circuit circuit, feeling;

    Exercises in grouping and ordering - didactic games, exercises for the assimilation of the features of geometric shapes;

    Comparison of the forms of objects with geometric samples;

    Analysis of complex shape.

    From children required deployed verbal designation of its actions (Describe the form of an object consisting of 2-4 parts: a nevosha, a car, etc.).

    L. A. Wenger, L. I. Sysueva, T. V. Vasilyeva developed 3 types of tasks in the field of familiarization of children of the fifth year of life with the form of objects and geometric figures:

    Assignment of geometric shapes;

    Tasks for comparing forms of real objects with geometric shapes;

    Tasks for spatial analysis of composite form.

    In the senior group M. etodyics of the formation of geometric knowledge in the group of the sixth year Life fundamentally changes. but the survey becomes more detailed and detailed..

    Along with practical and direct comparison famous geometric shapes, overlapping and applying, widely used as a methodological reception measurement of conditional measure.

    All work on the formation of ideas and concepts about geometric figures is built on comparison and comparison of their models.

    The models are first compared in pairs, then 3-4 shapes of each type are compared, for example, quadrangles.

    Based on the identification of essential signs of geometric shapes Children are summarized to a generalizing concept " quadrangles».

    So, familiar children with a rectangleThey show several rectangles, different sizes made from different materials (paper, cardboard, plastics). "Children, look at these figures. These are rectangles. " At the same time drawn attention to the fact that the form does not depend on the size. Children are offered to take a shape into the left hand, and the right hand to circulate along the contour. Children identify the features of this figure: the sides are pairwise, the corners are also equal. Check this flexion, overlapping one to another. They consider the number of sides and corners.

    Then compare rectangle with square, find similarities and differences In these figures. Comparing the square and rectangle among themselves, children set that all these figures have four sides and four corners. This is the number of sides and corners he is a common signwhich is based on the definition of the concept of "quadrilateral". However the rectangle is different from the square what at the square, all sides are equal, and the rectangle is equal to the opposite, pairwise.

    Special meaning Acquires work on the image and reconstruction of geometric shapes: laying out of sticks, paper strips. This work is carried out with both demonstration (near the table of the educator) and handouts.

    At one of the classes, the teacher lays out a rectangle from the strips on the flannelf. "Children, what is the name of this figure? How many sides of the rectangle? How many angles? " Children show the sides, corners, tops of the rectangle. Then the teacher asks: "How and which figures can be obtained from a rectangle (create smaller rectangles, squares, triangles)?" At the same time, additional paper strips are used. Children consider the parties to the figures received.

    In the older preschool age, children are formed the ability to endure the mined knowledge in the situation unfamiliar to them, use these knowledge in independent activities. Knowledge of geometric figures are widely used, clarified, fixed in classes on the visual activities, design. Such classes allow children to acquire skills in dividing the complex pattern to composite elements, as well as create drawings of a complex form from one or two types of geometric shapes of different sizes.

    So, during one of the classes, children distribute envelopes with a set of models of geometric shapes. The educator shows the applique of the "robot" composed of squares and rectangles different sizes and proportions. First, all together consistently consider the sample. Install from which parts (figures) each detail is performed. In the same sequence, children create an ornament. The teacher shows two or three ornaments and invites children to choose one of them, carefully examined it, lay out the same ornament.

    In bulk figures (such as cylinder, cube) children stand out and called side sides and bases. At the same time, they can be shown a few fingers or the whole palm.

    Children perform practical actions, manipulate with geometric shapes, reconstruct them.

    In the process of such training enriched "Mathematical" Speech of Children.

    Acquaintance with form, usually, occupies part of the classin mathematics, as well as on design, visual activity.

    During classes are widely used Outing, applying, circuit in contour, hatching, measurement. Flat geometric shapes The children are cut, bulk - pose from plasticine, clay.

    This work is closely related to the teaching of children to the elements of the letter: the circulation of cells, drawing circles, ovals, carrying direct and inclined lines. Children get acquainted with notebooks in a cage, consider how the pages in the notebook are rapidly. The tutor offers children to find and circle cells in different parts of the page: at the top, below, on the left, right, in the middle; Draw seven squares in size in one cell with pass between them in two (three) cells. At the same time he shows different methods Task Performance: Designation of the initial contour points, conducting lines from left to right and top down.

    Future schoolchildren teach distinguish and call polygons (triangle, quadrangle, pentagon, hexagon), call and show their elements (sides, corners, vertices), share geometric shapes on the part, compare among themselves, classify in size and shape. The work is directed, first of all, to improve the quality of these knowledge: completeness, awareness. The geometric material is widely used during classes as a demonstration and distribution in the formation of numerical concepts, dividing the whole to the part, etc.

    For preschool age Children learn examine a simple and complex Objects, hold specified sequence:

    First allocate general contours and the main part,

    Then define the form, spatial position, the relative size of other parts.

    You should teach them notice not only similarity, but also the differences Items from the familiar geometric shape. It has great importance To improve the visual and other types of independent activities of children.

    You already know that the main task of drawing is to learn how to see objects in bulk forms so that in practical work can be able to transfer the volume with certain expressive means - a line, a stroke, tone. If you correctly painted the subject, this means that in the pencil image it is correctly constructed its inner base - design and material properties (surface texture) are expressive. All this, it would seem, it looks simple, but it falls for a long time and persistently work to learn how to perform similar drawings. You should never rely only on certain abilities for visual art. Large painstaking work is needed, for knowledge, skills and skills do not come by themselves, but serve as the result of huge and intense efforts.

    There are no shapeless bodies in nature. If it was possible to imagine such a myself, except for some abstract (distracted) emptiness nothing else was conscious. Therefore, it is necessary to believe in shape as an organization of certain parts, constructed expediently and in strict accordance. The subject in the usual sense of the word is called a person created by a person, necessary people and performing a specific function. Studying the drawing, you must guide the form in your work. The famous teacher's artist Dmitry Nikolaevich Kardovsky in published in Moscow in 1938. The book "Drawing allowance" wrote: "What is the form? This is a mass having one or another character, like geometric bodies: Cuba, ball, cylinder, etc. The live form of living natures, of course, is not a correct geometric form, but in the diagram, it also approaches these geometric forms and thus repeats the same laws of light location according to prospectively leaving planes, which exist for geometric bodies.

    The challenge of the student is precisely in combining and coordinate the understanding of the form with techniques for the image (construct) on the plane with light ... surfaces that limit the form in space. When the ball draws, they know which techniques should be applied to the image of the transitions of its surfaces in the shade and in the light, as well as methods are known when the cube is images, pyramids, cylinder, or some more complex figure, etc. ... What is characterized, for example, the shape of a person's body? This is a cylindrical form. If the body was the right cylinder, then it would be very simple, but there are convexities, recesses and other deviations that violate the simplicity of the cylinder. At the same time, these bulges and recesses are located along a large form of a cylinder or aside that receives straight rays of light, or aside, not receiving them or in transition. When drawing, these deviations need to withstand, respectively, in the tone: 1) of light, 2) shadows and 3) of the half. The feeling of form, the ability to see and transfer it to develop a student in order for it from consciousness, as they say, "passed into the ends of the fingers," i.e. As an image of the form on the plane, the drawing should feel it just like a sculptor that sculpts the shape of clay or cuts it out of stone "(Kardovsky D. N. Drawing Manual. M., 1938. P. 9).


    People often use the word "form." All correctly understand the meaning invested in this concept. Yes, indeed, the term "shape" (from Lat. Forma) is translated as a concept that gives a person to comprehend the external outline, outdoor, contours of one or another item. In any image, it is always shown primarily the form of a drawdered item, i.e. truthful outlines of it. When artists say that in this figure is well transmitted a volume form, they emphasize the truthfulness of the image. In fact, the concept of "bulk form" essentially indicates two words close in meaning, for the volume of the subject also contains a mass, configuration inherent in the form. The volume itself should be regarded primarily as one of quantitative characteristics Geometric bodies - capacity, which is expressed by the number of cubic units. Faces visual arts And architectures understand this word the appearance of space bounded by planes.

    Thus, under the bulk form of objects should consider the patterns of the structure, i.e. Features of their design.

    For an image of a volume form, you need: the skill of drawing to see and understand the features of the design (structure) of items and the transmission of three-dimensionity - length (or widths), height and depth - the forms of the same items on the two-dimensional plane of the paper sheet.

    Therefore, the image of the form in any drawing from nature should be based on its construction, and not to draw the appearance of the subject. Such a construction assumes the presence of a clear constructive approach to the surrounding subjects. Since you are in front of you a two-dimensional plane, and you need to draw three-dimensional volumes, then imagine a sheet of paper a certain (conditional) space and try on the basis of the knowledge of the methods of promising drawing to place the image in it. Remember what examples from the world of geometric bodies can be used to resolve the task of placing the form in the sheet space using their combinations visible in nature.

    Tone drawing

    Drawing from the nature of any item, you simultaneously solve several tasks, one of which is transmitted in the image of lighting.

    To see the drawn object, it should be lit naturally (daylight) or artificially (electric light). The physical phenomenon of the distribution of light, thanks to which our vision distinguishes the surrounding reality, in the visual practice is called lightness.

    Perception various shapes It becomes possible because reflected light rays fall into the eye. Such radiated light allows you to visually perceive any object.

    Lighted objects located in space are varying as voluminous. The volumetric form of the subject in accordance with its structural structure is determined by the game of light and shadow. The peculiarity here is that the form of the subject is consisted of different surfaces under different angles to the rays of light, because of which the illumination of this object is uneven: on the areas that are perpendicular to the rays, the light falls completely, it is allocated to others. From the position of them at a certain angle - as if "slips", and it does not fall into others.

    For the draftsman, the degree of illumination of the surface of the subject is also important, which depends on the source force and from the distance to it. On the perception of illumination of the drawdered item also affects the distance between it and drawing. This is due to a light-air medium forming the "haze" (from the smallest dust particles, moisture droplets and other substances in suspension), which dissolves the sharp outlines of the boundaries of light and shadow, prevents the illuminated areas and lands deep shadows.

    So, the radiation of the light will give the light stream, which spreads in one direction, reaches the object and reveals the surface of its surface. Depending on the brightness of the light rays of the stem, the object becomes contrast. Under the word "Svetlota" should be understood as the reflectivity of the surface of the subject. You know; That everything that we see and distinguish is related to the physical nature of the light capable of producing the reflective ability of material bodies certain signals to our eye that responds to them with a wonderful property - color-point. It goes without saying that lightlot is determined primarily by the feature of the surface of the subject in the reflection of light. White, yellow, blue color reflect more light than black, blue and brown.

    Therefore, it should be necessary to tell about blacksies in more detail. Best, perhaps, detailed feature All lighting gradations are possible on the example of a spherical surface.

    The shape of the ball is remarkable in that it is uniform on all sides, is not distorted due to the peculiarities of promising changes in the subject and gives a complete concept of lighting laws. Being in space, the ball in any position is equally illuminated with one source of light and shaded from the opposite side. So, the rays of light fall on this geometric body, in different ways illuminating exactly half of its spherical surface. Why in different ways? - You can ask you. After all, if half is lit, therefore, the illumination is the same everywhere. The fact of the matter is that unequal. Only a unhappy draftsman can imagine the same tone illuminated surface, and even if he sees that this is not the case, nevertheless will retain his conviction. Not because in the figures of the ball in people who are unfamiliar with the concept of lighting, half of the image is left untouched with a pencil, and the second is stupid evenly.

    Let's figure out in the patterns of the distribution of light on the surface of the ball. Let the gypsum model of the ball be on the light gray plane at a distance of one of its magnitude from a white matte wall and illuminated with artificial light, flowing on the left side at the angle of 45 °. It will not be difficult to think correctly that the model is covered at this angle and that the brightest light on the surface of the geometric body is concentrated on the site, which is perpendicular to the direction of rays from the source. As you can see, we are talking about the direct hit of the light rays on the surface and, consequently, straight coal Surfaces and rays that fell on it. Part of the light rays falls on the surface of the ball due to the structure of it under increasingly sharp corners, and the sharper the angle, the less light falls on the sphere. It turns out that the curve surface with a decrease in light should gradually go into the shadow.

    Finally, in the distribution of rays in the sphere occurs when the curve surface goes beyond the reach of light and immerses in the shadow.

    The most bright illuminated spot on the surface of the ball is called the title, which is very well noticeable on any shiny surface, for example on glass. Around the glare is visible light half, proving the rules for the distribution of light on the ball surface. Artists call it halftone. Haltone of the first strip around the glare is imperceptible in its outer edge goes into the next, he is also imperceptibly merged with now the third, etc. All these transitions imperceptible to the eye merge with each other due to the spherical surface of the body, until the last of them is as much smoothly by its edge into the shadow. Each new halftone is slightly darker than the previous one.

    Shadow is a part of the subject that received its name due to the lack of light, being outside its distribution. But all that is in the shade, also obeys its laws, exposed to ambient. You remember that the condition was put on which the ball should defend 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 not profitable. You begin to guess that the wall is covered with the same source, and therefore, reflecting the light, should now make an amendment into black and white relations inside the spatial environment. Reflected from the wall light at an angle of 45 °, but now with right sideIt falls on the shadow, and although it is much weaker than direct, nevertheless its impact significantly affects the smooth decreement of the shadow. On the surface of the ball in the shade, due to the light reflected from the wall, a phenomenon called by reflex is formed. In that part of the ball, which is associated with the surface of the table, the reflex from this surface is visible.

    Shadow on a bowl is called his own shadow. On the table from the ball in strict accordance with the direction of the light flux from the source lay down another shadow, which is referred to as a falling shadow.

    The patterns of the distribution of light on the surface and around the visible item should be well known each drawing.

    The surrounding reality with all its phenomena, forms and volumes people perceives visually. In auditorium, the main role plays his ability to see the world with color. Do not be at our primitive ancestor of this innate ability, who knows, would exist humanity as such. The distinction of the shades of color helped people of those distant centuries literally survive in the fight against the harsh and merciless forces of nature. Would they continue to preserve if the world around them was absolutely bluishless, what is called gray or black and white?

    But why then, - can you ask with full right, - black and white literate drawings so truth and attractive? With the answer to this question, let's slip, but here you will come close to the concept with which we will have to associate the implementation of images, taking into account the requirements of truthfulness, tone.

    Before determining this concept, turn to the surrounding reality and let's call some examples related to the visual activities.

    Wonderful Russian landscape players Alexey Kondratyevich Savrasov, Ivan Ivanovich Shishkin and Fyodor Aleksandrovich Vasilyev in his work performed the rejection of the finished pencil drawings of nature. Each drawing not only amazes the magnificent skill of execution, but also has a number of advantages to which the correctly taken black and white relationships. In fact, how can the differences in the tone of the crown of wood and grass, front and distant plans, shrubs and weed plants? The masters sought such a difference with glitter, and a black and white pencil in their hands gave such tonal effects that fit to compare with picturesque.

    An ordinary graphite pencil can be transferred to the brilliance of water and from glass, velvet and satin fabric, bark of the tree and a gentle rose petal shape. And the point is here in tone, and only in it.

    The word "tone" (from Greek. Tonos - voltage) means the overall black-free image strength (in painting this concept corresponds to the color of the work).

    So, tone is called black and white image strength. Consequently, in front of the artist performing a long creative drawing of a landscape or household scene, there is a task to convey a tonal relationship between all elements of the image in its work so that the picture makes an impression on the viewer not only a deep life content, but also expressiveness.

    You already know that the largest paper is much darker than the genuine glare on the glossy surface, and the mild drawing material, not to mention the graphite pencil, giving the most black spot on paper, is still many times the brighter of natural black space. Therefore, it is always necessary to remember that the truthfulness in a dialing (tone) figure can be achieved only when the proportional nature reaches a black-free relationship.

    For a preliminary acquaintance with solving problems of the tone drawing, we turn to the analysis of still life, compiled in our imagination of three items. Let it be a glass jar with cherry jam, a light yellow apple and a white tablecloth. In your memory, all these items pop up and immediately, and one one. A brilliant bank filled with dark jam with an abundance of berries, looks wet-black, and an apple is darker tablecloths, despite its light shade.

    Still life is lit by daylight, and all its contrasting features are visible as it is impossible. All reflexes are clearly read on the bank, and an apple, which is ahead of the vessel with jam, even in the shade contrasts sharply with part of the dark silhouette. Snow-white tablecloth beautifully emphasizes bulk form of fetus and cans. Of course, such a still-life rightfully claims a picturesque decision, since the color advantages is evident.

    It is possible to draw this still life, while retaining in the image the first impression of this freshness and sowing to subordinate sharp contrasts between all objects to the total tony state of nature. Of course, you can draw such a still life, if you have the necessary knowledge and skills of visual activities based on a holistic vision of nature.

    In the process graphic image It is absolutely meaningless to try to convey the absolute relationship of Svetlot Nature. You already know why it is impossible. It is only necessary to adhere to the proportional relationship of brightness.

    All diverse tonal relationships can be transferred by modest means of drawing.

    Why start? With the establishment of a so-called tonal scale - the relationship between simply white paper and the thick layer of the graphite substance applied to its surface. Between these two extremes are in the appropriate relationship from light to dark all other tone gradations.

    So, in the still life, all illuminated and shadow places of objects are distinguished by a large variety of various tonalities that are detected by a simple graphite pencil. Therefore, when working on any teaching task, be sure to install a tonal scale. It can be depicted in the form of a strip of several (according to the number of basic spots of light and the shadows observed in nature) rectangles, shaded to transfer the entire gamma of shades in the right coencing. It will very help in work, will give an excellent opportunity to "feel" graduation and give confidence.

    It is very important to practice in the development of the ability to finely distinguish the gradations of Svetlilt in mynthematics. After some time, you will start capturing even small tonal differences in kind.

    But back to the imaginary still life. You have installed a tonal scale and it turned out that nine basic spots of light and shadows are visible on nature. These are glare glass bank Both apple, common stains of the tablecloth and background, as well as apples, two shadow stains of shadows from the can and apple, the total stain of the jar with the contents in the light and the general - in the proportion of the vessel.

    In the modeling of the image, you need to observe the proportional dependence between the luminosity of some spots of nature and the corresponding places in the figure. In this case, you can not be carried away by the study of some particular part of the image, but only all the time working with relationships, constantly comparing the pattern with kind. The study of a separate place in the figure without communication with other is fraught with complications associated with the impaired integrity of the image. By doing such a study, you begin to compare a separate piece with the same in nature and, of course, leave the conscious reduction in brightness or shadow thickness in the picture.

    All details in kind should never be transmitted in the figure. This is impossible. In kind, all the details are associated with the general, submitted to him, and in the figure it is unlikely that it is hardly possible to link it all. Thus, the tone pattern requires a developed feeling of shape, design, skillful formation of a shape of a light and final generalization so that the image looks assembled and solid, and, most importantly, in it should be transferred proportional nature of the relationship in tone.

    Drawing Cuba

    One of the outstanding artists of France Angr once said well about the figure: "It does not mean to draw at all to make contours; The drawing does not consist only of lines. The drawing is also expressiveness, internal form, plan, modeling "(Angg about art. Collection. M., 1962. P. 56).

    When drawing from the nature of plaster models of geometric bodies, you need to portray each body, carrying out its modeling of transmission of black and related relations. You learned about tone drawing from the previous paragraph.

    Essentially, this is your first pretty long pattern, in which the complex work is to be performed associated with the technique of the pencil image. You facilitate the choice of equipment - perform a drawing in a tone of hatching or tuber. It is recommended that the hatching is recommended, as it disciplines in many respects, it teaches the pattern attentively and focusing. The peculiarity of this technique is that the strokes need to lay on the form of the model, and if this requirement does not adhere to, it is very soon to see that the stroke paper surfaces coated as hit, i.e. Thoughtlessly, destroy the drawing, do not reveal the bulk form.

    The cube model should be lit by artificial light, the source of which must be placed on top of the left. In this case, it is clearly visible from your chosen point of view and the entire volume of the body, and black and white gradations. The cube is set at an angle to the drawing, slightly below the level of the eye so that the upper face is visible. The background should be light, and the model is located on gray drapery, without folds unsettled on a stand for nature.

    To get started, you need to remember previous exercises for drawing from the nature of the frames of geometric bodies. Such tasks you have to decide now. True, now the cube appears in front of you, in which it is truly perceived by volume. The framework allowed to see a cube, with all the edges and ribs. Now part of them is not visible, but the eye should be able to "see" them, so that when constructing, taking into account promising cuts, it will certainly show. Only then they talk about the structural structure of the shape of the geometric body.

    However, it is impossible to draw on paper without prior placement. Only some virtuosos of academic patterns could start an image of a statue from a single point and, without taking off a pencil from paper, carry out a very accurate contour of an ancient sculpture on a sheet. You need to act much easier and pencil many times to take away from the paper to look at homelighting and on your sheet and apply the general shape of the Cuba on it, placing the drawing in this way, and then check it, comparing with inouture. The general shape of the cube on paper is applied so that Abris is and not very big, but not small. It is most advisable to present a sheet of paper with a conditional space in which the Cuba model takes its decent place. Of course, at first, such a representation is difficult, but in each new exercise it is necessary to include this kind of "mechanism" in itself, in order to bring it to automatism over time.

    The scheduled Abris Cuba took his place on paper, and you can move a little back to see the design of the drawing at a distance and check out the correct or incorrect this case Location image in format. Of course, on how you first posted a drawing, it depends in many ways to work.

    Start clarifying values \u200b\u200bby visual comparison. By choosing a certain height of the front vertical edge of the cube, subordinate to it the rest, but already taking into account the promising changes in nature. BEFORE to determine the place of this edge to you in the planned image silhouette. Then, take the height of this edge, draw a vertical segment, and at the bottom point, swipe it strictly horizontal line, which will be auxiliary when building. It will be necessary to imagine a horizontal line a little later, perpendicular to the base of the edge in kind, to make an angle formed by a horizontal edge of the right face on paper. For comparison, put a pencil or ruler to the base of the cube plaster model to see the angle in kind.

    Further work on drawing a gypsum model Cuba is carried out as a gradual identification of the structural base of the subject. Taking advantage of the landmarks, build the bottom line, having experienced "see" her outlines from all sides, i.e. Show invisible edges, as was done when constructing a cube frame. At the same time, schedule all the other vertical edges, constantly comparing the magnitude of them with the edge, closer than all in relation to you.

    Knowing the rules of perspective, associate with the construction of visible changes in the form of the cube. Two points of the conditional continuation of the ribs at an angle to you remain guidelines for building all the remaining four tops.

    After you have built a "skeleton" Cuba, compare the pattern with kind and think that it strives first of all - the entire cube or details of the form. In this case, admitted inaccuracies will be visible. While it is easy to eliminate them, for you, when building a shape of a geometric body, we hope not to overdo it in applying traces of a pencil on paper. Remember, when building a form of the image of the subject, all lines should be carried out easily and confidently.

    Why did you see inaccuracy in the drawing? Our vision, as it became known thanks to the experimental data of psychologists, first seizes the general form of the subject, for a short time, as if fixes it.

    Eliminating the bugs of construction, once again deposit the image with nature and make sure that the design of the drawn cube corresponds to the visible model. Since the image of the cube on paper is relatively quick, with proper construction, you should not schedule a volumetric form of geometric body light Sharchka, showing this very shadow side of the subject, for it failed - it is known that we draw the similarity of the subject, and what sees our eyes in kind, he "wants" to see in the picture.

    Black and white relationship in the figure should also be built. We are talking in applied to the visual activities of different words, for example, the "scale scale", "tone scale". In the first expression, it is necessary to keep in mind the definition in the figure of the sizes and the ratios of the parts of the subject in comparison with nature.

    Drawing from nature, you perfectly legitimately try to transfer the image as you perceive the subject. With hatching or sharp, you simulate the volume of the subject, showing the illuminated, transient from light to the shade and shaded sections in the image. Finish this work, only making sure that black and white relationships are faced in the figure. These most you have withstood in the image of a tone scale, i.e. managed to find the proportional ratios of the darker and the brightest tones.

    Tone drawings are created by the skillful distribution of light, half and shadow with the help of a barcode technique.

    Modeling the shape of the cube tone, in no case are not in a hurry to immediately lay the shadow facet of the geometric body. First, it will not be possible, and secondly, as they do not draw and do not apply tone in parts. The point is here in the difference of natural light and whiteness of paper, in the materiality of the natural object and the shaded pencil surface sheet of paper, etc.

    To achieve faithful (and not exactly in-point) tones allow reasonable in the figure proportional nature of the relationship.

    Therefore, we recommend that you approach to the transfer of black and related relationships: Choose the most dark tone Hatching that use in a certain place of the picture and no longer repeat it anywhere, and all other gradations will vary from this dark to the tone of the paper itself.

    Follow the overall illumination of nature and transmit this in the picture.

    Diverse the technique of a pencil, do not cover the pattern of the thoughtless, monotonous "comfortable" for the hand of the hatching. The texture of the gypsum itself suggests a thoughtful handoff. Ways to cover paper with a pencil layer.

    At the end of the work, summarize the image, i.e. Get the elimination of cutting eyes of contrasts or a mechanical set of individual tones, and give the drawing into the overall coenplex of all tones (Fig. 18). Learn to transmit faithful tone relationships expressing the shape and material in the picture.

    Fig. eighteen

    Drawing cylinder

    The principle of illumination of the next model for drawing from nature remains the same. This time you will perform a tone pattern of the cylinder - a geometric body formed by the rotation of the rectangular plane around the single axis.

    The cylinder shape is peculiar. Unlike cube, light on the cylindrical surface is distributed in many ways. The bases of the cylinder are the round planes, and if they are under any angle (in the angle), they look already ellipses.

    You painted the wire model of this body and the structural basis has been practically studied.

    Building a cylinder located vertically, start with the layout of the total body shape. In order not to be mistaken in the placement of the general form (white silhouette) of the cylinder in the vertical format of the paper sheet, swipe a light vertical in the middle and visually define the height of the depicted body, and then its width.

    Next, the construction of the shape of the cylinder turns out effective tool Development of knowledge and practical skills in drawing, as it helps to learn the rules of perspective and constructive structure of objects. Performing this work, you must act confidently, to keep a pencil freely.

    By building a cylinder frame, in which both bases are correctly depicted in the future (the bottom is slightly wider, as it looked in nature), compare the image with kind and go to the model forming the tone. If the cube was a certain complexity, caused by the transmission of proportional natures of black-related relations, then in the tonal characteristic of the cylinder, additional effort is needed to understand the degree of distribution of gradations of light and shadow along its specific surface.

    Be sure to deal in gradations, since instead of transmitting the bulk form, the drawn image may look like a marked or flattened. That this does not happen, be extremely attentive in modeling the surface of the cylinder-built surface.

    Black and white solutions of the shape of the cylinder obeys the knowledge of the drawing. Each sees how the light is clearly covered by the cylinder surface, the shape of the geometric body. The most bright looks on the cylindrical surface a small plot. This is a glare, and its phenomenon is caused by the fact that the light rays fall into this part of the volume are strictly perpendicular. Next, the light begins to slide along the spinning surface and, of course, weakens the illumination of the subject, while its impact is interrupted by the region concerned abroad between it and the shadow, becoming the most dark spot. Consequently, the cylindrical surface gives a clear visual representation of the sequential distribution of black and white gradations in approximately so alternating: halftone, light, glare, light, halftone, shadow, reflex. Of course, the transitions between them are completely not distinguishable, and this is one of the difficulties of transmission in the figure of the cylinder formation. It means that you need to not achieve the absolute similarity of the drawn cylinder with nature, but to monitor the correct transmission of the ratios of gradation ratios (Fig. 19).

    Background in tone pattern serves an integral part of the spatial image. In addition, it affects the overall light of light, turning to be neutral, then actively affecting the perception of the subject.

    Fig. nineteen

    Figure ball

    The construction of such a geometric body, like a ball, no particular complexity, if we exclude impeccable in accuracy of the curve line. However, it is only needed when constructing, and in the completed tone figure disappears, as not at all. It has already been said that the non-line is the boundaries of the form.

    Fig. twenty

    The gypsum model of the ball, intended for drawing from nature, is located in front of the distance, not necessarily the corresponding triple size of the height of the nature. Well lit on the left and top view is visible from a few more distance.

    You can build a circle with a vertical line crossing it horizontal and two inclined at an angle of 45 °. Having postponing from the center everywhere the same radii, it is easy to spend a closed curve that will become the border of the mass of the ball.

    After the circle is scheduled, specify its borders, remove the auxiliary constructions and proceed to the detection of the spherical shape of the ball.

    It is quite suitable for the sculptural term "modeling". Indeed, it is possible to achieve a transfer in the figure in the figure of a spherical shape (spherical volume) only with the correct definition of the tonal relationship - as it were, "cutting out" the form.

    The graduality of the change in the illumination of the ball is also expressed by the same gradations as in the cylinder, differing only by characters, surfaces. The cylinder has all inconspicuous, brightening to the glare and gradually fading while approaching the shadow transitions are distributed in a straight vertical. At the ball, the spherical, the nature of the surface, and the light of it goes like in a circle.

    Light rays perpendicular to a spherical surface, form a glare on a ball, around which the inconspicuous darkening begins, and the stronger extending to gradually increasing arcs, until finally, does not go into the moon-shaped outlines of the shadow that does not reach the vigilant body of the body, for it Prevents the reflex, it itself is gradually brightening when approaching the incident shadow.

    Transfer such a distribution of black and white transitions for an inexperienced drawing is very difficult. This requires the adjustment and culture of drawing, an understanding of the task, the thoughtfulness of each stage of work.

    Please note that compliance with the rule of modeling the shape of the tone with a variety of incoming limits of hatching techniques gives inevitably positive results.

    Really taken in the image, black and white transitions transmit the illusion of the material of the gypsum (Fig. 20).

    Control questions. Practical tasks

    1. Determine the concept of lighting.

    2. Explain the patterns of light distribution in form.

    3. What is the tone?

    4. How to explain the tonal relationship?

    5. What are the main patterns of tuning relations?

    6. Perform several exercises aimed at mastering a variety of pencil techniques.

    7. Make an exercise on gradual strengthening tone.

    8. Draw from nature any ball object in tone.

    Acquaintance of children with the form of objects in the best way occurs when a combination of various methods and teaching techniques. Visual methods and techniques are used: "Look and find the same figure", "What is like a figure" and others. Widespread use in training Find practical methods and techniques: "Find, bring, show ... Lay out, draw, make a pattern" et al. Along with visual and practical, verbal methods and techniques are used: "What is called what is different than they look like; Describe, tell me "...

    N. A. Sakulina suggested a methodological model for teaching children to examine objects, determining the form as their main feature. This model highlights five components:

    1. Holistic subject perception;

    2. Analysis of the subject - the dissection of characteristic essential features, definition of the form separate parts subject (round, square, triangular, long, spinning ...), the likeness of this part of the geometric shape, closest in shape;

    3. Motor-tactile feeling of shape - filling movements with simultaneous pronaling, i.e., the subject examination;

    4. Again the holistic perception of the subject;

    5. Constructing a model from specified forms or parts.

    Based on this scheme of teaching children, a specific technique was developed - a sequence in the formation of knowledge of geometric figures (3. E. Lebedev, L. A. Wenger, L. I. Sysuva, V. V. Kolezko, R. L. Nepomnyaznaya).

    1. Demonstration of the geometric shape and calling it.

    2. Examination of the geometric shape through concrete practical actions.

    3. Show a few of the same geometric figures, but different in color and magnitude. Comparison of geometric shapes. At the same time drawn the attention of children to the independence of the shape from the size and color of the figure.

    4. Comparison of geometric shapes with objects close in shape; Finding among the surrounding items of such that are close in their form with this figure.

    5. Comparison of items in the form of each other using a geometric shape as a standard.

    6. Comparison of familiar geometric shapes, determination of common qualities and differences (oval and circle, square and rectangle, etc.).

    7. Fastening the properties of geometric shapes by measuring, modeling, drawing, laying, construction, etc.

    Children must learn the basic actions to survey the shape of the subjects. The examination of the geometric shape is carried out by concrete practical actions (enrolling the contour). An important element of the survey is the comparison of the figures, different in shape and magnitude. After the children have learned to compare geometric shapes with objects close to form, it is necessary to provide them with the ability to fix the properties of geometric shapes in drawing, modeling, appliqués, design.

    Children should teach properly show elements of geometric figures (angles, parties, bases, etc.). When recalcifying the corners, the child should only indicate the top of the angle. The educator does not explain what a vertex is, but shows the point where the two sides are connected. Showing the parties, the child should carry out the fingers along the entire segment - from one vertex of the angle to another. The angle itself as part of the plane is shown simultaneously with two fingers - large and index. In bulk figures, children highlight and call side sides and bases.

    In each age group, the method of familiarization with geometric figures has its own characteristics.

    In the second younger group, children learn to distinguish between a ball and cube; Circle and square using the reception of a pairwise comparison: a ball and a cube, a cube and bar - brick; Circle and square; ball and circle; cube and square. At the same time, the subject should be kept in the left hand, and the index finger of the right hand to circle it along the contour. To demonstrate the geometric figures, it is necessary to use different in size and color of the figure.

    Children look at and compare the ball and cube, find the general and different in these subjects (figures). Turning to the question of children, the educator attracts their attention to the features of the figures: "What is it?", "What color balls?", "Which one is less?"

    On the instructions of the teacher, one child takes a small ball in his hands, and the other is big. Children pass balls in a circle: a little ball drives a big ball. Then the direction of movement changes. In the course of such games, children clarify the features of the ball - he is round, he has no angles, it can be rolled. Children compare balls of different colors and sizes. Thus, the educator brings them to the conclusion that the form does not depend on the color and size of the item.

    Similarly specify and summarized the knowledge of children about Cuba. Children take a cube in hand, trying to roll it. He does not roll. Cuba has corners and sides (face), it is steadily standing on the table, the floor. From the cubes you can build houses, columns, setting one cube to another.

    The most important point when familiarizing children with the form is the visual and tactive-motor perception of the form, a variety of practical actions that develop its sensory abilities.

    In organizing work to familiarize children with the form of the subject, a significant place is made by the show (demonstration) of the figure itself, as well as the methods of its survey. The educator teaches children when examining the subject to keep the subject in the left hand, the index finger of the right hand to circle it along the contour.

    For the development of children's skills, the form of the subject and accumulation of relevant submissions are organized by different didactic games and exercises. So, in order to assimilate the name and clarification of the main features of individual geometric shapes, the educator organizes the games: "call a geometric shape", "magic bag", "Domino figures", etc.

    In the game "Magic Bag" The teacher teaches children to choose the shapes to the touch, find along the sample. On the table there are geometric figures familiar children, and the bag is the same. At first, attention is drawn to geometric shapes placed on the table. Children call them. Then, by instructions, the child finds such that stands on the table, and shows it. If the child cannot fulfill the task, the teacher once again resembles the ways of examination of the figure: the right hand slowly drives along the edge (contour) (you can help with your left hand). When re-conducting the game, the number of geometric shapes increases.

    In the game "Find the subject of the same form", "What lies in the bag?", "Geometric lotto" children exercise in finding items on geometric samples. Such tasks are difficult, but generally affordable for children. They develop their ability to analyze the surrounding environment, abstract when perceiving the form of objects. The child, perceiving the Estamp, which hangs on the wall in front of him, is distracted by the plot of the picture, and it allocates the shape of the frame (square).

    In class free children age group Very love game with cutting pictures, mosaic, building material.

    In the method of learning children middle group Distinctive is a more detailed examination of geometric shapes. With new geometric figures of children introduced, comparing their models with already familiar or each other: a rectangle with a square, a cylinder with a cube or a ball. From the immediate comparison of items with geometric samples, children go to the verbal description of their shape to generalize.

    The procedure for viewing and comparing the figures may be like this: what is it? What colour? What size (values)? What made? What is the difference? What are like?

    The main techniques can be: practical actions with objects (riding, put); imposing and applying; circuit circuit, feeling; Exercises in grouping and ordering - didactic games, exercises for the assimilation of the features of geometric shapes; comparison of the forms of objects with geometric samples; Analysis of complex shape. From children requires a deployed verbal designation of their actions (describe the shape of the subject consisting of 2-4 parts: a nevalea, a car, etc.).

    L. A. Wenger, L. I. Sysueva, T. V. Vasilyeva developed 3 types of tasks in the field of familiarization of children of the fifth year of life with the form of objects and geometric figures:

    § tasks for the absorption of geometric shapes;

    § tasks for comparing forms of real objects with geometric shapes;

    § tasks for spatial analysis of composite form.

    In the senior group, the examination of the geometric shape becomes even more detailed and detailed. An important element of the technique is to measure the conditional measure. Work on the formation of ideas and concepts about geometric figures is based on the basis of comparison and opposition of geometric shapes. The models are first compared in pairs, then 3-4 shapes of each type are compared, for example, quadrangles. Of particular importance is the work on the image and recreating the geometric shapes: laying out of sticks, paper strips. Based on the detection of essential signs of geometric shapes, children are summarized to the generalizing concept of "quadrangles". As a result of a certain work, children master the ability to endure learned knowledge into an unfamiliar situation, to use them in independent activities, in constructing.

    Senior preschoolers learn to dismember the complex pattern on the components of its elements, call their shape and spatial position, to form a pattern of complex shapes from the geometric shapes of one or two species, various in size (size).

    The technique of forming geometric knowledge in the group of the sixth year of life does not change fundamentally. However, the survey becomes more detailed and detailed. Along with the practical and direct comparison of well-known geometric shapes, overlapping and applying, is widely used as a methodological reception measurement of the conditional measure. All work on the formation of ideas and concepts about geometric figures is based on comparison and comparison of their models.

    So, the acquaintance of children with a rectangle, they show several rectangles, different in size produced from different materials (paper, cardboard, plastics). "Children, look at these figures. These are rectangles. " At the same time drawn attention to the fact that the form does not depend on the size. Children are offered to take a shape into the left hand, and the right hand to circulate along the contour. Children identify the features of this figure: the sides are pairwise, the corners are also equal. Check this flexion, overlapping one to another. They consider the number of sides and corners. Then compare the rectangle with the square, they find similarities and differences in these figures.

    At the square and rectangle four corners and four sides, all the ducks are equal to each other. However, the rectangle differs from the square in that the square all sides are equal, and the rectangle is equal to the opposite, pairwise.

    Special attention in this group should be given to the image of geometric shapes; Laying from counting sticks, strips of paper. This work is carried out with both demonstration (near the table of the educator) and handouts.

    At one of the classes, the teacher lays out on Flane-Legrafe from the rectangle strips. "Children, what is the name of this figure? How many sides of the rectangle? How many angles? " Children show the sides, corners, tops of the rectangle. Then the teacher asks: "How and which figures can be obtained from a rectangle (create smaller rectangles, squares, triangles)?" At the same time, additional paper strips are used. Children consider the parties to the figures received.

    Based on the detection of essential features of the geometric shapes, children are summarized by the "quadrangle" concept. Comparing the square and rectangle among themselves, children establish that all these figures have four sides and four corners. This number of sides and angles is a common feature that is based on the definition of the "quadrangle" concept. Next, children compare different in the form of quadrangles. In the equality of the parties and corners, children are convinced when overvolving one to another.

    In a senior preschool age, children are formed the ability to transfer the mined knowledge into the situation unfamiliar earlier, to use this knowledge in independent activities. Knowledge of geometric figures are widely used, clarified, fixed in classes on visual activities, design. Such classes allow children to acquire skills in dividing the complex pattern to composite elements, as well as create drawings of a complex form from one or two types of geometric shapes of different sizes.

    So, during one of the classes, children distribute envelopes with a set of models of geometric shapes. The educator shows the applique of the "robot" made up of squares and rectangles of different sizes and proportions. First, all together consistently consider the sample. Install from which parts (figures) each part is made (Fig. 32). In the same sequence, children create an ornament. The teacher shows two or three ornaments and invites children to choose one of them, carefully examined it, lay out the same ornament.

    In bulk figures (such as cylinder, cube), children stand out and called side sides and bases. At the same time, they can be shown by several fingers or with the whole palm.

    Children perform practical actions, manipulate with geometric shapes, reconstruct them. In the process of such training, the "mathematical" speech of children is enriched. Familiarization with the form, as a rule, occupies part of classes in mathematics, as well as on design, visual activity. During classes, imposing, applying, drawing along the contour, hatching, measurement are widely used. Flat geometric shapes The children are cut, bulk - pose from plasticine, clay. This work is closely related to the teaching of children to the elements of the letter: the circulation of cells, drawing circles, ovals, carrying direct and inclined lines. Children get acquainted with notebooks in a cage, consider how the pages in the notebook are rapidly. The tutor offers children to find and circle cells in different parts of the page: at the top, below, on the left, right, in the middle; Draw seven squares in size in one cell with pass between them in two (three) cells. At the same time, it shows different ways to perform the task: the designation of the initial contour points, conducting the lines from left to right and from top to bottom.

    Future schoolchildren teach to distinguish and call polygons (triangle, quadrilateral, pentagon, hexagon), call and show their elements (parties, corners, vertices), share geometric shapes on the part, compare among themselves, classify in size and shape. The work is directed, first of all, to improve the quality of these knowledge: completeness, awareness. The geometric material is widely used during classes as a demonstration and distribution in the formation of numerical concepts, dividing the whole to the part, etc.

    Throughout the preschool age, children learn to examine a simple and complex form of objects, adhering to a certain sequence: first allocate general contours and the bulk part, then determine the form, spatial position, the relative size of other parts. It should be taught to notice them not only the similarity, but also the differences of the form of the subject from the familiar geometric shape. It is of great importance for improving the visual and other types of independent activities of children.


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    The initial content of the concept of form are real items ambient reality.

    The form - this is the main visual and relatively perceived property of the subjectwhich helps to distinguish one item from another.

    Humanity created system of standards for the designation of forms of concrete subjects. it the system of geometric shapes.

    The grouping of geometric figures can be represented as follows:

    Flat and bulk,

    Having angles and not having them, i.e. rounded,

    Differing in external signs.

    In this way, geometric figures Speakers samples, references of the form of real objects or their parts.

    Using geometric shapes held analysis of the surrounding world, the need is consistent sort into a variety of forms, in that, "what does it look like." As a result, one object is likened to the other form (similar to the cucumber, like a window), etc.

    Classification of geometric figures Building both on sensual and logical basis. The perception of the surrounding items at first, as shown special researchdoes not mean shape isolation. Initially, the subject itself protrudes, and only then its form.

    In the geometric shape system Concentrated generalized experience of sensory activities.

    The form is perceived by a visual connate-motor. Acquaintance of children with the form of objects has always been the focus of psychologists, teachers and methodists of the past and present.

    Features and methods of development of preschool age forms of objects and geometric shapes

    The knowledge of the surrounding world is particularly significant orientation in the variety of forms of objects (objects) and geometric figures.

    Form belongs to a special place among the varieties of properties, known in preschool age.

    Perceiving shape, child stands out an object from other, learns and calls him, groups (sorts) and relates it to other objects.

    In parallel or after this child he knows geometric figures, highlighting before their form, and then - the structure.

    In knowledge of geometric shapes children of preschool age it is customary to allocate three stages.:

    In 3-4 years, geometric shapes are perceived as integers and differ in children mainly in shape;

    In 4-5 years, geometric shapes are perceived analytically, their properties and the structure of children are set empirically (experienced);

    In 5-6 years, geometric shapes are perceived in a certain relationship interconnection, properties, aware of their community.

    As a result psychological studies It became known that the process of knowledge of children of form as a property is long and complex.

    For children 2-3 years The main identification sign of Figuresurface, plane. They are take a figure in hand, manipulate; spend hand on the plane, as if trying to detect an object base.

    In this age children stand out among the others and called separate geometric shapes, using the words " circle», « cube», « ball».

    Or compare the form of the real object with geometric And use the expressions "it is like a cube", "it is like a handkerchief."

    Usually, they are " clerge» geometric figures, calling them " roof», « handkerchief», « cucumber" etc.

    Mastering the shape of objects and geometric shapes takes place at this age in active activities. Children put one cube to another, building the tower, put items into the car; ride figures, shift; Make up rows.

    Children of 3-4 years start distinguish geometric pieces from items, highlighting their shape. Calling the figures, they say: "The triangle is like a roof", "handkerchiefs - like a square."

    Children survey the figures with the motorway, trying hold hands by contour. At the same time, you willingly pronounce the words they liked, expressions. Start perception of structural elementsgeometric shapes: corners, parties. When perceiving figures abstracts from color, size, highlighting their shape.

    but the visual perception of the child remains running, his the view does not focus on the circuit or plane. Because of this, children are often confused similar figures: oval and circle, rectangle and square.

    Children 4-5 years old successfully examine geometric shapesconducted indicor finger along the contour. At the same time, they are usually call structural components: verses, side, corners. Track Move of hand corner-line lines; detect lines intersection points. Survey becomes accurateand Extensive.

    As a rule, at this age in children collect images of figuresreference ideas about them. They begin to successfully determine the similarities and differences in the forms of objects with geometric shapes; use their velocities to determine any unknown form; Display forms in productive activities.

    In 5-6 years Children are mainly summary perceive geometric shapes. Contactive motor examination becomes unnecessary. In the process of visual perception they are finish contour and on this basis, include a figure in a certain group., allocate types of figures, classified, streamlinedand We systematize objects in form.

    In senior preschool age prevailing spectatic recognition of figures and their distinctive signs, verbal characteristics of the form of objects and geometric figures.

    So, perception of the form of a child of preschool age implemented based The simultaneous examination of its visual and touch-moving method, accompanied by the name of the main features of one or another form.

    For example, round - no corners; Quadrangle - He has parties, corners and vertices.

    Geometric figures become references to determine the form of the surrounding items and their parts.

    It is in this age group that sufficiently certain knowledge of the form of objects and geometric shapes are being formed as the standards of the form. Detty learning to distinguish the ball, cube, square, circle, triangle, using the techniques of examination of these figures with the help of tactful motor and visual analyzers. In addition, on We will get acquainted with some elements of building material: cubes, bricks, plates, prisms, bars.

    We look at and compare the ball and cube, find the general and different in these subjects (figures). Turning to the question of children, the educator attracts their attention to the features of the phigur: "What is it? What color balls? Which one is less? "

    On the instructions of the teacher, one child takes a small ball in his hands, and other- big. Children pass balls in a circle: a little ball drives a big ball. Then the direction of movement changes. In the process of such games, the features of the ball are specified - he is round, he has no angles, it can be rolled. Deli compare the balls of different colors and sizes. However, the teacher leads them to the conclusion that the form does not depend on the color and Size of the item.

    Similarly specify and summarized knowledge about Cuba. Malyshi take the cube in hand, trying to roll it. It does not roll. The Cuba has corners and facets, it is steadily standing on the table, the floor. From the cubes you can build houses, columns, setting one cube to another.

    The most important moments when familiarizing with the form - the visual and tactive-motor perception of the form,

    more practical actions, developing sensory abilities of children. The examination of the form of the subject includes such actions: the show (demonstration) of the geometric shape, examination with the help of concrete practical (deployed along the contour) of actions; Comparison of figures, different color and size; Comparison of geometric shapes with objects similar in shape; Fastening the peculiarities of the geometric shape during drawing, modeling, appliqués.

    In organizing work to familiarize themselves with the form of the subject, a significant place occupies a show (demonstration) of the figure itself, as well as the methods of its survey. The teacher teaches children when examining the subject to keep it in his left hand, index fingering his right hand to circle it along the contour. In order for the guys better to highlight the features of geometric shapes, the model should be compared in pairs: a ball and cube, a circle and square, a cube and square. Figures necessarily need to take different in size and color so that they are easier to perceive to the touch, find the sample, and in conclusion - correctly call their distinctive features (Fig. 18).

    in the bag, a similar one that stands on the table, and shows it. If a child cannot fulfill the task, the teacher once again resembles the ways of examination of the figure: the right hand slowly drives along the edge (contour). You can help your left hand. When re-conducting the game, the number of geometric shapes increases.

    In the games "Find the subject of the same form", "What lies in the bag?", "Geometric lotto" children exercise in the compilation of the shape of items on geometric samples. Such tasks are difficult, but generally available to them. They develop in children the ability to analyze the surrounding environment, abstract with the designation of the shape of the subjects. The child, perceiving the Estamp, which hangs on the wall in front of him, is distracted by the plot of the picture, and it allocates the shape of the frame (square).

    Geometric shapes such as a circle and square are used in mathematics classes as a distribution material.

    Children of this age when conducting an appropriate targeted work with them can analyze complex forms. So, they create an ornament from color geometric shapes. At the same time, the drawing is analyzed, separate geometric shapes in it are examined, they examine them along the contour, called, and then displays this pattern.

    In the free time, the guys of this age group are very likely to love games with cutting pictures, mosaic, building material.

    Exercises for self-test

    For preschoolers, various didactic games and exercises are organized for the development of preschoolers in the preschoolers. So, in order to assimilate the name and clarification of the main features of individual geometric shapes, the educator organizes the games: "call a geometric shape", "magic bag", "Domino figures", etc.

    In the game "Magic Bag" The teacher teaches children to choose the shapes to the touch, find along the sample. On the table there are familiar geometric figures, and in the bag there are the same. At first, attention is drawn to geometric shapes placed on the table. Children call them. Then, by instructions, the child finds

    Children of the fourth year of life are formed certain knowledge of the form of objects and ... Figures as ... forms. Children learn to distinguish the ball and cube, ..., square and

    The main training is the reception ... of these figures ... and a visual way. A significant place in this process takes ... (demonstration) ..., as well as the show ... of his surveys.

    For development in children, survey skills ... subjects and accumulation of the corresponding ... Different games and exercises are organized.

    geometric Standards Circle Triangle Survey Tactile Motor Show Figure Figures

    forms of representations