How to learn to count numbers quickly. A surprisingly easy way to teach your child mental math

One of the main reasons bad results in mathematics on the OGE or Unified State Exam - this is the inability to count. Many schoolchildren find it difficult to solve an example even on a piece of paper, not to mention quickly counting in their heads. But some parts of the brain atrophy if a person does not use mental skills. Therefore, it is important to develop mental abilities to their full potential.

The basis for developing mental arithmetic skills

Some parents believe that teaching a child to quickly count examples in his head is not necessary: ​​he will not need it in the future, because he can always use a calculator. But at the same time, they forget that such training is simply necessary for brain development: any learned method (technique) of counting is a new neural chain (connection), the more such chains there are, the smarter the student. Therefore, the main benefit of the quick counting skill is the development of the brain and intelligence.

It is impossible to learn to work with numbers in your head if you have a weak understanding of them and actions with them.

Counting skills develop gradually from a visual representation of numbers and actions with them to an abstract logical one:

1. First, the child learns to count forward and backward with the help of rhymes, nursery rhymes, practical exercises while walking, eating, playing games (counting how many objects are on the table, cars in the garage, birds in the tree). Gets acquainted with numbers, learns what they mean, learns to correlate numbers and quantities.
2. Then he masters the concepts of “more - less”, “equally”, learns to compare the number of objects, sizes.
3. After this, he gets acquainted with addition and subtraction and learns the meaning of these actions. All examples are illustrative (the child moves 2 more apples to two apples and counts how many they get).
4. Learns to count objects with his eyes, first pronounces out loud the actions and the result of the actions, and then in a whisper: if you add 2 more cars to 4, you get 6.
5. Repeated repetition of actions will lead to the fact that the baby will learn to recognize examples that he has already worked with and say the result out loud, bypassing the stage of pronunciation.

At the stage of learning to count, it is important to interest the child, support him in case of failure and rejoice with him in victories, even small ones. When, the skill will need to be developed by introducing the student to various techniques and techniques.

Development of mental arithmetic skills

• Improving the ability to work with numbers in your head.
• Acquaintance with new techniques and techniques.
• Picking skills training optimal algorithm decisions in each specific case.

Ability to work with numbers

The following exercises will help you develop this skill:

• “Name the numbers in which...” - indicates the range and condition, for example, “Name the numbers from 5 to 50 that contain the digit 3” or “Name all two-digit numbers that contain the digit 0.” When performing this exercise, it is important to immediately work through all the mistakes made by the student. If he missed a number or said the wrong one, he starts over.
• “Maintaining progression” (range and arithmetic operations depend on age and development of counting skills). For example, “Go from 5 in steps of 3” or “Go backwards from 30 in steps of 4” - for children primary school. For those who have already learned the multiplication table, you can give tasks for multiplication and division: “Go from 2, multiplying all numbers by 3.”
• “Find the numbers from 1 to...” - children need to find and name in order all the numbers in the table.
• “Compare the numbers” - children determine which one is larger (smaller), by how much;
• “Examples” - schoolchildren are asked to solve examples in their minds, first the simplest ones (with small numbers), after working out the numbers are gradually increased. You should not introduce your child to two- or three-digit numbers if he does not know how to perform operations with numbers up to 5 perfectly.

Techniques for quickly counting numbers

Unfortunately, there is simply no single - universal - method that allows you to solve all examples equally quickly. Therefore, it is important to know and be able to put into practice several methods, from which you can then choose the most appropriate one.

Useful algorithms for solving some examples:

• To quickly subtract 7, 8 or 9 from a number, you must first subtract 10 and then add 3,2 or 1, respectively. For example: 45-9=45-10+1=36, or 36-8=36-10+2=28.
• You can also quickly multiply by 4, 8 and 16. To do this, you must first remember that 4=2*2, 8=2*2*2, 16=2*2*2*2. Then simply multiply the number by 2 several times: 6*16=6*2*2*2*2=96.
• To multiply a number by 9, it is first increased 10 times, and then the first factor is subtracted from the resulting one: 27*9=27*10-27=243. This technique will allow you to very quickly find the result of multiplying by 9, if you do not use a calculator.
• When multiplying by 2, it is more convenient to round non-round numbers, and then subtract or add (depending on which direction you rounded) the product of the remaining or missing number by 2: 132*2=130*2+2*2=264, or 138* 2=140*2-2*2=276.
• Similarly, numbers are divided by 2: 156/2=150/2+6/2=78, or 156/2=160/2-4/2=78.
• To multiply by 5, the number is divided by 2 and then increased by 10 times (the operation can be done the other way around): 27*5=27/2*10 or 27*10/2=135.
• Similar actions are performed when multiplying by 25: first divide by 4, and then increase by 100 times (simply add two zeros): 16*25=16/4*100=400. Of course, it is more convenient to use this method when the first factor is divisible by 4 without a remainder. Determining whether a number is divisible by 4 without a remainder is not difficult (non-tabular cases): a number consisting of its last two digits must be divisible by 4. For example, the number 124 is divisible by 4 (24/4=6), but 526 is not (26 is not divisible by 4 without a remainder).

And another way to multiply by multi-digit number to a single digit - you need to multiply the bit terms by the second factor and add the results. For example, 424*5=400*5+20*5+4*5=2000+100+20=2120.

In order not to make mistakes in calculations, it is important to be able to predict the future result, and several statements will help here:

• When multiplying single-digit numbers, the result does not exceed 81: 9*9=81.
• Likewise, 99*99=9801, so the result of multiplication is double digit numbers should not be greater than this number, and when increasing three-digit numbers, the maximum number is 998001.

Practicing mental arithmetic skills

The above algorithms are the basis for developing mental counting skills. Learn to count complex examples It is possible only with regular training, bringing the use of the skill to automaticity.

The effectiveness of work in this direction can be increased if during classes:

1. Create a game situation , transforming the ordinary educational process into an interesting and unusual process.
2. Keep your child engaged interesting material permanent shift activities.
3. Create a spirit of competition – the awareness that someone can do better will make you strive for new achievements; such classes will be more effective than memorizing “alone.”
4. Record personal achievements , set new goals to achieve new heights.

The ability to concentrate on solving a problem in any situation (even when others are in the way) also contributes to the development of counting skills (and not only). You can train this ability by solving examples with music on or while in a noisy company.

To prevent your child from becoming bored, it is important to learn how to deal with this feeling. Psychologists recommend using any action for this: for example, looking at what is happening outside the window, or observing the movement of the clock hands. If a child learns to cope with boredom and direct his energy in the right direction, then in class he will be able to absorb a greater amount of information, which will have a positive impact on his academic performance. .

Why count in your head when you can solve any arithmetic problem on a calculator. Modern medicine and psychology prove that mental arithmetic is a workout for gray cells. Performing such gymnastics is necessary for the development of memory and mathematical abilities.

There are many techniques for simplifying mental calculations. Everyone who has seen Bogdanov-Belsky’s famous painting “Oral Abacus” is always surprised - how do peasant children solve such a difficult problem as dividing the sum of five numbers that must first be squared?

It turns out that these children are students of the famous mathematics teacher Sergei Aleksandrovich Rachitsky (he is also depicted in the picture). These are not child prodigies - students primary classes village school of the 19th century. But they all already know how to simplify arithmetic calculations and have learned the multiplication table! Therefore, these kids are quite capable of solving such a problem!

Secrets of mental counting

There are mental counting techniques - simple algorithms that it is desirable to bring to automation. After mastery simple techniques You can move on to mastering more complex ones.

Add numbers 7,8,9

To simplify calculations, the numbers 7,8,9 must first be rounded to 10 and then subtracted. For example, to add 9 to a two-digit number, you must first add 10 and then subtract 1, etc.

Examples :

Add two-digit numbers quickly

If the last digit of a two-digit number is greater than five, round it up. We perform the addition and subtract the “addition” from the resulting amount.

Examples :

54+39=54+40-1=93

26+38=26+40-2=64

If the last digit of a two-digit number is less than five, then add by digits: first add tens, then add ones.

Example :

57+32=57+30+2=89

If you swap the terms, you can first round the number 57 to 60, and then subtract 3 from the total:

32+57=32+60-3=89

Adding three-digit numbers in your head

Fast counting and addition of three-digit numbers - is it possible? Yes. To do this, you need to parse three-digit numbers into hundreds, tens, units and add them one by one.

Example :

249+533=(200+500)+(40+30)+(9+3)=782

Features of subtraction: reduction to round numbers

We round the subtracted ones to 10, to 100. If you need to subtract a two-digit number, you need to round it to 100, subtract it, and then add the correction to the remainder. This is true if the correction is small.

Examples :

576-88=576-100+12=488

Subtract three-digit numbers in your head

If at one time the composition of numbers from 1 to 10 was well mastered, then subtraction can be done in parts and in the indicated order: hundreds, tens, units.

Example :

843-596=843-500-90-6=343-90-6=253-6=247

Multiply and divide

Instantly multiply and divide in your head? This is possible, but you can’t do it without knowing the multiplication tables. - this is the golden key to quick mental arithmetic! It is used in both multiplication and division. Let us remember that in primary school village school in the pre-revolutionary Smolensk province (the painting “Oral Calculation”), children knew the continuation of the multiplication table - from 11 to 19!

Although, in my opinion, it is enough to know the table from 1 to 10 to be able to multiply larger numbers. For example:

15*16=15*10+(10*6+5*6)=150+60+30=240

Multiply and divide by 4, 6, 8, 9

Having mastered the multiplication table by 2 and 3 to the point of automaticity, making other calculations will be as easy as shelling pears.

To multiply and divide two- and three-digit numbers we use simple techniques:

multiply by 4 is multiplied by 2 twice;

multiply by 6 - this means multiply by 2, and then by 3;

multiply by 8 is multiplied by 2 three times;

Multiplying by 9 is multiplying by 3 twice.

For example :

37*4=(37*2)*2=74*2=148;

412*6=(412*2) 3=824 3=2472

Likewise:

divided by 4 is divided by 2 twice;

to divide by 6 is to first divide by 2 and then by 3;

divided by 8 is divided by 2 three times;

dividing by 9 is dividing by 3 twice.

For example :

412:4=(412:2):2=206:2=103

312:6=(312:2):3=156:3=52

How to multiply and divide by 5

The number 5 is half of 10 (10:2). Therefore, we first multiply by 10, then divide the result in half.

Example :

326*5=(326*10):2=3260:2=1630

More simpler rule division by 5. First multiply by 2, and then divide the result by 10.

326:5=(326·2):10=652:10=65.2.

Multiply by 9

To multiply a number by 9, it is not necessary to multiply it twice by 3. It is enough to multiply it by 10 and subtract the multiplied number from the resulting number. Let's compare which is faster:

37*9=(37*3)*3=111*3=333

37*9=37*10 - 37=370-37=333

Also, particular patterns have long been noticed that significantly simplify the multiplication of two-digit numbers by 11 or 101. Thus, when multiplied by 11, the two-digit number seems to move apart. The numbers that make it up remain at the edges, and their sum is in the center. For example: 24*11=264. When multiplying by 101, it is enough to add the same to the two-digit number. 24*101= 2424. The simplicity and logic of such examples is admirable. Such problems occur very rarely - these are entertaining examples, so-called little tricks.

Counting on fingers

Today you can still find many advocates of “finger gymnastics” and the method of mental counting on fingers. We are convinced that learning to add and subtract by bending and unbending our fingers is very visual and convenient. The range of such calculations is very limited. As soon as the calculations go beyond the scope of one operation, difficulties arise: you need to master the next technique. And it’s somehow undignified to bend your fingers in the era of iPhones.

For example, in defense of the “finger” method, the technique of multiplying by 9 is cited. The trick of the technique is as follows:

• To multiply any number within the first ten by 9, you need to turn your palms towards you.
• Counting from left to right, bend the finger corresponding to the number being multiplied. For example, to multiply 5 by 9, you need to bend the little finger on your left hand.
• The remaining number of fingers on the left will correspond to tens, on the right - to ones. In our example - 4 fingers on the left and 5 on the right. Answer: 45.

Yes, indeed, the solution is quick and clear! But this is from the realm of tricks. The rule only applies when multiplying by 9. Isn’t it easier to learn the multiplication table to multiply 5 by 9? This trick will be forgotten, but a well-learned multiplication table will remain forever.

There are also many similar techniques using fingers for some single mathematical operations, but this is relevant while you are using it and is immediately forgotten when you stop using it. Therefore, it is better to learn standard algorithms that will remain for life.

Oral counting on a machine

First, you need to have a good knowledge of the composition of numbers and the multiplication table.

Secondly, you need to remember the techniques for simplifying calculations. As it turned out, there are not so many such mathematical algorithms.

Thirdly, in order for the technique to turn into a convenient skill, you must constantly conduct short “brainstorming” sessions - practice mental calculations using one or another algorithm.

Training should be short: solve 3-4 examples in your head using the same technique, then move on to the next one. We must strive to use every free minute - both usefully and not boringly. Thanks to simple training, all calculations will eventually be performed at lightning speed and without errors. This will be very useful in life and will help out in difficult situations.

Why do I call mine easy way and even surprisingly light? Yes, simply because I have not yet come across a simpler and more reliable way of teaching kids to count. You will soon see this for yourself if you use it to educate your child. For a child, this will be just a game, and all that is required from parents is to devote a few minutes a day to this game, and if you follow my recommendations, sooner or later your child will definitely start counting in a race with you. But is this possible if the child is only three or four years old? It turns out that it is quite possible. In any case, I have been doing this successfully for over ten years.

I outline the entire learning process further in great detail, with a detailed description of each educational game, so that any mother can repeat it with her child. And, in addition, on the Internet on my website “Seven Steps to a Book,” I posted video recordings of fragments of my classes with children to make these lessons even more accessible for playback.

First, a few introductory words.

The first question that some parents have is: is it worth starting to teach your child arithmetic before school?

I believe that a child should be taught when he shows interest in the subject of study, and not after this interest has faded away. And children show interest in counting and counting early; it only needs to be slightly nourished and the games imperceptibly made more complex day by day. If for some reason your child is indifferent to counting objects, do not say to yourself: “He has no inclination for mathematics, I was also behind in mathematics at school.” Try to awaken this interest in him. Just include in his educational games what you have missed so far: counting toys, buttons on a shirt, steps when walking, etc.

The second question: what is the best way to teach a child?

You will get the answer to this question by reading here the full description of my teaching methodology mental arithmetic.

In the meantime, I want to warn you against using some teaching methods that do not benefit the child.

“To add 3 to 2, you must first add 1 to 2, you get 3, then add another 1 to 3, you get 4, and finally add another 1 to 4, the result is 5.” ; “- To subtract 3 from 5, you must first subtract 1, leaving 4, then subtract 1 more from 4, leaving 3, and finally subtract 1 more from 3, resulting in 2.”

This unfortunately common method develops and reinforces the habit of slow counting and does not stimulate the child’s mental development. After all, counting means adding and subtracting in whole numerical groups at once, and not adding and subtracting one by one, and even by counting fingers or sticks. Why is this method, which is not useful for a child, so widespread? I think because it’s easier for the teacher. I hope that some teachers, having become familiar with my methodology, will abandon it.

Don't start teaching your child to count with sticks or fingers and make sure that he doesn't start using them later on the advice of an older sister or brother. It's easy to learn to count on your fingers, but difficult to unlearn. While the child is counting on his fingers, the memory mechanism is not involved; the results of addition and subtraction in whole number groups are not stored in memory.

And finally, do not under any circumstances use the one that appears in last years Line counting method:

“To add 3 to 2, you need to take a ruler, find the number 2 on it, count from it to the right 3 times in centimeters and read the result 5 on the ruler”;

“To subtract 3 from 5, you need to take a ruler, find the number 5 on it, count from it to the left 3 times in centimeters and read the result 2 on the ruler.”

This method of counting, using such a primitive “calculator” as a ruler, seems to have been deliberately invented in order to wean a child from thinking and remembering. Instead of teaching how to count like this, it’s better not to teach at all, but to immediately show how to use a calculator. After all, this method, just like a calculator, eliminates memory training and inhibits the child’s mental development.

At the first stage of learning mental arithmetic, it is necessary to teach the child to count within ten. We need to help him firmly remember the results of all variants of adding and subtracting numbers within ten, just as we adults remember them.

At the second stage of education, preschoolers master the basic methods of adding and subtracting two-digit numbers in their heads. The main thing now is not automatic retrieval from memory ready-made solutions, but understanding and remembering methods of addition and subtraction in subsequent tens.

Both at the first and second stages, learning mental arithmetic occurs using elements of play and competition. With the help of educational games built in a certain sequence, not formal memorization is achieved, but conscious memorization using the child’s visual and tactile memory, followed by consolidation in memory of each learned step.

Why do I teach mental arithmetic? Because only mental arithmetic develops the child’s memory, intelligence and what we call ingenuity. And this is exactly what he will need in the future. adult life. And writing “examples” with long thinking and calculating the answer on the fingers of a preschooler does nothing but harm, because discourages you from thinking quickly. He will solve examples later, at school, practicing the accuracy of the design. And intelligence needs to be developed in early age, which is facilitated by oral counting.

Even before starting to teach a child addition and subtraction, parents should teach him to count objects in pictures and in reality, count steps on a ladder, steps while walking. By the beginning of learning mental counting, a child should be able to count at least five toys, fish, birds, or ladybugs and at the same time master the concepts of “more” and “less.” But all these various objects and creatures should not be used in the future for teaching addition and subtraction. Learning mental arithmetic should begin with addition and subtraction of the same homogeneous objects, forming a certain configuration for each number. This will allow the child to use the visual and tactile memory when memorizing the results of addition and subtraction in whole number groups (see video file 056). As a tool for teaching mental counting, I used a set of small counting cubes in a counting box ( detailed description- Further). And to the fish, birds, dolls, ladybugs and other objects and creatures, children will return later, when solving arithmetic problems. But by this time, adding and subtracting any numbers in the mind will no longer be difficult for them.

For ease of presentation, I divided the first stage of training (counting within the first ten) into 40 lessons, and the second stage of training (counting within the next tens) into another 10-15 lessons. Don't let it scare you a large number of lessons. The breakdown of the entire training course into lessons is approximate; with prepared children, I sometimes go through 2-3 lessons in one lesson, and it is quite possible that your child will not need so many lessons. In addition, these classes can be called lessons only conditionally, because each lasts only 10-20 minutes. They can also be combined with reading lessons. It is advisable to study twice a week, and it is enough to spend 5-7 minutes on homework on other days. Not every child needs the very first lesson; it is designed only for children who do not yet know the number 1 and, looking at two objects, cannot say how many there are without first counting with their finger. Their training must begin practically “from scratch.” More prepared children can start immediately from the second, and some - from the third or fourth lesson.

I conduct classes with three children at a time, no more, in order to keep the attention of each of them and not let them get bored. When the level of preparation of children is slightly different, you have to work with them on different tasks one by one, all the time switching from one child to another. At the initial lessons, the presence of parents is desirable so that they understand the essence of the methodology and correctly perform simple and short daily homework with their children. But the parents must be placed so that the children forget about their presence. Parents should not interfere or discipline their children, even if they are naughty or distracted.

Classes with children in mental counting in a small group can begin from approximately the age of three, if they already know how to count objects with their fingers, at least up to five. And with own child Parents can easily begin elementary lessons using this method from the age of two.

Initial lessons of the first stage. Learning to count within five

To conduct initial lessons, you will need five cards with the numbers 1, 2, 3, 4, 5 and five cubes with an edge size of approximately 1.5-2 cm, installed in a box. For cubes, I use “knowledge cubes” or “learning bricks” sold in educational game stores, 36 cubes per box. For the entire training course you will need three such boxes, i.e. 108 cubes. For initial lessons I take five cubes, the rest will be needed later. If you are unable to find ready-made cubes, it will not be difficult to make them yourself. To do this, you just need to print out a drawing on thick paper, 200-250 g/m2, and then cut out cube blanks from it, glue them together in accordance with the instructions, fill them with any filler, for example, some kind of cereal, and cover the outside with tape. It is also necessary to make a box to place these five cubes in a row. Gluing it together is just as easy from a pattern printed on thick paper and cut out. At the bottom of the box, five cells are drawn according to the size of the cubes; the cubes should fit in it freely.

You already understand that teaching numeracy is initial stage will be produced using five cubes and a box with five cells for them. In this regard, the question arises: why is the method of learning with the help of five counting cubes and a box with five cells better than learning with the help of five fingers? Mainly because the teacher can cover the box with his palm from time to time or remove it, due to which the cubes and empty cells located in it are very quickly imprinted in the child’s memory. But the child’s fingers always remain with him, he can see or feel them, and there is simply no need for memorization; the memory mechanism is not stimulated.

You should also not try to replace the box of cubes with counting sticks, other counting objects, or cubes that are not lined up in the box. Unlike cubes lined up in a box, these objects are arranged randomly, do not form a permanent configuration and therefore are not stored in memory as a memorable picture.

Lesson #1

Before the start of the lesson, find out how many cubes the child can identify at the same time, without counting them one by one with his finger. Usually, by the age of three, children can tell immediately, without counting, how many cubes are in a box, if their number does not exceed two or three, and only a few of them see four at once. But there are children who can only name one object so far. In order to say that they see two objects, they must count them by pointing with their finger. The first lesson is intended for such children. The others will join them later. To determine how many cubes the child sees at once, alternately place different numbers of cubes in the box and ask: “How many cubes are in the box? Don’t count, tell me right away. Well done! And now? And now? That’s right, well done!” Children can sit or stand at the table. Place the box with cubes on the table next to the child parallel to the edge of the table.

To complete the tasks of the first lesson, leave the children who can only identify one cube so far. Play with them one by one.

1. Game "Putting numbers to dice" with two dice.
   Place a card with number 1 and a card with number 2 on the table. Place a box on the table and put one cube into it. Ask your child how many cubes are in the box. After he answers “one,” show and tell him the number 1 and ask him to put it next to the box. Add a second cube to the box and ask him to count how many cubes are in the box now. Let him, if he wants, count the cubes with his finger. After the child says that there are already two cubes in the box, show him and call the number 2 and ask him to remove the number 1 from the box and put the number 2 in its place. Repeat this game several times. Very soon the child will remember what two cubes look like and will begin to name this number immediately, without counting. At the same time, he will remember the numbers 1 and 2 and will move the number corresponding to the number of cubes in it towards the box.
2. Game "Dwarves in a house" with two dice.
   Tell your child that you will now play the game “Gnomes in the House” with him. The box is a make-believe house, the cells in it are rooms, and the cubes are the gnomes who live in them. Place one cube on the first square to the left of the child and say: “One gnome came to the house.” Then ask: “And if another one comes to him, how many gnomes will be in the house?” If the child finds it difficult to answer, place the second cube on the table next to the house. After the child says that now there will be two gnomes in the house, allow him to place the second gnome next to the first on the second square. Then ask: “And if now one gnome leaves, how many gnomes will remain in the house?” This time your question will not cause difficulty and the child will answer: “One will remain.”

Then make the game more difficult. Say: “Now let’s put a roof on the house.” Cover the box with your palm and repeat the game. Every time the child says how many gnomes there are in the house after one came, or how many of them are left in it after one left, remove the palm roof and allow the child to add or remove the cube himself and make sure his answer is correct. . This helps connect not only the child’s visual, but also tactile memory. You always need to remove the last cube, i.e. second from the left.

Play games 1 and 2 alternately with all the children in the group. Tell the parents present at the lesson that they should play these games with their children once a day every day at home, unless the children themselves ask for more.

Comment on the article "Amazing easy way teaching a child mental arithmetic"

Doesn't understand math. How to teach a child not to be afraid of tests? Good afternoon. I am not an experienced mother, I have experience with Mathematics in How to teach a child mental arithmetic. Presentation "Mathematics for little ones, counting from 1 to 10 with adding one": methodological...

Discussion

My child was born with hypoxia, and there were some other diagnoses that were not critical for me at that time.
This resulted in speech therapy problems, but they were quickly resolved with a speech therapist.
Hyperactivity immediately became visible, but it was compensated for by the age of 11.
But concentration and Mathematics became a problem, and in the lower grades it was also 3-4-5, but in the fifth grade it was 2-3-4.
There was always a math tutor. I changed because I thought it was the tutor who didn’t explain it well!
But in November, in the 5th grade, I brought my child to Moscow to a neurologist, based on recommendations, and he told us, after examination and tests, that it was attention deficit.
The purpose was stratera (but this is only by prescription), pantogam. Also mandatory classes with a Neuropsychologist and a psychologist (cognitive techniques).
You know, I can’t believe it myself, but there is a result!
Now it’s February and she’s firmly in her 4th trimester.
And the math tutor praises me for paying attention!
And the math teacher herself (otherwise she called me in September to say that she had a 2 on a test and needed to study with her daughter! How else could she study if she studied all August and September!)

12.02.2019 20:19:40, Veronica-strawberry

Mental arithmetic - how to teach? Once you've mastered counting well within ten, you won't have any problems with counting when you start counting beyond ten. A surprisingly easy way to teach your child mental math. Beginning Lessons first stage.

Discussion

1. Work with him yourself in addition to school + other specialists.
2. Completely move away from the school methodology from the specific to the general; this “doesn’t work” for our children; they “can’t see the forest for the bushes.” The approach should be “from the general to the specific”, i.e. First you give a general vision, without going into details, then you disassemble one aspect and repeat it ad nauseam. For example:
We say - speech - parts of speech - independent (nominal) and service-independent: noun, adjective, numeral, adverb, verb, participle and gerund; auxiliary: preposition, conjunction, particle + special part of speech - interjection. Noun - proper, adverb. etc. We always start with the simplest: We speak - speech. Until you learn it, don’t move on to parts of speech. Then, when everything is mastered, go over the entire tree 100,500 times every day until the child’s teeth begin to bounce off. Next comes the complication of the task, we now rely on some familiar subsection and dance from it. But we regularly repeat the entire design.
3. In mathematics, we count on our fingers for a long time and painfully. Then, when the counting becomes error-free and fast, we cover our fingers with a newspaper or towel, count by touch, then close our eyes and imagine the fingers in our minds, then we simply count in our minds.
4. We apply available types of differentiation (or selection). For example, number digits: ones are green, tens are yellow, hundreds are red. You can use tactile or sound - it depends on the child’s capabilities.
5. Work until you sweat, repeat until your tongue becomes calloused. No "hug and cry"! Our children have been given everything, the approach just needs to be DIFFERENT. And there the integrals with derivatives will also obey.

Where do you study?
Mine has the same thing, it’s also complicated by the fact that the beginning ends, there will be no continuation, I can’t imagine where to go(

Doesn't understand math. Education, development. Child from 7 to 10. I don’t understand what’s going on with math and how to help the child? My son is 11 years old and studies in the 6th grade. How to teach your child mental arithmetic. Print version.

Discussion

Hello, I would advise you to explain it more or less easily, let’s say the following example:
576-78=?
Please explain that I cannot subtract 78 from 76.
To 6 you need to add 10, that is, we take one ten.
Subtract 8 from 16 and get 8
So 8 is in the place of ones
Since we borrowed one ten from 70, it means not 70 but 60
Further:
From 560 I subtract 70 = 490, and we also remember that in place of units 8 we get 498.
I hope you improve your math!!!
Good luck.

26.12.2018 17:54:16, Kamilla Batrakanova

A tutor is needed if the child does NOT understand complex material, and the parents are NOT able to explain it. In your case, your daughter (having 3 explanations of the same thing) will be completely confused.
Try downloading flash games to your tablet or phone. Now there are many cool applications where you can improve mathematics, mental calculation, solve logic problems and generally practice spatial thinking in a playful way. Observe which tasks cause difficulties for your daughter, so you can highlight problem areas that are worth going over again.

08/14/2018 09:42:26, ​​Epsona

How to teach your child mental arithmetic. Presentation "Mathematics for little ones, counting from 1 to 10 with adding one": teaching material for educators. How to teach a child mental arithmetic and retain the skill of counting quickly for life?

Discussion

Peterson has successful translation schemes - look in the textbooks for grades 3 and 4. Or arrange it yourself - units of measurement in a row, from largest to smallest: 1t - 1c - 1kg - 1g. Between them at the bottom of the arc, under the arcs the ratio is (10, 100, 1000). And the arrows: to the right - we multiply (when converting to smaller ones), to the left - we divide (to large ones). Let's say, convert 35 tons into grams - 35 * 10 * 100 * 1000 = 35 * 1000000 = 35000000g.

I think the basic concept needs to be worked out very well. It is important for me not to go through the topic and forget, but for the child to understand and feel it.
I measured different things with the children using different MEASURES - for example, a room - with steps, rulers, briefcases, boa constrictors...
Then the area is also measured - a table, for example, with squares of paper: simply - how many of them will fit there, with notebooks. And if you take smaller squares, it will be more accurate, but longer.
Then we moved directly to calculations. But it turns out you can not lay out the measurements by hand each time, but divide it arithmetically... The room is the length of 3 boa constrictors, and there is so much in the briefcases (because one boa constrictor can fit four briefcases in length), and in the pencil cases so much ( because the briefcase is equal in length to two pencil cases).
Then, as one of the types of measurements, they took meters, centimeters, hectares, square values

There, mental arithmetic is the basis of first grade. Sorry, Len, for intruding, but the problem is the same, we are also suffering, but my some I know that I am not a mathematician, and I wanted to make his “first-class” life easier - to understand (or learn) the composition of a number. As soon as you haven't played it, you can't remember it by heart...

Discussion

To do this, you need to memorize the composition of numbers up to 10 very well. This knowledge is vital when solving examples of addition and subtraction. In order to remember the composition of a number well, you just need to repeat the pairs that make up this number many times. There is an application for iPad and iPhone that makes this process easier for the child, turning it into a game with attractive features and sounds. The application has already been tested by many users for several years. This application, despite its simplicity, is very effective, experts in Singapore respond very well to it, and many educational institutions around the world use it in their practice. Especially for visitors to the site, we are giving 5 gift promotional codes for this application:
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You can download the Composition of Numbers to 10 application in the App Store:

Discussion

Example 3+4 will recalculate, and if you ask how much 3 candies and 4 more candies will be, the answer will immediately be seven.
By the way, in our schools we teach counting with fingers.

At the age of 4, my son counted using the composition of numbers. Now he is counting by counting units. I don’t understand what the connection is with future difficulties with algebra. In Mikulina’s notebook “Fairytale Numbers” (one of the authors of the textbook on mathematics ED), Mishenka solves with the speed of a pig squeal all examples with symbols in systems linear equations. What kind of tragedy is that? For a programmer, the idea of ​​moving along a number series is even preferable; many problems are solved this way. In exam problems that need to be solved in integers, this enumeration method is also convenient. In general, it’s more convenient for me to create an algorithm for solving a system of equations and put all this mess into a computer than to worry about numbers. I really don’t like the fact that huge abacus books have disappeared from school classrooms for first-graders; Perelman has written well about abacus; at the age of seven I figured it out myself from his book and enjoyed playing with the abacus. For centuries they counted on these knuckles, my mother was a virtuoso, the knuckles just flew, she didn’t need any adding machine. On fingers, knuckles, when counting in the mind, numbers are seen somehow differently, some patterns are noticed differently. Even though the children will try everything while they are small, they are still very, very far from real mathematics with proofs.

IN Lately In Russia, a new method for developing intelligence is beginning to gain popularity in our country. Instead of the usual chess sections, parents send their children to mental arithmetic schools. How kids are taught to count in their heads, how much such classes cost and what experts say about them - in the material "AiF-Volgograd".

What is mental arithmetic?

Mental arithmetic is a Japanese technique for developing a child’s intellectual abilities through calculations on special soroban abacus, which is sometimes called an abacus.

“When performing actions with numbers in their minds, children imagine these abacus and in a split second they mentally add, subtract, multiply and divide any numbers - even three-digit, even six-digit,” says Natalya Chaplieva, teacher of the Volga club, where children are taught using this method.

According to her, when children are just learning all these actions, they count the numbers directly on the soroban, fingering the bones. Then they gradually move from counting to a “mental map” - a picture depicting them. At this stage of learning, they stop touching the abacus and begin to imagine in their minds how they move the bones on it. Then, the children stop using the mental map and begin to completely visualize the soroban for themselves.

Abacus soroban. Photo: AiF/ Evgeniy Strokan

“We recruit children from 4 to 12 years old into groups. At this age, the brain is most plastic; the child absorbs information like a sponge, and therefore easily masters learning methods. It’s much more difficult for an adult to learn mental arithmetic,” says Ekaterina Grigorieva, teacher of the mental arithmetic club.

How much does it cost?

The abacus has a rectangular frame that contains 23-31 spokes, each of which has 5 bones strung on them, separated by a transverse crossbar. Above it there is one domino, which denotes “five”, and below it there are 4 dominoes, denoting ones.

You need to move the bones with only two fingers - the thumb and forefinger. The counting on the soroban starts from the very first knitting needle on the right. It stands for units. The knitting needle to the left of it is tens, the next one is hundreds, etc.

Soroban is not sold in regular stores. You can buy such accounts on the Internet. Depending on the number of knitting needles and material, the price of soroban can range from 170 to 1,000 rubles.

At the first stage, children work with abacus. Photo: AiF/ Evgeniy Strokan

If you don’t want to spend money on bills at all, you can download a free application for your phone - an online simulator that simulates an abacus.

Mental arithmetic classes for children in Volgograd cost about 500-600 rubles per hour. You can buy a subscription for 8 classes for 4,000 rubles and 16 classes for 7,200 rubles. Classes are held 2 times a week. The Volga school gives out abacus, mental maps and notebooks to children free of charge, and students can take them home. At the end of the course, the child can keep the soroban as a souvenir.

Children have to learn mental arithmetic for about 1-2 years, depending on their abilities.

Assignments for students. Photo: AiF/ Evgeniy Strokan

If you don’t have money for classes at a special school, then you can try to look for video lessons on YouTube. True, some of them are posted on the website by organizations providing lessons for money for the purpose of self-promotion. Their videos are very short - 3 minutes long. With their help you can learn the basics of mental arithmetic, but nothing more.

What do experts say about this?

Teachers who conduct mental arithmetic classes are confident that the training is worth the money spent on it.

“Mental arithmetic develops well the child’s imagination, creativity, thinking, memory, fine motor skills, attentiveness, perseverance. Classes are aimed at ensuring that the child develops both hemispheres at the same time, which is very important, because the traditional preparation of a child for school only develops right hemisphere brain," says teacher Natalya Chaplieva.

Psychologist Natalya Oreshkina believes that in the case of children 4-5 years old, mental arithmetic classes will be effective only if they take place in a playful way.

“Children of this age generally have difficulty concentrating for such a time, unless we are talking about watching a cartoon,” says the expert. - But if the lesson is structured in a playful way, if children practice abacus and color something, then they will learn knowledge while being in their natural environment - in a game. In addition, it should not be difficult for children; they should not exceed the permissible load level. For example, for 4-year-olds, classes should last no more than 30 minutes. I can say that mental arithmetic for children is very interesting. But if a child lags behind his peers in some way, then such activities will be too difficult for him. If a child does not have an internal resource for activities, then it will be a waste of time, effort and money.”

Many parents probably dream that their baby will grow up special and certainly become something that they can be proud of. But if some fathers and mothers only boast about the abilities of their children, others take them to special schools that help develop the inclinations given by nature.

Is it possible to raise a child to be a genius? If in earlier times the answer to such a question was clear and required talent and amazing abilities, then today the task has become much easier. For example, in order for a child to show remarkable knowledge in mathematics and count as quickly and correctly as a calculator, an unusual program is offered that will teach the child mathematics. And it is called “mental arithmetic”. What is this program and what advantages does it have?

Popularity of the technique

Since 1993, mental arithmetic has been used to teach children in 52 countries, from Canada to the UK. Some of them recommend the technique for inclusion in the school curriculum.

Mental arithmetic is most widespread in the countries of the Middle East, as well as in China, Australia, Thailand, Austria, the USA and Canada. Specialized organizations are beginning to appear in Kazakhstan, Kyrgyzstan and Russia.

Mental arithmetic is one of the youngest and fastest growing methods used for children's education. Thanks to this technique, you can easily develop a child’s mental abilities, which are primarily mathematically oriented. Thanks to children mastering the technique of mental calculation, any math problem turns into a simple and fast computing process for them.

History of origin

The method of mental calculation has ancient roots. And this despite the fact that it was developed relatively recently by a scientist from Turkey, Halit Shen. What did he use for his mental counting system? Abacus, which was created in China 5 thousand years ago. This item represents an abacus, which made a huge contribution to the development of all world arithmetic. After its invention, the abacus began its gradual spread throughout the world. In the 16th century, it came from China to Japan. For four hundred years, the inhabitants of the Country rising sun not only successfully used such abacus, but also carefully worked on it, trying to improve such a necessary object for performing arithmetic operations. And they succeeded. The Japanese created the soroban abacus, which is still used to this day to teach children in elementary school.

Throughout the history of human development, mathematical science has been improved. And today she can offer us a huge number of her achievements. But despite this, scientists believe that using an abacus is more beneficial in teaching children accurate counting.

The benefits of mental arithmetic

It is believed that each of the hemispheres of the human brain is responsible for its own directions. So, the right one allows you to develop creativity, imaginative perception and thinking. The left is responsible for logical thinking.

The activity of the hemispheres is activated at the moment when a person begins to work with his hands. If the right one is active, then the left hemisphere begins to work. And vice versa. A person working with his left hand helps to activate the work of the right hemisphere.

The goal of menara is to force the whole brain to take part in the educational process. How to achieve such results? This is possible by performing mathematical operations on the abacus with both hands. Ultimately, menard contributes to the development of quick counting, as well as the development and improvement of analytical skills.

Scientists compared the calculator with an abacus and came to the clear conclusion that the first one relaxes brain activity. Abacus, on the contrary, sharpens and trains the hemispheres.

When should you start learning mental arithmetic? Reviews from adherents of this technique claim that it is best to master this method between the ages of four and twelve years. And only in some cases the period can be extended for another four years. This is the time when rapid brain development occurs. AND this fact is a wonderful message to instill in a child basic skills, to study foreign languages, develop thinking, master the game musical instruments and martial arts.

The essence of the mental technique

The entire program for mastering mental arithmetic is built on the sequential passage of two stages. At the first of them, one becomes familiar with and masters the technique of performing arithmetic operations using bones, during which two hands are used simultaneously. Thanks to this, both the left and right hemispheres are involved in the process. This allows you to achieve the fastest possible learning and execution of arithmetic operations. The child uses an abacus in his work. This subject allows him to completely freely subtract and multiply, add and divide, and calculate square and cube roots.

During the second stage, students learn mental counting, which is done in the mind. The child stops constantly becoming attached to the abacus, which also stimulates his imagination. The left hemispheres of children perceive numbers, and the right hemispheres perceive the image of dominoes. This is what the mental counting technique is based on. The brain begins to work with an imaginary abacus, while perceiving numbers in the form of pictures. Performing mathematical calculations is associated with the movement of the bones.

Learning quick mental arithmetic is a very interesting and exciting process. It is appreciated by hundreds of thousands of people and received a huge number of positive reviews.

Abacus

What is this mysterious and ancient adding machine? The abacus, or mental abacus, is very reminiscent of the old Soviet “knuckles.” The principle of operation on these two devices is also very similar. What is the difference between these accounts? It lies in the number of knuckles located on the knitting needles and in ease of use.

It is worth saying that to obtain a result, the abacus will require more movements with your hands. How does this ancient object, which came to us from China, work? It is a frame into which the knitting needles are inserted. Moreover, their number may be different. There are five pieces of strung knuckles on the knitting needles.

The length of each spoke is crossed by a dividing strip. Above it there is one domino, and below it, respectively, four.

The mental counting technique involves a certain movement of a person’s fingers. Of these, only the index and thumb are used. All movements must be brought to automaticity, which is facilitated by their repeated repetition.

Interestingly, this skill can easily be lost. That is why you should not skip classes when mastering the technique.

Number arrangement

What are the basics of counting in mental arithmetic? In order to master this technique, you need to know how the number lines are located on the abacus. In his right side there are units. After that there are tens, then hundreds, then thousands, tens of thousands and so on. Each of these discharges is located on a separate spoke.

The dominoes located below the dividing bar are “1”, and those above it are “5”. For example, in order to dial the number 3 on the abacus, you will need to separate three dominoes located under the dividing bar on the knitting needle located to the right of the others. Let's look at an example with double numbers, for example, 15. To dial it on the abacus, you should raise up one domino on the tens needle and lower the one located above the top bar on the units needle.

Addition Operations

How to learn mental arithmetic? To do this, you will need to study how arithmetic operations are carried out on the abacus. Consider, for example, addition. Let's see what the sum of the numbers 22 and 13 will be equal to. First, you will need to put two dominoes on the tens and units knitting needles located at the bottom of the dividing bar. Next, let's add one more to the two dozen. The result is 30. Now let's start adding units. Let's add three more to two. The result is the number “five”, which is indicated by the knuckle at the top of the dividing bar. The result is 35. To master more complex operations You will need to carefully study special literature. After mastering the most simple examples It is recommended to practice on the abacus. This way, learning becomes as interesting as possible.

Mastering the second stage

After operations on the abacus do not cause any difficulties, you can begin to perform mental arithmetic orally. This is the next level of learning. It involves mental counting, that is, done in the mind. To do this, you will need to make a picture of an abacus for your child. The most simple option is a printout of an image of this item, which must then be pasted onto cardboard (you can take it from a shoe box). If possible, the picture should be in color. This will make it easier for the child to imagine it in his imagination.

To avoid mistakes, it is worth remembering that mental counting should be done from left to right. What needs to be done to put a two-digit number on the abacus? To do this, the child should first pick up the knuckles corresponding to tens with his left hand, and then separate the required units on a knitting needle with his right hand.

So, for a set of 6, 7, 8 and 9 you should use the “Pinch”. This process involves bringing together the index and thumb to the dividing bar and collecting the dominoes indicating the number 5, and the required number of them on the knitting needle, which is located at the bottom of the abacus. Subtracting numbers is done in a similar way. The same “Pinch” simultaneously discards “fives” and required quantity seeds at the bottom.

Goals and results of the methodology

Learning mental arithmetic allows a child to achieve unprecedented success in the field of mathematics. Children who have completed a special course can easily calculate ten-digit numbers in their heads, multiply and subtract them. But it is worth saying that this is not the main goal of such training. Counting is just a way by which a person's mental abilities develop.

Mastering mental arithmetic contributes to the following:

• activation of visual and auditory memory;
• ability to concentrate;
• improving ingenuity and intuition;
• creative thinking;
• manifestation of self-confidence and independence;
• rapid mastery of foreign languages;
• realization of abilities in the future.

In cases where menara was used to master professional approach and the specialists have achieved the goals set for them, the child easily begins to solve both simple and complex tasks mathematics. And it performs arithmetic operations for multiplication and addition even faster than a calculator.

Schools for teaching mental arithmetic

Where can you learn this unique technique? Today, to study mental arithmetic, you need to enroll in a specialized educational center. In them, specialists work with children for two to three years. In addition to the steps described above, with which you can master the technique, there are ten more steps. Moreover, students complete each of them in 2-3 months.

Each of these specialized centers develops its own training programs. However, despite this, there are also general rules which absolutely everyone adheres to. They consist in the fact that groups of students are formed depending on their age. So, there are three basic types of such groups.

These are kinder, kids and junior. Classes are conducted by experienced, highly qualified psychologists and teachers who have undergone appropriate training and have the necessary certification.

In addition to centers for teaching mental arithmetic, today there are also specialized schools that train specialists in the relevant profile. As a rule, menara teachers are people who have not only psychological and pedagogical education, but also some experience working with children. And this is very important. After all, learning mental abacus is not only about mastering skills that allow you to work with ancient abacus. In this process, the methods used in teaching practice must be taken into account. psychological characteristics in child development.