Kudryavtseva Oksana Igorevna, student of the Institute of Pedagogy and Psychology of the Vyatka State Humanities University”, Kirov [email protected]

Features of the mathematical readiness of children for school

Annotation. The article is devoted to the issue of mathematical readiness of children for school. The components of both general and special (mathematical) readiness of children for school are defined and analyzed. Based on an empirical study to identify the characteristics of children's mathematical readiness for school, recommendations were made to parents and teachers to improve the level of knowledge, skills and abilities in the field of mathematics. Key words: mathematical readiness, general readiness of children for school.

The general readiness of children for school provides for a specific organization pedagogical work. Such an organization creates conditions conducive to raising the level general development older preschool children. In addition to general development, the work of a preschool educational institution also involves special preparation of children for the study of subjects in primary school.

In this article, we will pay attention to mathematical readiness, since in the 21st century the problem of teaching mathematics is becoming increasingly important. Mathematics is a complex science that causes difficulties for children in mastering the school curriculum in mathematics. It is possible that some of the children who come to school do not know elementary mathematical concepts and have no inclination to study this science. Consequently, the effectiveness of the mathematical development of the child in preschool age depends on the success of teaching mathematics in elementary school. Summing up the above, it should be concluded that one of the main criteria for the readiness of children to study at school is mathematical readiness.

Before addressing the issue of mathematical readiness, one should take into account brief description general readiness of children for school. Issues related to the general readiness of children for schooling, such domestic and foreign authors as A.L. Syurotyuk and M.M. Bezrukikh, D.B. Elkonin, L.A. Venger, V.S. Mukhina, A.V. Zaporozhets, L. I. Bozhovich, A. Anastazi, I. Shvantsar, Sh. A. Amonashvili, R. S. Bure, A. M. Raeva, G. N. Tsukermani, etc. of the above authors, it should be considered as a general development of a person who successfully masters the school curriculum, is systematically included in the learning process and has certain properties and qualities that need to be mastered at preschool age through mental, mental, aesthetic and physical development. Thus, the concept of "readiness for schooling" holistic education, which requires complex psychological and pedagogical research. In order to conduct a study to identify the level general readiness for schooling, you need to know that in the structure of general readiness it is customary to distinguish the following components:

1.Motivational readiness.2.Volitional readiness.3.Intellectual readiness.4.Social and psychological readiness.5.Personal readiness.

Study and analyze the components of children's readiness for school, put forward in the works of the following authors O. O. Gonina, N. I. Gutkina, G. V. Fadinoi et al., can be presented in Table 1. Table 1 Components of school readiness

No. Readiness component Essence of the component Features of the component 1 Motivational Motivational readiness for school includes the child’s developed need for knowledge, skills, as well as the desire to improve them. to school, understands the importance and necessity of learning, shows a pronounced interest in acquiring knowledge). If the educational motivation of the child is not formed, then difficulties arise in adapting him to new conditions, for example, to the class team and the teacher. There may be the following manifestations: the child does not perceive the school material well enough, insufficient emotional stability, apathy, etc., which leads to maladjustment in the class team. 2 VolitionalAbility of the child to work hard, fulfilling the requirements of the teacher, adaptability to the school regime, the ability to control their behavior and mental activity. in case of overcoming an obstacle, evaluate the result of your action. 3 Intellectual The ability of a future student to master such mental operations as analysis and synthesis, comparison, generalization and classification; ability to install in the process learning activities causallyThe development of intellectual readiness for learning at school involves: 1. Elements indicators representation of living and inanimate nature, some social phenomena, the systematic nature of these representations. 2. Level cognitive activity Keywords: attention, perception, memory, thinking, imagination, speech. The prerequisites are investigative connections between objects and phenomena, resolve contradictions. The development of intellectual readiness for learning at school also implies certain knowledge of the world around us and some learning skills. For the formation of learning activities: the ability to perceive tasks, direct an adult and be guided by it yourself, follow the rules.3 .Elementary study skills: exercise sound analysis words, readings, counting and calculations, preparedness of the hand for writing.

4 Socio-psychological It implies the formation in children of the communicative qualities necessary for communication with other children, teachers. Includes the presence social position schoolchild: the child must be able to establish contact with older peers, fulfill the requests and requirements of the teacher, control his behavior. 5 Personal Formation in the child personal qualities necessary for the adoption of a new social position. The parameters necessary for the successful mastery of educational activities by a child: 1. The ability to listen carefully to the speaker and accurately complete the tasks offered orally. 2. The ability of children to consciously subject their actions to a rule that determines the method of action. to a given system of requirements. 4. Independently perform the required tasks according to a visually perceived pattern.

Therefore, the concept of "readiness for schooling" is complex. If we consider each component separately, then it gives an idea only of a certain side of the child's readiness for school. The integrated use of the five components of readiness in the study will allow the educator or psychologist to carry out corrective work with the future first grader in time for his successful transition to systematically organized learning. Having determined the essence and content of the general the readiness of children for school, one should move on to characterizing the mathematical readiness of children for schooling. Issues related to the mathematical readiness of children for school were dealt with a large number of scientists, but the most important, in my opinion, are Doctor of Pedagogical Sciences, Russian pedagogical methodologist L. G. Peterson and Doctor of Pedagogical Sciences, Professor N. B. Istomina. mathematical content aimed at developing the creative and cognitive abilities of children as the ability to identify, compare, generalize, establish patterns, etc. In the structure of the mathematical readiness of children at school, proposed

E.I. Shcherbakov, includes the following components, the characteristics of which are presented in Table 2. Table 2 Characteristics of the components of mathematical readiness

ComponentsEntityComponent Features1

Motivational

A positive attitude towards school and learning activities in general. Positive motivation is an incentive that determines the achievement of a positive result for future learning activities. Interest in the mathematical side of reality V early age will greatly facilitate his schooling. desire to study mathematics

In the process of studying mathematics, the child develops a cognitive interest, a desire to learn new things, the formation of primary mathematical representations, motivational states (interest, curiosity, desire, etc.). Interest in mathematics leads to a deeper and more solid study of the material.2

Volume and quality mathematical knowledge: awareness, memorization strength, flexibility. Awareness of mathematical knowledge is expressed in understanding the connections between them, in understanding the principle of the connections and the mechanism of their formation. Such a quality as the flexibility of mathematical knowledge is characterized by the possibility of mastering them in independent activity. features of speech development (mastering mathematical terminology) Approximate knowledge of words prevents the full assimilation of concepts, in addition, it makes it difficult to use them at the time of production of coherent statements. level cognitive activity In general, the success of mastering educational material depends not only on the activity of the teacher, but also on the cognitive capabilities and abilities of students. 3

procedural

1. Knowledge of numbers up to ten 2. Counting and counting objects of a given number. 3. Naming numbers within ten. 4. Knowledge of plus, minus, equal signs, the ability to use arithmetic action signs. the subsequent number from the given one.6.Knowledge of the composition of the numbers of the first ten (from separate units) and from two smaller numbers.7.The ability to navigate on a piece of checkered paper.8.The ability to correlate the number and the number of objects.9.The ability to compose and solve simple tasks on addition and subtraction. self-control and self-esteem.

The motivational component provides an orientation towards the assimilation of knowledge and the development of the skills necessary for the formation of mathematical readiness. The action of the content component is aimed at enriching preschoolers with knowledge, developing speech and increasing the level of cognitive activity. The procedural component is aimed at mastering in practice by preschoolers the skills necessary for the formation of mathematical readiness. Having illuminated the theoretical essence of the issue of general and mathematical readiness of children for school, it is necessary to conduct experimental work in order to identify the features of the mathematical readiness of children for school. In order to identify the features of the mathematical readiness of children for school, a study was carried out experimental work, which includes a stating experiment. The procedure for diagnosing mathematical readiness for school was carried out using an experimental conversation, observation and a comprehensive methodology consisting of seven tasks. The result of the observation is that 4 out of 12 (33%) subjects have some deviations in the development of speech, in 8 out of 12 subjects the development of speech corresponds to the norm. In 3 subjects out of 12 (25%), a low level of cognitive activity is observed, while in 9 subjects the level of cognitive activity is above average. and 16% low. Summarizing the results of an experimental conversation, a comprehensive methodology and observations aimed at identifying the formation of mathematical readiness, can be presented in the form of a diagram (See Fig.).

Rice. 1. The general result of the ascertaining experiment to identify the level of mathematical readiness of children for school

Thus, it can be concluded that 67% of children have high level mathematical readiness, which indicates that they are highly motivated and have a sufficient level of mathematical knowledge, 8% have average level motivation and readiness, and 25% have low level motivation and readiness to master mathematics at school. In order to increase the level of general and mathematical readiness of children with a low indicator, it is necessary to draw up the following guidelines teachers for the formation of children's motivation to study at school, knowledge, skills in mathematics for the successful development of the school curriculum in mathematics and the formation of a general readiness for learning in general:

1. Arouse the child's interest in mathematics, motivate him to study this subject. To do this, it is necessary to associate the performance of mathematical tasks with interesting history some character who needs to reach the intended goal. 2. Develop spatial thinking in the child, i.e. teach him to determine where is right and left, where is up and down. To do this, offer tasks like: “Count the butterflies flying to the left, write down ...”. 3. Teach the child to name the previous and subsequent number from the given one. logical thinking. To do this, you should solve logical problems with the child. For example, "... paint in blue the numbers that are more than 7, but less than 9, and in red the numbers that you get in the answer by solving the examples ...". 5. Develop and form in the child the ability to compose and solve examples, tasks for addition and subtraction. For this you can use plot pictures, as well as conditional drawings. 6. Develop the child's ability to identify basic geometric figures and perform various tasks with the help of them. For example, “Look at the picture and tell me how many figures it took to make a giraffe?” 7. Learn to use the plus, minus signs, more, less, equal .8.Shape in the child competent speech, in particular mathematical (assimilation of mathematical terminology). In the process of completing tasks, require the child to think aloud. develop the volitional component of readiness. This development is facilitated by tasks aimed at helping the protagonist (or his friend) and the desire to achieve a specific result.10.

Form a positive motivation for school in your child. game form with children at home. eleven.

Raise the general intellectual level of the future student for successful mastery school curriculum, in particular, in mathematics. Offer tasks for classification, comparison, generalization, memorization, etc.12.

Raise the level of cognitive activity.

Form qualities in children, thanks to which they could communicate with other children, teachers. Every child should be able to interact both with peers and with elders.14.

Contribute to the formation of the child's personal qualities necessary for the adoption of a new social position (independence, responsibility, diligence, attentiveness, etc.).15.

Create a situation for the child to succeed.

Thus, it should be concluded that one of the important tasks of parents and teachers is the development of the child's existing knowledge, skills and abilities in mathematics and the development of children's motivation to study mathematics at school. The use of the developed methodological recommendations when working with children will contribute to the development and formation of elementary mathematical concepts and motivation for learning at school.

Links to sources 1.Antonyuk, V.Z. Formation of the intellectual readiness of an older preschooler to study at school [Text] / V.Z. Antonyuk // Baltic Humanitarian Journal. Kaliningrad. 2013. No. 3 (4) P. 57.2. Gonina, O.O. Motivational readiness for schooling and the content of communication between preschoolers and parents [Text] / O.O. Gonina // International Journal of Experimental Education. 2014. No. 3. S. 8184.3. Koryukova, N.N. On the issue of the problem of socio-psychological readiness of children with general underdevelopment of speech for learning at school [Text] / N.N. Koryukova, V.N. Ponikarova // Bulletin of the Magistracy. 2012. No. 910. WITH. 3538.4. Shcherbakova, E.I. Theory and methods of mathematical development of preschoolers [Text] /: textbook. allowance / E.I. Shcherbakov. M.: Izvo of the Moscow Psychological and Social Institute; Voronezh: Izdvo NPO "MODEK", 2005. 392 p.

Mathematical preparation of a child for school in a family setting

Usually, parents start teaching their children to count very early and are proud of their children's counting skills.

My Kolya will be an excellent student: he is not six years old, but he can count up to a hundred. I'm only afraid that at school he will start to indulge - after all, he already knows everything!

Many of you heard such conversations, admired the mind of Kolya, who counts to a hundred, sympathized with Petya's mother. Does this mean that Petya already now, at the age of six, is predetermined by the fate of a poor student in mathematics?

Yes, much of the success of first graders, including mathematics, depends on their preschool education. There are no people incapable of mathematics. The reasons for poor performance in mathematics can be different, and one of them is improper teaching at a very early stage, in particular, excessive passion for counting, the desire to teach children to count as early as possible, faster, further. The child does not get used to thinking about the content of the actions that he does, mechanically after the adults calls the words-numerals, not understanding the meaning of counting activity.

The textbook for the first class is called very seriously "Mathematics". This means that in the first grade, the student will not only count, but also get acquainted with arithmetic operations, calculation techniques, master some elements of mathematical speech, learn how to solve simple problems and equations, get acquainted with the elements of geometry, with quantities and methods of their measurement. All this will be taught by the teacher. But you can teach only that student who is ready to learn new material, otherwise it is difficult for the child to follow the teacher's explanations, he will not understand some words, expressions of the teacher, he will not be able to quickly complete the task at the right pace. And, of course, as a result, it will lag behind.

Such troubles can be avoided. It is only necessary to pay a little more attention to the mathematical development of the child before school. For this, it is not necessary to force the child to count, solve problems, or forbid him to play. The first and main condition is to make mathematics lessons interesting, entertaining, to teach to see the mathematical relationships of objects in surrounding things and phenomena. Then the child himself will find, highlight these relationships in the most familiar environment: in the kitchen, in the room, in the yard, in the store, in his play corner. And mathematics will become close, understandable and interesting, and then there will be a desire to overcome the difficulties that may arise in the study of this science. At home, training can be carried out slowly, returning at a convenient time to the material that for some reason the child did not immediately learn, repeating the familiar several times, using the objects that surround the child.

The task of teaching counting is not to teach a three-year-old child to count to 3, a five-year-old to 7, but a seven-year-old to 10. The main thing is to master the correct counting techniques, the ability to consciously apply these techniques in a wide variety of conditions.

For mathematical development, it is important to master the concepts of "greater than", "less than", "equal to". Their children master gradually. At first this is done without numbers, in a one-to-one ratio. Then equality - inequality is established on different quantities: two is more than one, one is less than two. Having established that two groups of objects are equal (or unequal) in quantity, the child must make them unequal (or equal) by adding (or removing) the required number of objects.

The guests are coming soon. How many guests are expected? For six guests, you need to prepare six appliances. They brought 6 saucers, and 5 cups. How many cups should be added? Put 7 forks. How many forks should be removed. One guest did not come. How many appliances will we remove from the table.

You can use a variety of life situations to once again exercise the child.

You sew on buttons. The child nearby examines, sorts through them, admiring the color. Take this opportunity and offer: “Take 4 buttons, lay them out one at a time. Put on another button. How many buttons did you get? How did it get 5 if we already have 4? How to make 4 again if we have 5 buttons? Similar exercises can be done with different objects, for example, put each doll on a chair, put each soldier near his gun, etc. At the same time, the child is asked if there are enough appropriate items (for example, chairs for all dolls), what will change if we remove one item, or remove one item).

Offer children a variety of objects in color, shape and size for counting: toys, dishes, furniture, vegetables. It is easier to count objects located in a row, close to each other. Therefore, older preschoolers should practice counting objects that are far from each other: cars on the street, windows of a house, trees in a park. Mastering the account will be more perfect if this activity involves not only vision, but also hearing, and musculoskeletal sensations. Therefore, it is useful to count objects by touch, without seeing them, count sounds (clapping hands, the number of beats on the drum), count movements.

To reinforce children's knowledge, use printed board games more often, which can be purchased at any store for children. Among them there are specially designed for the exercise of children in the account. For example, loto "How much?" introduces children in an interesting, exciting way to the composition of the number, the game "Knock-knock" is designed to count sounds, "Learn to read and count" will help introduce numbers and signs of mathematical operations.

By the age of seven, a child should count from any number to 10 and back, be able to count the right amount from larger group objects, understand that the number does not depend on the size of the objects taken for counting and their spatial arrangement, understand the relationship between adjacent numbers, know the quantitative and ordinal value of the number, be able to decompose the number into groups within five, be able to independently compose simple tasks and solve them, distinguish and name a circle, square, triangle, rectangle, oval.

Introduction

1.2. The concept, essence and meaning of mathematical readiness for learning at school

1.3. The problem of preparing children for teaching mathematics at school

Chapter Conclusions

Chapter 2

2.1. Research program

2.2. Identification of the level of readiness of future first-graders for teaching mathematics at school. Analysis of results

Conclusion

Bibliography

Annex 1

Annex 2

Annex 3

Appendix 4

Introduction

Perhaps it will not be an exaggeration that all conscious parents and teachers are concerned about the preparation of future first-graders for schooling. Is the child ready to become a schoolboy in all respects? Are there any gaps, shortcomings in terms of this training? What is the child's developmental potential? What are the main sources of development? Only by finding the right answers to these questions (and taking appropriate actions) can one not worry about the worthy entry of a first grader into the walls of the school.

Mathematical readiness is rightfully among the most important criteria for the readiness of children to study at school. Especially today, in the century the latest technologies, there is no point in arguing about the importance of this criterion. Therefore, the problem of studying the mathematical readiness of future first-graders to study at school is today undeniably relevant and interesting enough to be worked out both at the theoretical and practical levels.

In general, if we talk about the psychological and pedagogical literature, the above problems are covered by specialists quite widely, which is not surprising, given the above. The issues of readiness of children for schooling in general, and mathematical readiness in particular, were directly and indirectly addressed in their works by such famous authors as Sh.A. Amonashvili, L.A. Wenger, Yu.N. Karandashev, Ya.L. Kolominsky, E.E.Kravtsova, E.A.Panko, N.G.Salmina, U.V.Ulyenkova and others (general questions), V.A.Antonov, L.P.Knyazeva, L.I.Kuzminykh, V .M.Nazarova, E.M.Fadeeva, S.A. Yalichev and others (questions of mathematical readiness).

The purpose of this work is a theoretical and practical analysis of the problem of the mathematical readiness of future first-graders for schooling.

Analyze scientific literature on the subject of mathematical readiness of future first-graders to study at school, namely: to identify the basics and nuances of preparing children for school, to reveal the concept, essence and meaning of mathematical readiness for learning at school, to highlight the problem of preparing children for learning mathematics at school;

Form and motivate two samples of future first-graders to participate in the study (see below);

To identify and compare the level of development of elementary mathematical concepts in children from different samples;

Formulate conclusions;

The subject of the study is mathematical readiness as an important criterion for the general readiness of future first-graders for school.

The object of the study is older preschoolers who are preparing to enter the first grade of the school; the first sample is preschoolers who participated in the implementation of a special program for the development of elementary mathematical concepts, the second sample is preschoolers who did not participate in the implementation of this and similar programs (teachers and parents during preschool age studied mathematics with them, but unstructured, from time to time).

Hypothesis: the implementation of purposeful classes, which in their totality form a program of mathematical training, provides better development elementary mathematical representations of preschoolers, compared with the implementation of unstructured, periodic classes.

The structure of the work included a theoretical chapter, a practical chapter, practical advice, conclusion, bibliography and appendices.

Chapter 1. Theoretical foundations for preparing children for teaching mathematics at school

1.1. Issues of preparing children for school in the psychological, pedagogical and methodological literature

The admission of a child to school poses a number of tasks for psychologists and teachers during the period of work with a future first grader:

To identify the level of his readiness for schooling and the individual characteristics of his activities, communication, behavior, mental processes, which will need to be taken into account in the course of training;

If possible, compensate for possible gaps and increase school readiness, thereby preventing school maladaptation;

plan the strategy and tactics of teaching the future first-grader, taking into account his individual capabilities.

Solving these problems requires deep study psychological features modern first-graders who come to school at the age of 6-7 with different "baggage", representing the totality of psychological neoplasms of the previous age stage - preschool childhood.

Understanding the psychological readiness of the child for school as a multicomponent education, consisting of certain level development of mental activity, cognitive interests, readiness for arbitrary regulation of one's cognitive activity and for the social position of a student, it is necessary to agree that there is not and cannot be a single test that measures a child's readiness for school, a set of methods is needed,,.

The choice of methods for diagnosing a child's psychological readiness for school depends on the approach to organizing a diagnostic examination, chosen by a particular psychologist.

One of the organization options may be the initial general diagnosis, which is detected during mass examinations of children in in general terms level intellectual development, development of fine motor skills of the hand, coordination of hand movements and vision, the child's ability to imitate the model. Further, assessing the level of readiness for school, the psychologist continues to work with children with a low and especially low level of formation of the components of psychological readiness for school, who need additional individual psychological examination. Thanks to the latter, a detailed qualitative characteristic of the features mental development child, necessary both to clarify the conclusions made on the basis of the frontal examination, and to select directions corrective work.

Orientation tests, for example, the Kern-Jirasek school maturity test, can be used to implement the initial diagnosis, to compile a general idea of ​​the level of readiness of the child for schooling. Such tests have a number of significant advantages for the initial examination of older preschoolers:

do not require a long time to conduct;

Can be used for both individual and group surveys;

have standards developed on large samples;

do not require special means and conditions for holding

Correctional work in elementary school should be carried out in several directions and be associated: with the development of thinking and the emotional-volitional sphere, with the development of learning motivation and the “arbitrariness complex”, with the formation of writing, reading, accounts and intellectual abilities, with the development of the sphere interpersonal relationships child.

It is important to emphasize that when carrying out specific corrective work with younger students(correction of learning skills, the formation of arbitrariness, the development of mental processes, etc.), Special attention must be corrected personal development. Special problems of correction are such personal characteristics as inadequacy of self-esteem, anxiety, self-doubt, reflecting the increased emotional tension of the child, as well as conformism, passivity, lack of initiative,,.

The main methods of developing and psycho-correctional nature used in primary school schools are game methods. In the form of game methods, both subject training and psychotherapeutic training work should be carried out. This requirement is dictated by the need to create a permanent supportive psychological "background" for children, to create optimal psychological conditions for the successful development of their personality.

The main condition for this is that the games, classes, exercises, presented material should create a favorable emotional background, stimulate positive emotions. Correctional lesson must necessarily end with a positive emotional attitude.

Personal readiness to school is expressed in relation to the child to school, to educational activities, to teachers, to himself.

As a rule, children express a desire to go to school. It is always necessary to consider what attracts a child to school. “They will buy me a beautiful uniform”, “I will have a brand new satchel and a pencil case”, “Borya studies at school, he is my friend” - approximately such statements are typical for older preschoolers. External accessories school life, the desire for a change of scenery really seem tempting. But it turns out that these are not the most important motives. It is important that the school attracts the child with its main activity - teaching (“I want to study in order to be like dad”, “I love to write”, “ Learn to count ”, “I have a little brother, I will also read to him”, “I will solve problems at school”). And this desire is natural, it is associated with new moments in the development of an older preschooler. It is no longer enough for him to join the life of adults only in the game. But being a student is another matter entirely. This is a step up, already realized by the child, to adulthood, and studying at school is perceived by him as a responsible matter. The attention of a 6-year-old child does not pass by and the respectful attitude of adults to study as a serious activity.

,
speech pathologist.

What should a child be able to do when entering the 1st grade of school:

Check

A preschool child should be able to count up to 100 units and tens (10, 20, 30, 40 ...), name numbers in forward (from 1 to 10) and reverse order (from 1 0 to 1), correlate a given number objects with a number, identify the missing number by ear, name it, determine the previous and subsequent number to the one named or indicated by the number. It’s good if the baby answers immediately, without the help of an adult, to questions such as: “how much?”, “Where is the place?”.

Number Composition

A preschool child should be able to visually compose numbers within 10 of units, explain that, for example, 5 is 1, 1, 1, 1 and another 1, or 1 0 consists of 10 units.

In order for a child to understand what numbers a given number consists of, he must be able to decompose it into two smaller numbers (to begin with, within 10 and on a visual basis) and make up a larger number from two smaller ones. For example: the number 8 consists of 4 and 4 or 3 and 5; and, conversely, the numbers 5 and 5 make up the number 10. The child must be able to determine the missing component number. For example, the number 7 is made up of 4 and...? The child must name the number 3.

It’s good if the baby knows how to make numbers within 20. And within 100, it will be enough for him to be able to make numbers in tens. For example: 60 consists of six tens, etc.

Number Comparison

A preschool child should be able to compare numbers visually and verbally. It’s good if the baby knows how to compare both adjacent and non-adjacent numbers. For example, six is ​​greater than five and five is less than six; two is less than eight and eight is greater than two.

The child should be able to understand the difference comparison of numbers. For example, five is less than six by one, and six is ​​greater than five by one.

It’s good if the baby knows how to get equality from inequality or inequality from equality by adding one object to a smaller number or removing one object from a larger one. For example, five is less than six: if you add one more to five objects, then there will be six objects each, i.e. equally; six is ​​more than five: if one of the six objects is removed, then there will be five, that is, equally.

By this age, children should recognize and understand such mathematical signs, like greater than (>), less than (

Solution of examples

A preschool child should be able to solve examples for addition and subtraction within twenty, as well as within a hundred by tens. It is good if the child is able to make calculations in his mind within the first ten, without relying on visual material. More complex examples within the second ten, the child can solve with the help of counting sticks or other counting material.

A preschooler should know and be able to write mathematical signs "+", "-", "="; distinguish and name arithmetic operations - "addition" and "subtraction"; independently write examples under the dictation of an adult.

Problem solving

A preschool child should be able to compose and solve math problems for addition and subtraction, as well as write down their solution and know the mathematical signs "+", "-", "=".

It is good if a preschooler knows how to single out its components in a task: condition, question, solution, answer; understands that it is impossible to solve the problem if there is no condition or question.

By the time of entering school, the child should be able to solve not only problems accompanied by illustrations, but also perceive problems by ear or read the condition and the question on their own.

Logic tasks

The development of logical thinking is one of the important conditions successful learning child math. In this section, you will find several types of logical problems that are usually given to future first graders in school testing.

A preschool child should be able to solve entertaining problems with mathematical meaning. Some problems are solved with the help of arithmetic operations, others - with the help of logical reasoning.

Tasks for logical thinking encourage the child to think, reason, analyze, establish connections between phenomena.

Geometry

A preschool child should be able to distinguish between geometric shapes (circle, square, rectangle, oval, triangle, trapezoid, rhombus), draw them on a piece of paper, recognize the shape of familiar geometric shapes in surrounding objects. For example: the sun is like a circle, a book is like a rectangle, road sign- into a triangle, etc.

It’s good if a preschooler knows how to make one out of two figures. For example: out of two or four triangles, one polygon, out of small quadrangles, one large one. The child should be able to distinguish between geometric bodies, compare them and find differences.

The kid must understand that geometric bodies are three-dimensional figures. From volumetric figures, he must distinguish between a ball, a cube, a cylinder, a cone, a parallelepiped.

The child must know straight, curved and broken lines. It is good if he can distinguish between a line, a segment and a ray, straight, obtuse and sharp corners; can show the vertex and sides of an angle, measure the length of a segment with a ruler, draw a given segment, show the point of intersection of lines.

Orientation in space

A preschool child should be able to navigate in space, as well as on a notebook or landscape sheet. Orientation in space includes the ability to determine the direction of movement, to move in a given direction (forward-backward, up-down, right-left). A preschooler should be able to indicate in words the position of an object in relation to himself (in front of me is a table, behind me is a closet, to my right is a door, to my left is a window).

It is good if the child is able to determine the position of various objects in space, using the words: “below”, “above”, “in front”, “behind”, “before”, “behind”, “between”, “next”.

On a sheet of paper, the baby should be able to show the upper right corner, the upper left corner, the lower right and lower left corners, the middle of the sheet.

On a sheet of paper in a cage, depicting various objects and figures, the baby must understand the words “to the left”, “to the right”, “above”, “below”, “from”, “to”, “above”, “under”. He must also be able to draw figures on a sheet of paper, copying from a sample or from dictation (graphic dictation: one cell up, one cell to the right, one cell down, etc.).

Orientation in time

By the time of entering school, the child must clearly navigate the time of day (morning, afternoon, evening, night), their sequence, and also in such concepts as yesterday, today, tomorrow, understand the meaning of these words. He must know the sequence of the days of the week, name what day it is today, what was yesterday, what will be tomorrow, combine these concepts into one - these are all the days of the week.

It is good if the baby knows the names of all the months of the year, while he knows how to call them in right order. The preschooler must also divide all the months of the year into winter, spring, summer and autumn, know that there are three months in each season.

We all want our child to be the smartest, most educated, most successful and, of course, happy. For his sake, we are ready to sacrifice everything, give him the whole world, teach him everything, and learning to count is not the last in this series. But, unfortunately, we do not always know where to start teaching mathematics, what to require from him, and in general, how to prepare him for school.

WHY DOES A BABY DO MATHEMATICS?

There are two reasons why children should be taught math. Mathematical calculations are one of the highest functions of the human brain. Only man is capable of counting. In addition, we cannot do without an account even a day. Everyone counts: schoolchildren, housewives, businessmen, and scientists.
The second reason is that the account contributes physical development brain, and hence the intelligence of the child. The main thing for a preschooler is to learn logical thinking processes.

PREPARATION FOR SCHOOL
What should a future student know?

To prepare your baby for school, the main thing is to teach your child to count to ten (back and forth), add and subtract within ten. Then it will be much easier for him to master counting up to 20, 30 or up to 100. Now there are a lot of books and coloring books for kids "Learn to count", "Learn to think". On reverse side books, the authors explain their tasks. When choosing literature, proceed from this.


By school, the child must know the forward and backward counting up to 10 (minimum) or up to 30 (it depends on the child), be able to add and subtract within these limits. A 6-year-old preschooler should be able to solve various arithmetic problems when you can visually count objects.
For example, they show 2 vases with apples. One has 2 apples, the other 3. How many apples do you need to add to the first vase to get as many as the first vase?"
The child must be able to solve problems that are solved in the mind. For example, "Imagine that there are 4 pencils in the pencil box, and I add 2 more pencils. How many pencils are there in the box?"


By school, the child forms the beginnings of abstract ideas. In the preparatory group, the child must know geometric shapes, directions of movement, navigate by the clock. He must have formed measuring skills, he must be able to compare sets (more - less). For example, there are 5 pencils in one box and 6 in the other, which means that there is one less pencil in the first box than in the second.

WHERE TO START LEARNING MATH?
OUR FINGERS COUNTERED

Learning to count should start at the age of 3.
The first stage is the development of quantity. We start with quantitative representations, such concepts as "a lot - a little", "one - a lot", "nothing - a lot". Then, when the baby is aware of the number "one", gradually add the following numbers.
The child gets acquainted with mathematics, starting from himself, from his body. He learns that he has one nose and two eyes, two arms, two legs and one mouth, and five fingers on one hand. Count his ears, eyes with him ("how many pens do you have, peephole?"), count the fingers on one hand, on the other, on your feet. Periodically ask him questions: how many legs (eyes, ears) does mom, dad, grandmother, doll, bear have (how many upper legs, how many lower ones).

You can teach math to your child in between times. For example, playing, walking, washing dishes (how many cups, plates I washed, how many are left). While walking, count the leaves, flowers and petals, birds and pebbles.
When the baby plays with toys, ask how many cars, dolls, cubes, balls he has, how many cars are on the floor, and how many are in the box. Learning to count girls and boys is exactly the same. Just operate with toys depending on the gender of the child: talk with the boy about his cars (how many wheels, steering wheels the car has), with the girl - about dolls.
So, take the doll and her things (for example, 2 panties, 5 dresses, socks). Invite the girl to play: "Let's dress the doll. How many dresses, socks do you need to dress the doll? How many panties did you take? Socks?"
When a child learns to easily count objects, we complicate the task: we look at pictures with objects and count them in the picture.
Learn tongue twisters, songs, rhymes with your baby, including counting. They help the child remember the sequence of numbers.

LEARNING TO COUNT: TWO PLUS TWO - FOUR.

The second stage of learning to count is folding.
Take one ball (glass, cube) and at the same time slowly say "one plus". Then take the second object and at the same time say "one equals" and, pushing both objects towards the baby, say "two". Repeat these steps again with the words "one plus one equals two" or "one plus one makes two". Let the child talk to you.
Then you can put one ball in front of him, then another and ask how many balls are in front of him. Help, prompt the baby, without being annoyed. He doesn't have to be a prodigy. Explain why there are two balls by counting both balls again.
When the child has mastered that one plus one equals two, complicate the task: add one more ball to two balls. After the child solves one problem (but not before), put another one in front of him. Each lesson should consist of no more than three equations.

Don't be afraid of the words "plus" and "equals". No need to explain their meanings, the child will understand this from the context.
Always stick to the same manner of presentation, using the same terms. If you once said the phrase: "one plus two equals three," then you should not change it to others, for example: "add two to one equals three."
Children see not symbols, but facts. When you teach them facts, they themselves draw conclusions and comprehend the rules. If we change the terms, then the child has reason to believe that the rules have changed with the terms.
Children are little scientists. They have an amazing ability to discover laws if we give them the facts. During the first three years, the child learns more facts than for the rest of your life. He then systematizes them in order to discover the laws to which they are subject.

THE NEXT STAGE OF LEARNING MATH - SUBTRACTION.

The principles of teaching mathematics at this stage are the same.
You show 2 dice, then remove one while saying "two minus one equals one".
In the beginning, teach your baby to add and subtract on objects, then on pictures that depict these objects. And only then use plot pictures. For example, a clearing is drawn in the picture, there are 4 mushrooms on it. The squirrel takes 1 mushroom. You carefully examine the picture: a clearing, mushrooms (count them), a squirrel with a mushroom, then ask: "how many mushrooms are left in the clearing?"

ONE, TWO, THREE, FOUR, FIVE, LEARNING TO COUNT ...

At the age of 4, we begin to introduce the baby to numbers. A number is a symbol for quantity, and when we use the word "number" we mean the actual quantity (not a symbol, but a fact) of the objects themselves.
Make cards out of white cardboard, write the numbers with a red felt-tip pen (children's attention is best attracted by this color, especially since it creates a good contrast against a white background). When writing, use the same font.
At the beginning, select a set of numbers from 1 to 3. Show in order, then in a breakdown. Then write easy equations. Use the plus, minus, equal signs.
By the way, preschool mathematics also includes ideas about the form, size, duration, length, space, location between objects and location in relation to the child (front-back, left-right).

At 4 years old, a child should not only be able to count to 5, but also get acquainted with the concepts of equality - inequality. For example, if there are 2 pebbles in one hand and two pebbles in the other, then the number of pebbles in both hands is equal, and "two equals two." If in right hand one pebble, and in the left - two, then the number of pebbles is unequal, and "two is not equal to one."
At 5 years old, a child should be able to count up to 6-8, at 6 years old - up to 10, add and subtract within these limits.

PREPARATION FOR SCHOOL: QUICK COUNT. DOES IT NEED?

I wanted to teach my child quick count, - the mother of 9-year-old Igor shares with me. - I made special cards (up to 100), pasted dots on them (on the last cards there were 99, 100 dots each). She quickly showed them to the baby, he determined the number of points on the card. Then she made equations with cards, and quite complex ones (for example, twenty points plus fifteen). My son could already solve mathematical problems at the age of three. But it turned out that everything was in vain. When I sent him to kindergarten, the teachers were not too happy about my son's success. And at school, he generally began to have problems with mathematics. It turned out that, having carried away the technique of counting and bringing it to automatism, we missed another, no less important thing - logical thinking. Now let's catch up with the rest."


This - main mistake parents. Deciding to raise a little genius, they strive for the heights of mathematics and computer science, and forget (of course, out of ignorance) to instill elementary skills in children. For example, there are children who are great at counting and decisive tasks, but not knowing the composition of numbers within a dozen. They know how to count automatically, but they do not understand logically how to do it. An unreasonable account will later result in problems with mathematics, the child will be confused. And relearning is always harder.
What other mistakes do parents make?

PREPARATION FOR SCHOOL: MISTAKES OF PARENTS

1. Parents often try to speed up their child's learning of mathematics by stepping over milestones its development and the knowledge necessary for a child at his age. Under no circumstances should this be done. There are children who can play computer games but they don't know how to play with toys and don't know Chukovsky's poems. And toys (learning to count on toys) and nursery rhymes, counting rhymes for him at this age are MORE IMPORTANT. And this omission will certainly affect the development of the child in the future.


2. Some parents, chasing high results in learning to count, forget to give the baby ideas about the size, shape, space, time, length and duration. Some children count up to 100, but do not know how to compare values: a tall house or a low one, a long or short road, a narrow or wide scarf, they do not know geometric shapes. By the way, tasks for comparing objects by features and properties develop logic. And they cannot be neglected. The kid should understand this at preschool age, then it will be more difficult for him, and subsequently this will lead the child to problems with geometry at school.


3. Another mistake of parents: they often overestimate the requirements for the child, not taking into account his age. For example, at 2 years old, they require a baby to know numbers, but at this age he still does not have abstract thinking.


4. Parents often scold their children, get annoyed if they count slowly or incorrectly, do not understand something. Not everyone is born mathematicians and logicians. Maybe your baby is a humanist and art and creativity are close to him. Then you should not forcibly "sculpt" a genius of mathematics out of him. Be glad that he is so emotional, affectionate, feeling, understanding.


5. Parents, unfortunately, do not have a system for learning to count. They tend to jump from one level of difficulty to another in teaching mathematics. As a result, the child has not yet mastered the very concept of a number, and he is already being asked how much 2 plus 3 will be. It is especially difficult for children brought up at home.


6. It is even worse when parents set several tasks for the child at once. It is not possible for a child to solve them at once. Let him first cope with one task, understand the essence of its solution, and only then give him another task.


7. Most often, mathematics at home is explained to children on the fingers. It is difficult for a child to understand what in question due to lack of visual material. To understand, he needs to see and touch everything. Therefore, at home (even if the child goes to kindergarten), there must be counting material so that the child can consolidate what he has learned kindergarten material.
You can buy counting material, or you can make it yourself together with your child from thin cardboard, preferably colored (or stick it on white cardboard colored paper), and then cut out figures in the form of houses, mushrooms, Christmas trees, boats, birds, mice.


8. Many parents are impatient and rush the child while learning to count ("well, well, how much?"). The main thing is not speed, but understanding the essence.


9. When preparing a child for school, many parents turn learning to count into boring, tedious activities that resemble school lessons.
Mathematics is an abstract science, so when teaching a child to count, you need to be interested. Remember that classes should be fun for both you and the child, and take place in the form of a game.
Play is the main activity of preschool children. Engage only in a good, high spirits (so as not to discourage the child's desire to study, learn, learn something). As paradoxical as it may seem to you, in order to attract a child's interest in this abstract science, you need to be very emotional with him, even emphatically emotional. So, be joyful and benevolent.