Features of mathematical perception of a preschooler

In order for our classes to only benefit the baby, it is necessary to represent his real opportunities and needs. We must understand that the mental apparatus of a small child is still immature, and he does not know how to fully generalize and draw conclusions. So a two-year-old baby can, pointing his finger at objects, followfine to pronounce:
- One two three four.
However, to the question: "How many items?" - the child cannot answer yet. Only at three and a half is he ready for the beginning of meaningful, and not mechanical, teaching of mathematics. He is already able to learn how to add and subtract numbers in his mind within five, but to do the same actions with large numbers, usually up to four or four and a half years old, the baby is still beyond his strength.
For kids preschool age it is perfectly normal to assume that any mathematical operation is true only in this moment and only with these items. Kids believe that if you move objects apart, there will be more of them, and if you put them closer to each other, then they will become smaller. If you move or change the position of objects, then their number will also change. The kid, adding 4 and 3, will definitely count all the items first:
- 1, 2, 3, 4, 5, 6, 7, - and only after that will give an answer.
A more mature child will begin to count and reason differently:
- There are 4 items, so 4 + 1 + 1 + 1 = 7.
The baby also does not represent the volume and weight of objects quite correctly. The preschooler believes that the flattened candy has become smaller, and the elongated one has become larger, and that cotton wool is always lighter than iron, since he relies on his feelings, and not on incomprehensible readings of the scales.
The French psychologist Jean Piaget was the first to notice and describe such features of the development of preschoolers. They are called “Piagetian phenomena” in his honor.
Many of these phenomena in the process of growth and learning of the child are weakened by 6-7 years, but some of them persist until 9-10 years. Despite this, all children can learn to count, add, subtract and solve simple problems by school.

Where does mathematics begin?

Any learning goes through three stages: habituation, understanding and meaningful memorization. At the same time, mathematics should not be something abstract, but a natural part of a child's life, otherwise he will soon forget everything we have taught him.
First, while playing and talking with a child, we teach him to compare objects and their properties, to distinguish a big thing from a small one, a long one from a short one, a heavy one from a light one, a round one from a rectangular one, and much more.
Usually, even before the child can comprehend what a simple account is, we mention numbers and mathematical concepts in a conversation with him:
- There were three bears.
- You have a lot of toys. Share with Sergei!
Your bucket is smaller than mine.
- Give, please, Masha one piglet, and take the other one for yourself.
Do you want to play alone or will you come with me?
- You have two pens - so there were two mittens. Where is the second glove?
- Wait five minutes, please.

Together with Agnia Barto's poems, children are usually offered to learn a rhyme about a bunny.
One two three four five -
The bunny went out for a walk.

As a result, most children after three and a half years old can count, and even add and subtract within four or five. However, they may not know about it, and they need help to show their knowledge, but first the child must learn to count meaningfully, and not mechanically.

Understanding the score in the game and movement

“Olenka willingly counts everything and knows how many items there are, and yet I’m not sure that Olenka counts intelligently enough.
To make the account more meaningful, Olenka and I slightly transformed the well-known rhyme:
We shared an orange
There are many of us, but he is one.
This slice - for a hedgehog - once.
This slice - for siskin - two.
This slice - for kittens - three.
This slice is for ducklings - four.
This slice - for a beaver - five.
And for the wolf - peel!
The wolf got angry - trouble,
Run away in all directions!”

Comprehension of the score is sometimes a rather difficult process and can take quite a lot of time, so we, slowly and without getting upset, try all new tricks and games.
“I tried again to bring Olenka closer to understanding the account.
First, I lined up four toys one after the other in a queue. Then we counted them and put an ordinal number on each. Then we discussed which animal is before and which is after, for example, a bunny. I tried to ask clear questions:
- Who is standing in front of the bunny? Who is behind the bunny?
Then they remembered a cartoon about a kid who could count to 10, and again they counted everyone:
- Dog - 1, bunny - 2, fox - 3, cat - 4.
And only after that I began to ask:
What is the number after one? What is the number before 2?
Olenka clearly answered both questions, but since the usual ten minutes of our classes came to an end, we had to interrupt.
Only when the child can clearly say without errors which number is in front of any of the first five numbers, and which one is behind, can we assume that he understands what he is doing and proceed to comprehend counting to ten and simultaneously master addition and subtraction.

What is the best way to represent a number

In order for a child to distinguish different numbers well, images of these numbers must arise in his mind. Of course, a child can create these images without us, but we can help him find more suitable and capacious ones. The colored dots of a large children's domino are best suited for this. However, they can also be replaced with balls, bunnies or daisies. The main thing is that the objects are small enough, and they can, if desired, be represented as domino points. Agree that it is easier to imagine the number five if it is depicted compactly in the form of small objects, so it is impossible to come up with anything more convenient than images on dominoes.

However, the child has a great need to touch everything and see for himself, so the children and I began to make an additional manual from quickly hardening plasticine, which we called “math balls”. These are several small rectangles, each with five recesses for balls. The round holes are arranged in the same order as the dots on the dominoes. You can insert a ball (or other convenient figure) into each recess. You can shift the balls to another, the same quadrilateral, and notice how the same numbers look, or think about what to do to make these numbers equal.

The clarity of the manual and the fact that a child can turn one number into another with his own hands helps him a lot to understand how different numbers differ. At this stage, this is a very important task. This is what distinguishes a child who can count from a child who simply memorized numbers without any understanding and cannot really count.

We form images of numbers from 1 to 5

We divide this important topic in teaching kids into four steps.

1. We remember what the numbers from one to five look like. We learn to count to five and get used to the correct layout of numbers in squares in the form of domino dots.
Tutorial:
- These are houses. Bunny balls live in them. Let's count how many bunny balls live in each house.
After that, the teacher invites the child to populate another house with the same number of characters and in the same order.

2. We translate passive knowledge into active. To do this, let's play our favorite game: "Guess what I hid." It will help the kid learn to find out how many balls are placed on one square, without even counting, and remember which numbers this number of balls corresponds to.

It is better to start with two quadrangles, which in the game can be called different, more pleasant names for the child's hearing, for example, houses or cars. You can, of course, complete our squares with a roof or wheels for this, but kids usually have such a good imagination that it’s enough to say that this square is now a flying carpet and they already see it. We also need plastic numbers, from 1 to 5 for now.

The course of the game might look something like this:
- Look, I have two houses. These colored balls live in everyone. How many red balls live in the first house, and how many yellow balls live in the second? That's right, 3 balls live in the first house, and four in the second. Now a cloud (a piece of paper) has crawled onto the house. How many balls are hidden under the cloud? That's right, the cloud closed the house with three balls. Now find the numbers 3 and 4 in the box and put the three next to the house in which three balls live, and where do we put the four? Of course, next to the house in which 4 balls live.

Gradually, the number of hidden "houses" is brought to 3-4, not forgetting to come up with all the new plots of the game. For example, somehow our squares turned into sea ships, and the balls into sailors. Part of the ships hid behind a rock, and I had to urgently remember how many sailors on each ship needed to be saved.

For greater clarity, we will invite the child to close his eyes and tell from memory what a number looks like, and then open his eyes and draw it on paper or type it on the box yourself.

3. Fixing the material. At this stage, it is useful to learn how to play the game of "dominoes" itself. We play openly, turning all the bones upside down. Each player puts his knuckle and loudly announces the number of dots, for example: "five - three." It is good if plush toys take part in the game. The child and I can make moves for them. The winner is the one who runs out of bones or there are fewer of them left.
Of course, an adult wins very rarely - otherwise the game will quickly get bored.
Another one fun game with an imaginary Baba Yaga. The teacher lays out a number series from one to five, then distracts the child and breaks the order of the numbers.
Tutorial:
- Baba Yaga mixed up all the numbers again. Can you fix everything?
The child knows that this is a game, and Baba Yaga is imaginary, but joyfully plays along with us:
- Look, Baba Yaga. We put all the numbers back in place!

4. Deepening the understanding of concepts: equally, the same number, the same number and how the numbers differ.

We take three squares and lay them out so that two of them have the same number of balls, for example, 3, and the third has another, for example, 4.
- Look, these are three nests. Sparrows sit in them. What nest of sparrows has the same number of sparrows? Are these two equal? What needs to be done so that they have the same number of chicks? That's right, remove one!
We invite the child to “guess” how three points differ from two, two from four, etc.
The answer, undeniable to an adult, is not so obvious to a child. The child should respond like this:
- Three differs from two by one point.

With the help of colored dominoes, you can make the game more difficult and interesting. Compare domino dots in three ways: by color, location and number of dots.

Math mobile games

“Sometimes Olin's friend Yura joined our classes. They already knew how to add and subtract a little, but in order for the guys to better understand the difference between addition and subtraction, we decided to go back a bit. I remembered how, on a walk, Olya and Yura jumped up the stairs with passion, counting the steps, and invited them to jump along the music track with numbers. First, they jumped forward, from number to number, from 1 to 10, each time saying:
- We add one more - it will turn out ...
Then in reverse side from 10 to 1, saying:
- We subtract one more - it will turn out ...
The children liked the game so much that now Yura, no matter how he comes in, asks from the threshold:
- Today we will jump and count?
When the guys stopped making mistakes by adding and subtracting one, they began to count back and forth in deuces:
- Two, add one and one more - four, add one and one more - six ... "

A similar rug can help us too. You can buy it or make it yourself by drawing 10 cells on fabric or paper with the first ten numbers of the digital series from 1 to 10. Below are a few games that kids especially like.

1. The game will help the kid learn to count meaningfully from one to ten and vice versa. Of course, jumping with someone in turn is more interesting.
- One, two, three, four, five - five, four, three, two, one, - the kid says, jumping from number to number back and forth. For a change, you can jump on one leg, then on two or something else. Over time, we bring the number of cells to ten.
When the child remembers the counting order, you can ask him to count out loud again, but with his eyes closed.

2. This game will help the child get closer to understanding what addition and subtraction are.
Now the baby jumps from cage to cage with the words:
- One, add one - two. Two, add one - three. Three, add one - four. Four, add one - five. Five, subtract one - four. Four, subtract one - three. Three, subtract one - two. Two, subtract one - one, - the baby carefully says, jumping from number to number back and forth.

3. Another game that is also perceived by children as fun entertainment. Despite this, it is extremely clear how numbers change with the addition or subtraction of one.

The child jumps from cell to cell with a "bast basket" and takes out of it and puts one berry (or other toy) on each cell, saying:

1 berry, add 1, get 2 berries; 2 berries, add 1, you get 3 berries; 3 berries, add 1, you get 4 berries; 4 berries, add 1, you get 5 berries.

Then in the opposite direction, with each jump, collecting one berry:

5 berries, subtract 1, 4 berries remain; 4 berries, subtract 1, 3 berries remain; 3 berries, subtract 1, 2 berries remain; 2 berries, subtract 1, 1 berry remains; 1 berry, subtract one, nothing remains - zero.

At first, the child does not understand that he is already adding and subtracting one, he is only getting used to these concepts, understanding will come later.

"Grandmother! - Katyushka asks for a walk, - let's play numbers. I'm a five and you're a four.
- Well, - I agree, - so who's the first?
- I, of course, I'm more! The girl runs ahead.
- Then I'm now a seven, - I say and stand ahead of Katya.
- And I'm already ten, - says Katya and again stands in front.
- Okay, - I say, - then let's play, who is less. I am a seven!
- And I'm a six, Katyushka runs ahead again.
The baby really likes this game, because it feels some kind of rivalry.

It is very good when not we, but the child becomes the initiator of classes. Sometimes it is helpful to set aside your own "adult" things so that the child can feel the importance of his little things.

Quicksave's excellent selection of arithmetic tests and puzzles is an effective educational material that will help prepare children for entering school. Preschoolers will learn to count with interest, moving step by step in learning, successfully coping with the tasks of developing online toys.

Fun practice of math skills

All puzzles are solved in a game format - this contributes to the speedy memorization of important information. Popular tutorials for the youngest gamers allow children to fully unleash their potential: form logical thinking, improve memory and concentration, pump creativity and perseverance.

Users will not need to buy a product, activate it or install it on a personal computer - browser-based flash games without registration allow you to enjoy the process for free without being distracted by unnecessary actions. The most sophisticated aesthetes will appreciate the incomparable graphics of fresh new products from Quicksave.

Gameplay Features:

• Outstanding story line with the search for the correct answer from several proposed options to move to the next level, it allows the player to be as free as possible and grasp the essence of the task with lightning speed;
• The difficulty of missions grows depending on the progress of the student;
• The time limit and the desire to know the right answer becomes the main motivational factor that contributes to further progress.

The ability to correctly count will help the tomboys to correctly navigate in any life situation. Figures, numbers, geometric shapes - this is an unknown world that is only opening up to young inquisitive minds. The main task of parents is to show their child the right direction in which to develop. And the collection of logical computer entertainment is the most affordable and understandable way implement the idea.

We play and count with pleasure

Share your emotions from passing the next intellectual quest with your friends. You will receive an additional charge of positive energy by experimenting with figurative and logical thinking- very soon you will feel the amazing effect of mastering the material covered. If you regularly play exciting fun from the category:, the result will not be long in coming.

Deep learning math is a bit different from the usual one, two, three. If you want your child to come to school well-prepared, read the overview of methods dedicated to the topic how to teach a child to count. Who are the authors of these systems? How do benefits work? Are they effective and which one to choose? All this you will know right now.

A Little Preface: Is Early Mathematics Yes or No?

Perhaps someone will be surprised to see familiar names in the subheadings - Montessori, Doman, Zaitsev and the Nikitin family. No wonder, because they appear as innovative authors who offered the world fundamentally different reading methods or teaching methods, like Maria Montessori.

Nevertheless, each of these people invented something that deserves the closest attention - non-standard techniques for teaching mathematics. Please note - neither counting, nor addition and subtraction, namely mathematics. Each method is valuable. They have no contraindications and special limiting recommendations. They overlap in many ways. They can be used as the child likes or seems rational to you: all together, in turn, part of the technique or the whole technique at once.

The Nikitin family: learning to count by dots

Teaching children to count "according to Nikitin" can be done in different ways. This technique is a screening test that has been transformed into a game. The manual consists of small squares on which, in a certain symmetry, numerical figures are built from large dots. They come with digital cards of the same size.

It is necessary that the baby learns to systematize the cards: first by color, then by number and numbers. The following is a standard set of mathematical tasks, selected specifically to teach a child to count:

• how many - in different versions;
• pick a number;
• find quickly;
• compare;
• count;
• what is superfluous and others.

Thus, in the game, children form an idea of ​​the number and its connection with the figure.

Nikitinskaya table "Hundreds" - a way to overtake peers

You will probably be interested to know why many authors of developmental methods prefer simple geometric shapes - circles, squares, etc.? As you know, children are distracted people. So why once again risk losing useful and short minutes by posting bright pictures?

The Hundreds table itself looks like a grid. In its central part there are numbers, and along the perimeter - dots in the corresponding quantities. She easily solves that other problem for parents - how to teach a child to count up to 100. Actions with numbers containing tens and hundreds are added to the tasks listed above.

Actually, these two simple but voluminous techniques cover the program elementary school regarding the account with the signs "+" and "-." The Nikitins themselves give an example of how their six-year-old daughter surprised her parents and made up a difficult task. logical task, using numbers from 50 to 500. And this is aerobatics even for a fourth grader. In addition to these games, teachers have developed other equally useful techniques, which we will talk about in future articles.

Zaitsev's "No!": teaching mathematics not up to ten, but up to a thousand ... at least

How to teach a child to count to 10 is a puzzling question that makes more than one diligent mother sob. If it were enough to simply count, otherwise you still need to learn the composition, understand the plus and minus, learn how to compare and even solve equations!

Nikolai Alexandrovich thought and invented a technique as innovative as the cubes, but under the name "Stoschet". The author himself warned that a hundred is the minuscule that the brain of a five-year-old child is capable of. Having changed the types of activities in places, Zaitsev determined that the calculation in the mind is more important and initial, and only then do written calculations come.

"Stochtet" - a set of benefits, in which, again, the theme of numbers and geometric shapes. The figures are necessary for the quantitative illustration of the figure.

The Hundred Account tape introduces children to all kinds of mathematical operations with numbers. Children who have mastered the tape algorithm easily go beyond a hundred, reach a thousand, and even step over this line. The child is learning mental arithmetic as if imperceptibly. In addition, he is passionate, and this is worth a lot.

The chips that make up the tape look like a double didactic set: the required number of circles, squares and the corresponding number. The figures are arranged symmetrically and clearly show the structure of the number in two versions.

The "One Hundred Account" table consists of the same chips, but they are placed in a rectangle. The tasks invented by the author for children are constructed in such a way that children do not solve, but search. During the game, they master the composition of the number, learn to count and compare, and all this without poring over a notebook until 23.00.

The Genius of Glenn Doman: Teaching Math

The most famous and the most useful technique rehabilitation of seriously ill children with brain damage ... We cannot but say a few words in defense of Glenn Doman. Being a doctor who restored children after injuries, the author invented his own system as one of the methods of treatment and adaptation. The technique gave an excellent result on this very difficult audience.

In Doman's cards, created for children with disabilities, a new method of teaching children to count was “seen”.

What are Doman cards for an account? These are sets of squares on which points are located either systematically or randomly. By showing cards for a few minutes a day, parents can teach children to recognize numbers and count. Considering that Doman operated with large numbers, the effectiveness of solving examples without special counting of points raises doubts.

How to teach a child to count according to Doman? Is learning from the author's math flashcards suitable for ordinary children? As the formation of the perception of a number at the level of intuition (without counting units) - yes. But as a separate method, it leaves many white spots in the mathematical thinking of a person.

Maria Motessori - the richest set of techniques for teaching mathematics

The most capacious and universal method that helps parents figure out how to teach counting to a preschool child. It is no secret that most of the innovative systems are based on the developments of Maria Montessori. This attractive Italian was not a teacher either. But she came up with all the best that only exists in the world of pedagogy even today, after almost a hundred years from the foundation of the system.

Based on the various everyday experiences of children (sensorics, memory, imprinted images), Montessori based her method, which includes exercises to develop abilities of all kinds. The author's manuals are made taking into account many parameters: weight, tactile sensations, sound, size, color. This approach allows you to use all types of human memory and makes it possible to assimilate the material in a complex way, through sensations.

Montessori math aids up to ten

Benefits in the form of wooden bars from 10 cm to 1 m long - Montessori bars - will help to cope with the first ten. Children in practice will be able to compare the values, because the rods have different length and divided into units - segments of 10 cm. How to teach children to count even faster? Use Montessori cards. These are chips that show circles and numbers up to 10.

In addition to the named bars, the Montessori system includes spindles, wooden chips, diverse digital cards, skittles and much more.

Golden Montessori beads - learning to count from 10 to ... infinity

Spectacular and effective remedy knowledge of mathematics is Montessori's golden asset. With him, parents do not have a headache, which is called how to teach a child to count correctly. Working with beads, kids 4-5 years old learn the number on an intuitive level. Benefits, specially designed from "golden" beads, reveal the concept of number.

The same beads, but in other configurations, tables, boards of a special design, voluminous chips with addition examples, materials "Fractions", abacus of the original design - this is a small list of Maria Montessori's materials for comprehensive teaching of mathematics.

Montessori materials convincingly illustrate mathematical formulas. With golden beads backed up with digital cards, you will not have a problem how to teach a child to count with a column. Sorting sets by category and matching numbers to them, children in game form understand the relationship mathematical concepts and action.

Interesting facts about column arithmetic

Having prepared the child for school, later we invariably ask ourselves the question: where do the deuces come from? Why can't a student who solves well at home tell the teacher the answer?
No matter how trite, but it only says that in his "mathematical building", where every brick should be in its place, there is a marriage. Most often, these are such problems as: ignorance of the composition of a number, multiplication tables, the principle of dividing a number into digits.

Despite the effectiveness of the described methods, all of them should lead to a theory. That is, the student, having learned the numbers figuratively, should be able to answer all program questions. Definitely, you will have to grind. However, this is only for the good. The Russian program gives the clearest algorithm on how to teach a child to count in a column. This was told to us by parents whose children studied in foreign schools.

It turns out that the traditional recording with the transfer or borrowing of bit units gives an excellent result, provided that it is supported by knowledge of the theory.

Early methods - mathematics "excellent"

Separately, I would like to comment on the negative point of view regarding the methods of early teaching mathematics. If a child wants to know, then this knowledge must be given to him. Moreover, the authors do not offer to seat the kids at the desk. All classes are held "in between times" in a friendly environment. child health form. And this is a great alternative, given the pre-school fever, when the child is urgently seated at the desk, given a textbook and counting sticks, and told to get ready for school.

In fact, the methods of early teaching mathematics are several solutions to one problem. A sort of Rubik's cube, in which the only possible and quite real result is the child's mathematical knowledge. As always, we advise you to combine the useful and the necessary: ​​non-standard methods, which are certainly useful, and the school curriculum, compiled and tested by the most experienced experts in their field.

Children are predominant visual-figurative thinking. The problem is that most mathematical concepts are abstract and poorly perceived or remembered by younger students. Therefore, any mathematical operations must be based on practical actions with items.

Teachers use three main ways to teach a child to count in his mind:

• based on knowledge of the composition of numbers;
• memorizing tables of mathematical operations by heart;
• using special techniques for performing mathematical operations.

Let's consider each of them.

Preparation for teaching oral counting

Preparation for mental counting should begin with the first steps in the study of mathematics. When introducing a child to numbers, it is imperative to teach him that each number denotes a group with a certain number of objects. It is not enough to count, for example, to three and show the child the number 3. Be sure to invite him to show three fingers, put three candies in front of him, or draw three circles. If possible, connect the number with fairy-tale characters or other concepts known to the child:

• 3 - three piglets;
• 4 - ninja turtles;
• 5 - fingers on the hand;
• 6 - heroes of the fairy tale "Turnip";
• 7 - gnomes, etc.

The child should form clear images tied to each number. At this stage, it is very useful to play mathematical dominoes with children. Gradually, they will imprint in their memory pictures with dots that correspond to the corresponding numbers.

You can also practice learning numbers with a box of dice. Such a box should be divided into 10 cells, which are arranged in two rows. Getting acquainted with each number, the child will fill in the required number of cells and memorize the appropriate combinations. The benefit of these games with cubes is that the child will subconsciously notice and remember how many more cubes are needed to complete the number up to 10. This is a very important skill for mental counting!

Alternatively, you can use Lego parts for such an exercise or apply the principle of pyramids from the Zaitsev technique. The main result of all the described ways of getting to know numbers should be their recognition. It is necessary to ensure that the child, when looking at a combination of objects, can immediately (without recalculation) name their number and the corresponding number.

Mental counting based on the composition of the number

Based on the knowledge of the composition of the number, the child can perform addition and subtraction. For example, to say how much “five plus two” is, he must remember that 5 and 2 is 7. And “nine minus three” will be six, because 9 is 3 and 6.

Without knowledge of the relevant tables, a child is unlikely to be able to learn how to divide numbers in his mind. Constant exercise in the use of tables greatly improves the speed of obtaining results when performing calculations in the mind.

Use of computational techniques for oral counting

The highest degree of oral counting skills is the ability to find the fastest and most convenient way to calculate the result. Such techniques should begin to be explained to children immediately after familiarizing them with the actions of addition and subtraction.

So, for example, one of the first ways to teach a child to count mentally in grade 1 is the method of counting and “jumping”. Children quickly learn that adding 1 produces the next number, and subtracting 1 produces the previous number. Then you need to offer to get acquainted with best friend the number 2 is a frog that can jump over the number and immediately call the result of adding or subtracting 2.

Similarly, there is an explanation of the principle of performing these mathematical operations with the number 3. This will help the example of a bunny that can jump farther - immediately through two numbers.

Also, children need to demonstrate the techniques:

• permutations of terms (for example, to count 3 + 68, it is easier to swap numbers and add);
• counting in parts (28 + 16 = 28 + 2 + 14);
• reduction to a round number (74 - 15 = 74 - 4 - 10 - 1).

The counting process facilitates the ability to apply the associative and distributive laws. For example, 11 + 53 + 39 = (11 + 39) + 53. At the same time, children should be able to see the easiest way to count.

How to learn to quickly count in the mind of an adult

An adult can use more complex algorithms for oral counting. by the most convenient way counting quickly in the mind is rounding numbers followed by addition. For example, example 456 + 297 can be calculated like this:

• 456 + 300 = 756
• 756 - 3 = 753

Subtraction is done in the same way.

To perform multiplication and division, special rules have been developed for operating with individual numbers. For example, these:

• to multiply a number by 5, it's easier to multiply it by 10 and then divide it in half;
• multiplying by 6 involves performing the previous steps and then adding the first multiplier to the result;
• To multiply a two-digit number by 11, you need to write the first digit in place of hundreds, and the second in place of units. In place of tens, the sum of these two digits is written;
• Divide by 5 by multiplying the dividend by 2 and then dividing by 10.

There are rules for computing operations with decimal fractions, calculating percentages, raising to a power.

You can get acquainted with these techniques at school or find material on the Internet, but in order to learn how to quickly count in your mind based on them, you need to train and train again! In the process of training, many results will be memorized, and the child will call them automatically. He will also learn to operate with large numbers, decomposing them into simpler and more convenient terms.

Very often, parents, trying to give their child a first understanding of mathematics, focus exclusively on ordinal counting or memorizing numbers. Naturally, both are useful activities, however, if you really want to teach a child to count, then you need to introduce him not to numbers, but quantities and not just memorize the count to ten with the baby, but help him understand the spoken meanings, develop mathematical thinking. For a child, the words “Four apples” should not be an empty phrase, the kid should clearly understand how many apples it is and understand that, for example, four is more than two.

Mathematics for kids. Basic principles

The math games I want to talk about in this article are best for for children 2-4 years old (and something even earlier). The main goal of these games is to teach the child to visually recognize the number, to understand which is larger, which is smaller, which are the same, how many correspond to each digit, and what will happen if one more is added to three apples. I would like to note that these are games, not lessons. Children at this age will not like it very much if you constantly torture them with questions like “Show the number 3” “Tell me, how many sticks are there?”. They need to be interested, unobtrusively add mathematical problems to everyday story games. I notice the highest interest in my daughter when her favorite toy personally tells her about her problem and asks for help (for the toy, of course, I say).

Do not try to play with big numbers at once! It is enough to limit yourself to games within 4-5. Agree, it is much more attractive to help a child master various operations with numbers not exceeding the number 4, to develop mathematical thinking, than just to learn how to count up to ten, not knowing how to act with each of these numbers. A child who has mastered operations with small numbers will then easily transfer his skills to large numbers.

So, math games for kids:

1. Ordinal counting in everyday life

First of all, draw your child's attention to the fact that everything around us can be counted and enter the account into your everyday life. Count the stairs you climb, the cars in front of the house, the spoons before dinner, the pigs in the fairy tale, the stick candles on your sand cake, and so on. So gradually the child will remember the sequence you regularly say “one, two, three ...” and slowly begin to correlate it with the amount seen. You can do this from 1 year old.

2. We study the concept of "The same"

Here are a few examples of our very first number games (played around age 2):

We seat 2-3 toys at the table, inform the baby that one of them has a birthday today, so all the guests need to be fed. To begin with, we count together how many guests there are and with the words “So, there are only 3 guests, which means that we will also need 3 plates,” we count three plates with the baby. We arrange them for the guests, check that everyone had enough, which means that the plates as many how many toys. Similarly, you can give tasks for the distribution of spoons or chairs for toys.

Then, in the voice of Masha's doll, we say "Can I have 3 mushrooms, please." We count Masha 3 mushrooms. Then we argue that it would be necessary to put the frog the same amount so as not to offend. We also count 3 mushrooms for him. Re-established the concept as many ».

In the game, you can use any available counting material (cones, buttons, counting sticks), as well as purchased ( mushrooms, carrots, tomatoes).

• It is not necessary to be limited only to the theme of tea drinking, mathematics can be added to any role-playing game. For example, put as many houses as there are animals, draw as many berries as there are hedgehogs in the picture, etc. The main thing is to harmoniously weave the task into the plot of the game, telling the story that the little animals were left without housing, etc.

3. Compare "More-less"

• Continuing the theme of the birthday of the toy, we lay out 2 mushrooms for one of the guests, and 4 for the other, together we think about who has more and who has less. To begin with, we give the baby a try to determine by eye, if he is mistaken, we count together.

• If the child is already good at comparing similar objects, you can offer him more difficult task : put 2 different numbers of items in front of it different sizes, for example, buttons. For example, we put 3 large buttons and 5 small ones and ask where there are more. At first, babies usually get confused, pointing to large buttons. Your task is to explain that in this problem you are not comparing the size, but the number of buttons.

4. We study the concept of "Zero"

Even the smallest, one-year-old children can easily notice the fact that the items were and ended, as well as catch the moment when this happened. Therefore, having distributed sweets, mushrooms and other joys to toys, spread your arms in bewilderment and say, “But we have nothing left - zero sweets.” The concept of "zero", as a rule, is acquired by children very easily.

5. Board games

Board games with dice and chips - one of the most and best and interesting ways practice ordinal counting with your child. In addition, by constantly counting the same number of dots on the cube, the baby learns to recognize the number without recalculation, which is also very useful and will help in the future to easily operate with numbers in the mind.

Taisiya and I started playing board games at 2.5 years old, at this age, she could already catch what you need to play by the rules, there is an order of moves, etc. I wrote in detail about all our first board games. And you can download a walking game made especially for kids.

6. Countdown

Show your child not only direct, but also reverse counting. So, for example, when putting rings on a pyramid, count as usual, and when disassembling a pyramid, count in reverse order, thereby showing that the number of rings is decreasing. The same can be done by folding / laying something out of the box, assembling / disassembling a path (turret) from cubes. This is very useful game, it prepares the child well for the subtraction operation.

7. Simple operations with objects: addition and subtraction

No, of course, I will not write here that it would be time to solve examples. We will simply unobtrusively during the game give the child an elementary and very simplified idea of ​​\u200b\u200bsuch mathematical operations as addition and subtraction. Everything is just in the form of a game! If the child finds it difficult or does not want to count, we simply pronounce the conclusion from the game situation ourselves "There were three sweets, one was eaten, two remained." Here are a few examples of games that can be used to train a child's mathematical thinking (let me remind you that so far we use only the smallest numbers in our games - within 4-5):

We take some toy and go with it together into the forest in search of berries. For example, we played with a cat. Walking around the room, we found pebble-berries of two colors under the chairs and tables. Well, at the end they counted: “How many orange berries did the cat find? Three. How many yellow ones? Two. Now let's count how many berries he found in total. Five. It turns out that we have collected 2 yellow berries and 3 orange ones, and only 5!”

• The fixies were going to fix the chair. They have 3 bolts. Let's calculate whether each fix is ​​enough for a bolt. How many more bolts do you need to find?

• We transport the cubes in the car to the construction site (let's say 3 pieces). During transportation, one cube falls out. We count how many cubes are left.
• We give the bear three sweets, he eats two. We count how much he has left.
• It is very interesting to play the so-called "hide-and-seek-reader". For example, we draw four apples, then close one with our palm, how many are left? Then we close two, and so on.

8. Composition of the number

It is very useful to decompose numbers into their components with the child (for example, 3 is 2 + 1, 1 + 1 + 1, 3 + 0). This will help the child with the count in the future. Game options:

• Look, you and I have three apples, let's divide them between a bear and a bunny. We will give one apple to the bunny, and two to the bear. Try to redistribute the apples between the toys in different ways, showing different variants expansion of a number.

You can attach several clothespins to the hanger, install along the edges small toys and redistribute clothespins between them, imagining that these are, for example, sweets. It turned out to be an excellent replacement for the usual boring bills. Another option: you can put bagels on a ribbon and redistribute them in the same way, saying who got how much.

9. Get acquainted with the numbers, establish the relationship between numbers and quantities

When the child has some idea of ​​the quantities, you can begin to enter numbers. Now, having counted something, you not only call the number, but also show the corresponding figure. Here are some more math game options:

We build towers from the designer or cubes of the appropriate size;

• We attach a suitable number of clothespins-hair ( HERE YOU CAN DOWNLOAD our head templates);

• We select dominoes with the required number of dots (to diversify the game, you can offer the child to deliver dominoes to numbered houses on a typewriter);

• We lay out the tracks from the counting sticks and select the appropriate numbers - the length of the resulting tracks will help the child understand which number is larger;

• We put the right number of matches in numbered boxes;
• We impose the required number of cubes in cars with numbers (cars can be drawn on paper);
• You can also use ready-made solutions, like this games "Numbers" (Ozone,labyrinth, My shop)

or insert frame (Ozone, My shop,read)

10. Repeat numbers

To consolidate the numbers, games in which the child needs to find the same numbers and combine them will be useful. For example, you can select houses for toys by numbers, arrange cars in numbered garages, etc.

Or play in math game"Engine" . To do this, draw on paper or build a steam locomotive from the designer by numbering the cars. Each passenger, approaching, will call the number of his car, and let the kid seat everyone in their places.

Books with poems about numbers like "Merry Account" Marshak (Ozone, labyrinth, My shop). We were lucky, and the size of the numbers in the book exactly matched the size of our soft numbers, so we superimposed them while reading.

I also really like "Merry Account" by N. Vladimirova (Ozone, labyrinth, My shop), I wrote about it earlier.

11. Sequence of numbers

In my opinion, before 3 years there is no need to focus the child's attention on the sequence in which the numbers are in the number series, so as not to confuse the baby while he forms his idea of ​​​​quantities. Well, after three children, such mathematical games may already be of interest:

• « Baba Yaga mixed up the numbers". The kid must put the confused numbers in order.
• . In fact, this is the same game as the previous one, only more interesting, in my opinion, because by arranging the numbers, the kid can see beautiful picture. A few examples of puzzles can be DOWNLOAD HERE.

• "Name the neighbors of the number." Having added the numbers by numbers, you can ask the baby what neighbors, for example, the number 4 has.
• Connect dots by numbers. The easiest number mazes, which are ideal as a first, in my opinion, are presented in workbook KUMON "Learning to count from 1 to 30" (Ozone, labyrinth, My shop)

Well, in conclusion, I would like to give a few more useful books that will help you teach your child to count.

• Zemtsov "Numbers and counting". Sticker books (Ozone, labyrinth, My shop)

The books contain simple tasks for counting, memorizing numbers. The tasks are quite diverse, the presence of stickers in books definitely increases the child's interest in them. Benefits will be a great help in mastering mathematics.

• Felicity Brooks "Playing and Learning Numbers" (Ozone, labyrinth, My shop)

• Magnetic book-toy "Account" (Ozone, labyrinth, My shop)

• Photobook "Learning colors and numbers" (Ozone, labyrinth, My shop)

In this book, the child is asked to look for different objects while simultaneously counting them. An excellent book for practicing conscious counting skills, attention. We did not immediately become interested in her, somewhere after 2.5 years.

So, if you introduce simple mathematics into your daily game situations with a child from an early age, then this science will be easy for the baby. I wish you interesting and rich games!