Nikitin fractions. Nikitin Family Early Development Methodology Why is this game needed?

Boris Pavlovich and Lena Alekseevna Nikitin are called by many classics of Russian pedagogy. Using the example of their own large family back in Soviet times, they demonstrated how, by breaking established stereotypes in upbringing, they could help a child turn into an independent, harmoniously developed personality.

People first started talking about the Nikitin family in the late 50s of the 20th century. The village of Bolshevo near Moscow, where the teachers lived, was shocked by the way the young couple raised their children. The local community was surprised by the fact that the Nikitin children, who ran barefoot in the snow and were able to perform dizzying gymnastic exercises, were simply bursting with health and amazed with their intelligence. By the age of three or four, these kids had already mastered reading and the basics of mathematics, enthusiastically played logic games invented by their father, and as soon as they started school, they skipped grades.

It was then, in the 1960-1970s, that the Nikitins laid the foundations of Russian parental pedagogy, which are still used today.

Basic principles of education “in Nikitin’s way”

According to the Nikitins, adults traditionally allow two extremes when communicating with a child. The first one is well-organized. That is, super-caring care and continuous activities, entertainment, games. The child has no time for independent activities.

The second extreme is abandonment child. This means that communication with the baby comes down only to serving him (feeding, drinking, putting him to sleep). This approach leads to deprivation (psychological starvation), hospitalism (delayed emotional and mental development) and, ultimately, mental retardation.

The Nikitin system is based, first of all, on labor, naturalness, closeness to nature and creativity. The guys are masters of themselves, their actions and routine. Parents do not force them to do anything; they only help them understand complex life and philosophical problems. Adults push, rather than get ahead of children, and enter into dialogue with them. The main task of education, according to the Nikitins, is maximum development creativity a growing person and his preparation for life.

Firstly, freedom of creativity for children in classes. No special training, exercises, lessons. Children exercise as much as they want, combining sports with all other activities.

Secondly, light clothing and a sports environment in the house: sports equipment is part of the daily life of children from early childhood, becoming a natural habitat for them, along with furniture and other household items.

Third, parental concern for what and how the kids are doing, the participation of adults in children's games, competitions, and in general - in the very lives of children.

Parents should have only one goal: not to interfere with the child’s development, but to help him, not to put pressure on children in accordance with some of their own plans, but to create conditions for their further development, focusing on the children’s well-being and desires.

Lena Alekseevna and Boris Pavlovich did not initially set themselves the goal of teaching their kids everything as early as possible. They noticed that children develop earlier those aspects of intelligence for which appropriate “advanced” conditions have been created. Let's say a child has just begun to speak, and among his toys he already has cubes with letters, a cut alphabet, plastic letters and numbers.

How to make a child want to study?

So, the conditions for development must precede this process. This means they need to be prepared in advance. That is, on the walls of the children's room you need to hang a map of the hemispheres, tables of hundreds and thousands, printed and capital letters, measuring instruments, books. And first impressions can involuntarily arouse a child’s interest in some area of ​​knowledge and even develop certain abilities. Working together or working side by side is a mandatory interest in each other’s work process and its results, and at the same time, it is a reason for conversation and exchange of opinions. Here you should pay attention to one very important point: you should never do for a child what he can handle on his own, and never decide for him what he can decide on his own. In any activity for children, adults should try to encourage creativity without imposing their opinions, and without rushing to be sure to prevent a mistake or immediately point out it. And in case of failure, do not reproach or shame the child. But success must be celebrated and not stingy with praise. The main thing is that adults never remain indifferent to what the children do and how they do it, what they do.

Physical development

Children must be ready to perceive knowledge not only mentally, but also physically. The child's body is itself an instrument of knowledge. Not overloaded with unnecessary clothing, not burdened with super-calorie food, it easily and willingly “meets” the demands of mental order. Sports equipment should be part of a child’s life almost from infancy. The Nikitins paid special attention to hardening. And their experience has shown that this is an effective way to protect a child from most colds.

Intellectual games of the Nikitins

Methodology

In addition to the advanced conditions for development discussed above, Nikitin has developed a number of educational games for children of any age. No specific educational program is imposed on the child. He is immersed in the world of the game, in which he is free to choose his field of activity. No one explains the new rules to the child, he simply gets involved in the game with the help of a fairy tale, imitating his elders, participating in group games. As a rule, the active participation of adults or older siblings is required at first, but then the child can study independently. So naturally, the baby performs a number of tasks that gradually become more complicated. At the same time, you cannot give any hints to the baby. He must be given the opportunity to think for himself. If the child cannot cope with the task, you need to return to easy, already mastered tasks, or temporarily leave this game. If it is noticeable that the baby has reached the ceiling of his capabilities or has lost interest in the game, it is better to postpone it for a while.

This technique allows the child to independently seek solutions to problems unknown to him, to create new things, that is, it leads to the development of his creative abilities.

Features of the Nikitin Games

The main difference is the versatility of games and limitless scope for creativity. They can interest and captivate all family members. Games teach children, moving from simple to more difficult tasks, to get joy and satisfaction from mental activity, to think, sometimes torment, but always achieve the goal.

Each game is a set of problems that the child solves with the help of cubes, bricks, squares, and parts of a mechanical designer. Tasks are presented to the child in various forms: in the form of a model, a flat drawing, an isometric drawing, a drawing, written or oral instructions, and thus introduce him to different ways of transmitting information. The tasks are arranged from simple to complex.

There are several levels of difficulty, from accessible to a two- or three-year-old to beyond the capabilities of the average adult, so the games can excite interest for many years. And the gradual increase in the difficulty of tasks allows the child to improve independently, that is, to develop creative abilities.

When using Nikitin’s educational games in classes with a child, you should adhere to certain principles.

1. You cannot explain to a child the method and procedure for solving problems, and you cannot suggest it with a word, a gesture, or a look. By implementing the decision practically, the baby learns to take everything necessary from the surrounding reality on his own.
2. You cannot demand and ensure that the child solves the problem on the first try. He may not have matured yet, and you need to wait a day, a week, a month or even more.
3. The solution to the problem appears before the child in the form of a drawing, pattern or structure made of cubes, bricks, construction kit parts, that is, visible and tangible things. This allows the child to check the accuracy of the task himself.
4. Most educational games are not limited to the proposed tasks, but allow children and parents to create new options and even invent new games, that is, engage in creative activities.

So, the main feature of Nikitin’s educational games is that they managed to combine one of the basic principles of learning - from simple to complex - with a very important condition for creative activity - doing everything independently.

The educational games developed by Boris Nikitin are described in his book, which is called “Intellectual Games”. Here are just a few examples of the most popular ones.

Frames and inserts

This game is accessible to the little ones. It consists of 16 frames with inserts in the form of geometric shapes: circle, square, triangle, ellipse (oval), rectangle and so on. A better place to start is by showing the inserts. Take a circle, an oval, a square, an equilateral triangle and, naming them, show them to the baby. In this case, it is better not to hold them in your hands, but to lay them out on a plain surface (not on a colored tablecloth or carpet, but at least on a sheet of paper). Having shown one figure at a time, you can give them to the baby for independent actions - let him look at them and play. It would be appropriate to offer him a box or jar in which he can put all this and then pour it back. Gradually, the little one will get to know all 16 figures in the set. If you start with a small number of figures, you can attract the baby to play starting from 10-12 months. When the child grows up, you can complicate the tasks: trace the outlines of the figures with a pencil, first along the frames, then along the inserts (this is more difficult), make a double outline, shade the resulting image, draw figures on the count (three circles, two squares), create plot drawings ( herringbone of three isosceles triangles).

Fold the pattern

This game consists of 16 wooden cubes with an edge measuring 3 cm, where each side has a certain color. The cubes must be placed in a wooden or cardboard box (its presence is required). Nikitin advises starting to play with them at the age of one and a half years. In the beginning (especially with the smallest ones), you just need to sit down next to the child and look at the cubes together: “Look, what beautiful cubes! Here I took 4 cubes: one, two, three, four. Look, this is the blue side, and this is the yellow side "What a beautiful blue path I have! Let's take the bunny, see how he likes to jump along it? And now the path has become multi-colored: blue, yellow, blue, yellow." Perhaps the baby is no longer listening and is looking around. This means that the acquaintance with the cubes should have been completed a few minutes earlier. The game should not bore the child. And one more thing: like any other, it is advisable to store it in a place where the baby can see it, but cannot get it out himself. When the baby has a desire to play, he can say or point to the box if he does not yet know how to talk. These cubes promote “the development of spatial imagination, accuracy, attention, graphic abilities, the ability to analyze, synthesize and combine.”

Fold a square

This game originated from a puzzle in which several pieces of various shapes were required to form a square. This was a rather difficult puzzle, so Nikitin decided to do a series of simpler tasks. The result is a game for children aged two years and older. It has three difficulty levels. Each contains 12 multi-colored squares. All 12 squares are located on plywood the size of a landscape sheet and seem to be inserted into windows. For children 2 years old and younger, you need to leave 4 of the simplest squares. Let it be a whole square, a square of two rectangles, of two triangles and - cut into two parts along a broken line. Now you can start playing with your child. The parts need to either be arranged into piles (each with parts of the same color), or shown how two halves make up a whole square. Then the child is given the opportunity to act on his own. Gradually, the baby will master this level and move on to a more complex one. According to Nikitin, this game promotes the development of color perception, the assimilation of the relationship between the whole and the part, the formation of logical thinking and the ability to break a complex problem into several simple ones.

Fractions

The age range for starting this game varies, from 3 to 5 years. It is a set of three plywood pieces the size of a landscape sheet. Each of them has 4 circles. They all have the same size but different colors. The first circle is whole, the second is cut into two equal parts, the third into three, and so on, up to 12 “slices”. At first, only the first plywood with four circles is left for the game. With their help, you can repeat colors, count the inserted pieces, and compare them with each other. With their help, you can repeat the colors, count the inserted pieces, and compare them with each other. In this way, the child becomes familiar with mathematical terminology. You can try making a multi-colored circle. It is very interesting to build a ladder: at the bottom there is a whole circle, then half, then a third. With its help, you can clearly understand why one second is greater than one third.

Unicube

These are universal cubes that introduce the baby to the world of three-dimensional space. The development of spatial thinking will allow the child in the future to master drawing, stereometry, and descriptive geometry. The game teaches clarity, attentiveness, precision, accuracy.

"Unicube" consists of 27 small wooden cubes. The faces of each cube are painted in such a way (three colors in total) that this combination of faces is rare, if not unique. That is why it is so difficult to complete tasks according to the proposed schemes. Nikitin offers 60 tasks for the “unicube”. The author performed the first of them with children aged 1.5-3 years, and the most complex ones are not accessible to all adults.

Their daughter Anna Ermakova spoke about the Nikitins’ method

Discussion

Hello, dear fellow readers... Actually, I have no direct connection to the discussions... I’m just writing an abstract on the Nikitins... Please, if anyone has such an opportunity, write some links on the topic.. Thank you all in advance.

Why does a child have to be a genius???? The main thing is an EDUCATED man, and whether he is a Nobel laureate or an Olympic champion, who cares? For me, the main thing is that the child is healthy and well-mannered...

Taken from here:
http://www.kp.ru/daily/22570/10110/
“Alexey, the Nikitins’ eldest son, now lives in London and practically does not communicate with his family.”
“The second son, Anton, became a talented chemist. He graduated from the Chemistry Department of Moscow State University and runs a laboratory.”
“Olya, the eldest daughter, works as a lawyer and heads a department at the Moscow Registration Chamber. Another daughter, Anya, is a nurse and mother of four children.”
"Yulia is a tourism manager."
“The second-to-last child in the family is Ivan. They experimented on him the least. For example, he wasn’t taught to read at the age of three. And that’s probably why he’s the only one who doesn’t wear glasses now.”

“Lyuba, the youngest and with many children herself, is raising her own five children. Motherhood is her profession and calling.”
“And almost all Nikitins (now not only Nikitins, but also daughters-in-law and sons-in-law) live in their father’s old house. When I asked how many people simultaneously live under the roof of the Bolshevsky house, no one could answer for sure...”

Alexandra from 6.11.07
Alexandra, having looked at your link, I must disappoint you, because... The Nikits who will be there are artists and singers, Tatyana and Sergei. And, as far as I know, Boris Nikikin is no longer with us, only his wife remains alive. By the way, Oksana’s question dated August 23, 2005 whether the Nikitins have a website also interests me. So far, unfortunately, I haven’t found it myself.

I’m 22, my parents raised me according to the Nikitins’ method, but they put more emphasis on physical development (hardening, swimming, a minimum of clothing and more movements from the first days of life). I can say with confidence that I am a happy and harmonious person, I had a wonderful childhood and I adore my parents. Now I have 2 higher educations, knowledge of 2 languages ​​(I received one education in English). Now I am also studying part-time. I've been involved in sports all my life. But this is not the main thing, what is important is the zeal for new knowledge and achievements, which not everyone is born with, but which can be developed (according to the Nikitins’ method). And yet, I never did anything under pressure, I did everything myself (my parents simply created the conditions). My baby is 3 months old, no diapers, more movement and of course hardening, which he loves. There is complete harmony and love in the family, which was passed down to me from my parents, from my childhood. The Nikitins’ technique is great; thanks to them, mothers and newborns are now in the ward together in our maternity hospitals.

It’s strange that some people consider early development to be harmful.
I knew the alphabet at 1.5, read from 2.8, my parents took me to the theater from 3 (not under duress, but - both they and I liked it). The result is quite modest. Member of the Writers' Union from the age of 18 (at the same time she became a happy wife), 2 educations, so far only Ph.D. Philosopher Sciences, laureate of several all-Ukrainian poetry competitions, musician (violin, guitar), 3rd category in badminton.
As you have already seen, I did not become a genius, however, I was not raised to be one. They raised an educated and healthy person - perhaps something worked out. People don’t usually call me emotionally poor, but rather the opposite problem :)

I love parents, I will try to repeat their system with my children.
And about the Nikitin children I really want to remember that they just... didn’t get sick in childhood. At all. Few?

My son is 19 months old. Fold the square 1 ur collects halfway. Of course, it develops mathematical and logical thinking, etc. I believe that the most important thing for a child is the love and affection of his parents, and everything else (developmental programs) is at the discretion of the parents.

I can tell you about myself:

No one personally taught me specifically, it’s just that my sister is 1.5 years older, according to the diagnosis she should have been developmentally delayed, and my mother took it upon herself to overcome the symptoms corresponding to the diagnosis.
I hung around out of boredom.

There were large letters on the wall above the dining table because my sister had problems with diction.
Then the numbers appeared
As a result, by the age of 3 I was reading fairy tales to myself...

Well... I graduated from college, graduate school,
everything is modest - I work as a programmer, I lead a group.
(there’s no motivation for more)
Lilya

Until 2006, I lived in the village of Barabash, Primorsky Territory, in December 1987 I gave birth to a son, Sasha, a year later I gave birth to a daughter, Tanya, and during pregnancy I heard on the radio about the methods of raising children and about the Nikitins’ books. In 1988 I found the Nikitins’ book, and in subsequent years of raising children I tried to follow the Nikitins’ advice. I think that books helped our family a lot in raising our children; they grew up erudite, smart, healthy. Now they are students studying in the budget department, both are excellent students. Thank you for the books.

Our son is one year and three months old, we are waiting for the second one. We use different techniques - dynamic gymnastics, swam for 4 months in the sea, really harden ourselves, use early development techniques (Doman). We can’t do otherwise, it’s interesting for us ourselves, and the boy is growing up happy.
Regarding the Nikitins. Imagine yourself in their place! Seven children, meager incomes, and the parents were no longer quite young, as far as I know. This is how much effort they had to put in so that their children would just somehow succeed and survive in our society. As far as I know, all the Nikitin children are successful people, not oligarchs, not Nobel laureates, but in practice, socially significant. This result is quite expected for more or less conscientious parents of one child - but here, dear ones, there are already seven children! Still, their work, I think, brought good results.

Nikitin's games are designed to develop a child's intellectual and creative abilities from the very first years of life. Their authors are famous innovative teachers, spouses and parents of seven children Boris Pavlovich and Lena Alekseevna Nikitin. This outstanding family also developed a unique method of early development. It is based on nurturing and raising a child as a free individual: he independently learns about the world while playing. After all, according to B.P. Nikitin, “play is usually called the main activity of a child.”

It is assumed that the child completes the proposed tasks without outside help. The role of an adult comes down to providing the child with the right environment: games should always be easily accessible and the demands on the player should be moderate. Don’t demand an immediate answer from your child; maybe you should wait a little longer - and he will find a solution in no time!

This principle of education develops in a child not so much performing qualities as independent creative initiative, the ability to invent, create and make decisions on his own.

The child's interest in Nikitin's educational games only increases over the years. The reason for this phenomenon lies in a special, carefully thought-out system of game tasks. Each game comes with many tasks of varying difficulty levels: a child can cope with some at 2-3 years old, while others will become tough for him only at school (and even after it).

Most of Nikitin’s games are all kinds of cubes: “Fold the Pattern”, “Unicube”, “Chameleon”. By turning and combining their multi-colored edges, your baby will create an endless variety of designs and three-dimensional models. First, it is better to work according to the model, and then show your imagination and come up with your own buildings. There are even special albums for playing with the “Fold the Pattern” set, where the child is invited to decorate colorful pictures with multi-colored cubes.

A special place among Nikitin’s games is occupied by “Cubes for Everyone” and “Bricks”. The first game, with its intricate details, resembles three-dimensional Tetris, while the second, on the contrary, consists of identical wooden blocks. Both sets teach one thing: to assemble three-dimensional figures using real drawings. After this part of the tasks is mastered, the child will look at the game from the other side: after all, you can first create your own drawings and then assemble various models based on them.

Nikitin’s games, made on the principle of “cut pictures”: “Fold the square” and “Fractions”, are widely known. These kits are divided into categories according to difficulty level, and the higher the category, the more parts the child needs to assemble a circle or square.

Even in the recent past, parents made all these manuals with their own hands. The author himself emphasizes that this is possible in his book “Intellectual Games”. However, why waste time if you can buy Nikitin games at very attractive prices in the Smart Toy online store!

Educational games Nikitin

Boris Nikitin came up with many educational games for his children. These games and exercises are truly unique, and so far nothing has been created either in our country or abroad that could surpass Nikitin’s cubes in their didactic capabilities: “Fold the pattern,” “Fold the square,” “Unicube.”

Educational games Nikitin combine one of the basic principles of learning - from simple to complex - with a very important condition for creative activity - doing everything yourself. This union allowed the game to solve several problems related to the development of creative abilities:

1. Educational games can provide food for the development of creative abilities from a very early age.

2. Their stepping stone tasks always create conditions that are ahead of the development of abilities.

3.

Rising each time independently to his “ceiling”, the child develops most successfully.

4. Educational games can be very diverse in their content, and besides, like any games, they do not tolerate coercion and create an atmosphere of free and joyful creativity;

5. By playing these games with their children, parents quietly acquire a very important skill - to control themselves, not to interfere with the child’s thinking and making decisions, not to do for him what he can and should do himself.

Game Features

The main difference between Nikitin’s games is that when playing them, the child acts as an active party and he is not taught the ability to perform work according to the proposed template, but develops logical and imaginative thinking, creativity, the ability to recognize and construct an image, and the ability to be independent.

Most games are presented in the form of multifunctional puzzles that provide scope for creativity. You can customize them to suit yourself, your level, your interests. Each game has a set of problems that the child solves with the help of cubes, bricks, squares made of cardboard or plastic, parts of a mechanical designer, etc.

Nikitin's games can be expanded, improved, and new tasks can be invented.

Rules of the game

At first, no one explains to the child the rules of the game, no one shows him how to do it. The kid solves the problem himself from start to finish.

This technique allows the child to independently search for solutions to problems unknown to him and create new ones, which precisely leads to the development of his creative abilities. The adult makes sure that the level of the task is not too easy and not too difficult, and “corrects” and “directs” the child’s actions. And rejoicing will be the reward for a successfully found solution, and an incentive for future victories. Using Nikitin’s educational games in classes with a child, certain principles should be adhered to

1. The game should bring joy to both the child and the adult. Every baby’s success is a mutual achievement: both yours and his. Rejoice at it - it inspires the baby, it is the key to his future success. Observe how happy children are if they manage to make us laugh or make us happy.

2. Get your child interested in playing, but don’t force him to play, don’t let him play games to the point of satiety. And one more thing... refrain from making offensive comments like: “Oh, you’re a fool!”, “How stupid you are!” etc. Do not offend the child in the game.

3. Educational games - creative games. Children must do all tasks independently. Be patient and do not suggest with a word, a sigh, a gesture, or a look. Give the opportunity to think and do everything yourself and find mistakes too. By rising gradually and coping with more and more difficult tasks, the child develops his creative abilities.

4. To get a feel for the relative difficulty of tasks, be sure to try them yourself before assigning tasks to children. Write down the time it took you to complete a particular task. Learn to do it faster.

5. Be sure to start with feasible tasks or with simpler parts of them. Success at the very beginning is a prerequisite.

6. If a child fails to complete a task, it means you are overestimating his level of development. Take a break, and after a few days, start with easier tasks. It’s even better if the child himself begins to choose tasks based on his capabilities. Don't rush him.

7. If there is more than one child in a family, then everyone needs a set of games; it is best if there are boxes for all those playing.

8. In what order should the games be given? The author would start with the game “Fold the Pattern” or “Montessori Frames and Inserts.” Here the child needs to distinguish colors and shapes. And the general rule is to observe the child’s development, record his progress in a diary and determine when and which of the games to “turn on.” This is a creative task for dad and mom.

9. Children’s hobbies come in “waves”, so when a child’s interest in the game cools down, “forget” about the game for a month or two or even more, and then “accidentally” (show it, for example, to guests or a friend and teach him to play) let the baby remember her. Returning to the game can often feel like catching up with an old friend you haven't seen for a long time. Try to record the successes, shifts, achievements of each of the “waves” of passion for the game.

10. Take care of games, do not put them on par with other toys in terms of accessibility. After all, the forbidden fruit is sweet, and it is better if the child asks for them or offers to play. Let them stand in a visible, but not very accessible place.

11. For the little ones (1.5-3 years old) enliven the game with a fairy tale or story, give “names” (together with the baby, of course) to patterns, models, drawings, figures, invent, fantasize until the child begins to be captivated by the process of overcoming difficulties in solving problems, achieving the desired goal.

12. The more developed a certain quality is in a child, the more eager it is to be manifested. The strong want to fight, the fast want to run and play outdoor games, but the weak don’t like this. A child may “not be interested in playing” for two main reasons: he has poorly developed the qualities needed in the game, or... adults have discouraged him by forcing him to play or causing trouble at the very beginning. Therefore, praise more for successes and in case of failure, encourage the baby.

13. Create a relaxed atmosphere in the game. Don’t restrain your child’s physical activity so that you can jump with delight, do somersaults on the rug, and fly to the ceiling in daddy’s arms.

14. When folding patterns or models using ready-made tasks has already been mastered, move on to inventing new ones. Get a notebook and sketch there (or better yet, if the child does it himself) new tasks, patterns, figures.

15. It’s better to use a stopwatch, but you can also organize competitions on the speed of solving problems by the clock. Rapidly developing children can already defeat adults from the age of 6-7. In this case, you must muster courage and honestly admit your defeat in a knightly manner. It's hard to think of a great reward for a child. Don't think that your credibility will suffer.

16. etc. - these are the rules that you... find yourself to make the game even more exciting.

Briefly about the most popular games of B. Nikitin

Montessori frames and inserts . This game is accessible to the little ones. It consists of 16 frames with inserts in the form of geometric shapes: circle, square, triangle, ellipse (oval), rectangle and so on. The main task is to choose your own insert for this frame. In addition, frames and inserts can be outlined and then shaded.

Fold the pattern. This game consists of 16 wooden cubes, where each side has a certain color. The cubes must be placed in a wooden or cardboard box (its presence is required). Nikitin advises starting to play with them at the age of one and a half years. With such small children, you can lay out paths from cubes: blue, red, yellow. Then the child learns to place the blocks in a box with a certain color facing up. And only after this the baby begins to make simple patterns.

With this set you can study using the books “Miracle - Cubes. Album with tasks for the game “Fold the Pattern” for children 2-5 years old and “Miracle - Cubes - 2.” Album with tasks “Fold the Pattern” for children 4-8 years old.

Fold it into a square. This puzzle game is for children aged two years and older. The game includes 12 multi-colored squares, cut into pieces: two rectangles, two triangles, etc. The child needs to reassemble the squares from the cut pieces.

Unicube. These are universal cubes that introduce the baby to the world of three-dimensional space. "Unicube" consists of 27 small wooden cubes with colored edges. The child needs to put them together into various three-dimensional shapes and compositions according to the proposed patterns. The game is intended for children from 1.5 years old.

Dots. Dots from zero to ten are marked on square multi-colored cards. In addition, there are cards with numbers. First, the child needs to arrange the squares by color, then in order: from 0 to a card with ten dots (or numbers), etc.

Cubes for everyone. The game consists of small cubes, glued together in different ways in the form of 7 figures, different in shape and painted in certain colors. From such figures it is necessary to construct various models, resembling a cube or parallelepiped, houses, cars, animal figures, etc., according to the proposed drawings-tasks. Toddlers can build their models using only 2-3 shapes.

Fractions. The game is intended for children from 3 years old. It is a set of three plywood. On each there are 4 equally sized circles of different colors. The first circle is whole, the second is cut into two equal parts, the third into three, and so on, up to 12 “slices”. With their help, you can repeat the colors, count the inserted pieces, and you can make a multi-colored circle and compare them with each other.

B. Nikitin's educational games are described in more detail in his book, which is called “Intellectual Games”. It also provides tips on how to play with your child.

You can refer to Lena Danilova’s book “A New Look at Nikitin’s Games”, in which she complements and enriches the tasks for Nikitin’s games and helps parents look at his games a little differently. In her book she writes: “The Nikitins’ games can be compared to musical instruments, unique, multi-voiced universal instruments.”

Material for the lesson.

Game - Fractions

A child constantly encounters the concept of whole - part in everyday life from birth. We cut pies, divide pizza and oranges, look at the clock, pour a certain amount of liquid into a measuring cup. Why not tell your child what fractions are? You can also introduce your child to fractions using special aids. To warm up, you should take a regular orange and divide it, accompanying the division with the famous rhyme:

We shared an orange
There are many of us - but he is one!
This slice is for the hedgehog!
This slice is for the siskin!
This slice is for ducklings!
This slice is for kittens!
This slice is for the beaver!
And for the wolf - peel!
She is angry with us - trouble!
Run away in all directions!

The game "Nikitin's Fractions" consists of twelve multi-colored circles. One circle is whole, the rest are divided into parts: two, three, four, five, six, and so on until twelve. “By using the whole circle and its parts in the game,” Nikitin believed, “kids acquire many ideas about fractions and their relationships, although for some reason the school postpones their mastery by 5-6 years - to the 3rd-4th grade.” In the game "Nikitin's Fractions" there is no clear sequence of tasks, as in other games. Each time, all 78 parts must be poured onto the table or on the floor, and then put back in circles in the box, if, of course, you use the wooden "Oksva" manual. In this case, Nikitin defines the first problem:

a) pour fractions onto the table or floor
b) turn them over with the colored side up
c) arrange the fractions in piles so as to bring together equally colored ones
d) make a circle of the same color from each pile
e) put the mugs in frames.

What are the parts of the circles called? For little ones, this task can last for days, weeks and even months, Nikitin believes. There is no need to force things, just be happy if the child immediately names some: “green quarter”, “yellow half”, etc. For those who can count to 100, this task can be solved in one sitting. The names of the parts should be given not only everyday, but also mathematical: one second, one third, one fourth, one fifth.

Put it in a row put one part of all colors in a row: a) in order: put the largest part first, then smaller and smaller, and so on until the smallest, so that each next one is smaller than the previous ones. b) place the same parts next to each other, but in a stack. Place the largest one at the bottom and the smallest one at the top.

Which part is bigger One fifth or one fourth? How can I check this? Yes, just superimpose a smaller one on a larger one, and everything will be OBVIOUS, as N. Zaitsev likes to say. Problems of this kind can be given until it becomes clear to you that the child has grasped the principle of definition: “the more parts a circle is divided into, the smaller the parts.” By the way, how do you write down that 1/4 is greater than 1/5 mathematically? This is where the “more than” sign and the “less than” sign will appear.

How many pieces fit? How many quarters fit on one half? How many sixths, eighths, tenths, twelfths? How many times is one second greater than one fourth? One sixth? What parts and how many will fit exactly on one third, but on half? How many times is one sixth less than one third? Is it possible to make a whole circle out of pieces of different colors? What parts do you need to take for this? How many multi-colored circles can you add from the game "Nikitin's Fractions"? What is the largest number?

With your own hands Nikitin's book gives detailed instructions on how to make a manual yourself, so if for some reason the finished game is ready, it can be easily cut out of polystyrene foam. The sheets must be marked using a compass, divided into parts and cut with scissors or a sharp paper knife. And then move on to the actual games. Overall they are similar to the classic games with a plywood purchase manual. But there are also differences due to the lack of wooden frames.

First, let's take out a whole circle and show that it is a whole. Let's ask, what does it look like? To an apple, to the moon, to a wheel? Then let's take the second circle and show that it breaks into two halves. Let's ask for half of the second circle, apply it to the whole circle, etc. You can outline the circles with a felt-tip pen, then add colored faces. From half, if you circle it, you can make an umbrella or a mushroom. Using parts of a circle, you can talk about concepts such as “same”, “different”, “same”, “not the same”. Ask questions to fill in: “what is more: one second or one third.” And then show it, give the children the opportunity to select the parts themselves. Line up the pieces from smallest to largest. Go through each circle, naming the parts. If there are two parts, then one will be called one second or half. If there are three parts, then one third, and if there are twelve, then one twelfth. Let the child have the entire set of the game "Nikitin's Fractions", that is, all 78 parts. Now ask for one sixth, two sixths, six sixths? What different parts can be used to make a whole? Is it possible to divide a circle into two parts? How about three? How to make a circle using only red and yellow parts? Is this possible in principle? Let your classes contain as much kinesthetics as possible, let the kids let everything pass through their hands. Fractions are a complex topic; it is better to approach it from different angles, inventing new tasks. Lay out four slices of the eight-piece green circle. Ask how much is missing. Go through all the circles with this question. When playing, focus on the following expressions: “divide into equal parts”, “whole”, “half”, “in half”, “one of two”, “one second”, “one twelfth”, “part”.

The Nikitin family's method is my favorite. Probably because this is the only development method that has at least somewhat suited Sanya. Once upon a time, when he was exactly one year old, I bought the first level of the game “Fold the Square”, just to add to the order, for the future. And a month later I was simply amazed that a child, who in some places didn’t even have an awl, but a whole rocket, sat in one place for 20-30 minutes, sorting through pieces of squares and folding them over and over again in different ways, like -as if trying to check all the ways in which a square can be assembled. Let me clarify - the child was 13 (!) months old at that time, and I did not at all expect such interest in such things. And he “asked” for squares 5 times a day, pointing to the shelf on which they lay, and took them away from his cousins ​​when they came to play with us. Now I understand that this was the first manifestation of his logical-mathematical mindset, but then it seemed like a miracle... and some kind of relaxation))) Because I knew for sure that if he “collects squares”, then for about 20 minutes I I can sit relatively calmly without running after him throughout the apartment)))
Needless to say, after such a resounding success of one of the Nikitins’ manuals, I bought all their games that could be bought, including Fractions.

I must say that in the case of the Nikitins’ manuals, Sanya and I found it very easy to follow one of the basic tips for working with their games. The advice goes something like this: “Do not help the child complete the task, do not prompt him with a word, a movement, or a glance.” It was this rule that I tried to adhere to from the very beginning, fortunately Sanya himself did not really want help, and it is possible that this very well spurred his innate logical thinking, because he did not receive ready-made answers, and sometimes did not even receive questions))) For example, in the case of in fractions He initially worked on folding them like the same game “Fold a Square”, that is, he took the parts out of the recesses and folded them back in various ways. I don’t know what was going on in his head at that moment, he still couldn’t tell, because he was not even 1.5 years old, but clearly some concepts were forming, because he was trying to fit and identical parts, and different ones, and sometimes he had the idea to put as many parts there as possible.
In general, although in general the Montessori method is not very suitable for Sane, because he does not accept preliminary explanations, it is precisely the moment of “experiments” with the Nikitins’ manuals that, in my opinion, is very reminiscent of this method - the child does everything himself, and the adult is simply in the wings, on case of difficulty. By the way, it was from the Montessori methodology that the Nikitins drew their ideas, and their fractions-squares are nothing more than reworked and supplemented frame-inserts that Montessori used in her classes, and the approach was clearly taken from her, and the Nikitins did not hide this .
I was once amused by the story of a friend of mine who wanted to buy the Nikitins’ manuals in an offline store, and the “knowledgeable” sellers said that the Nikitins’ method was outdated, and the most modern method now is Montessori, and it is necessary to buy the manuals according to this method. It’s a pity, they apparently haven’t read either about Montessori or the Nikitins, otherwise they would have known for sure that one method follows from the other, and both of them are quite modern and in demand.
But this was a lyrical digression; I’ll return to fractions.
I must say that fractions We have a very long-lasting benefit. As I already mentioned, Sanya was introduced to them before he was 1.5 years old, and used them more as insert frames, and then they were used more for the development of fine motor skills than for the development of logic or mathematical concepts. There were periods when I put these tablets on the shelf and didn’t take them out for several months, and then Sanya grew up and we moved on to the next stage of studying the manual. For example, sometimes I could show him that if you put two red semicircles on one large yellow circle, they will coincide, and if instead of one red semicircle you put two green parts, you will again get a full circle.

I usually call the parts of the circle by their proper names - half, quarter, third, one-fifth. I can’t say that two years ago, or even a year ago, Sanya was particularly interested in such things - but after my explanations, he arranged some of his own games, drew some of his own conclusions, not always correct - but it was a process of reflection. It seems that now this process has borne fruit - against the backdrop of a passion for mathematics, and in particular, geometry, we again got fractions, and it turned out that there was no need to explain anything in particular - everything was clear and understandable to the child. Now we are learning to recognize these parts in graphical notation, as well as adding fractions and bringing them to a common denominator. Actually, all this is taught at school and not in the first grade, but when using such a manual, this is not at all a difficult task for a child, because he can clearly see why 2\4 suddenly became 1\2, or why, if you add 2 \3 and 2\6, then you get a whole one. Probably, if fractions were explained in this way at school, children’s performance in geometry would increase sharply.

It must be said that in this tutorial it is fundamentally important that all the circles are the same size - after all, this is the only way to clearly see how much 1\7 differs from 1\2, 1\4, 1\6, and that in the case of fractions, the larger the number written in the denominator, the smaller the fraction itself. This is very easy to do by simply overlaying different pieces on top of each other:

Due to the fact that all the pieces fit into the recesses, and there is no way to “spread them” wider to fit any fraction, you can again very clearly show that by adding, for example, 2\4, 2\8 and 2\11, another 1/11 will no longer fit:

Or replace one of the parts in each circle with a part of a fraction smaller by 1, and see how much smaller each of these parts is, and what can be done about it, and is it possible...

Games with fractions that Nikitins described, I think, I shouldn’t rewrite here, they are in Nikitins’ books and on their website.
I'll tell you more about the quality of the manual. They are produced in Russia, by the St. Petersburg company "Oksva". This particular set has the quality that suits me most, both in size and thickness. In this case, this is the Standard category, there is also Economy, but the planks there are much thinner and the wood is kind of brittle, I didn’t like it.
In this set, all the fractions that were assumed by the Nikitins come together - the circles are divided into parts from whole to 12.

Each “tablet” contains 4 types of fractions. Each tablet is A4 size:

The tablets are thick, 7 mm, they have recesses into which parts about 5 mm thick are inserted. The edges of the parts and the inside of the recesses are laser processed; immediately after purchase they may get dirty, but not much. On top, all the parts and the tablets themselves are covered with a colored film, it is glued very well - as you can guess, we have had this manual for about 4 years, but nothing has come off, scratched or chipped off. By the way, the game “Fold the Square”, which I mentioned above, has the same quality - nothing came off or broke either. Sanya, until about 2.5 years old, was a great rodent, he even chewed the back of the bed, but for some reason these benefits remained untouched - either they turned out to be tasteless, or they were simply very exciting, there was no time for gnawing)))

I think that these fractions will be useful to us more than once and for many years to come - after all, school is ahead, and the study of fractions there is quite serious, and having a visual embodiment of them makes learning more interesting and easier.