The child himself will tell you, when he needs knowledge of figures and numbers. This will be the moment when instead of one apple he wants to take two or he needs to distinguish the number of his favorite channel on the remote control button.
More often 2-3 year old children begin to master counting on their own, and the task of parents at this moment is to maintain interest in numbers.
Some parents prefer “not to take away their children’s childhood” and leave the expense to the school.
But this is the worst thing you can do for a child.
If he comes to first grade already prepared, it will be much easier for him to adapt, especially since almost all school programs are now designed for children who can read, write and count at the elementary level.
3-5 years is the age at which children are capable and can learn to count to 10 and even 100, especially if you use simple techniques.
Exercises, methods and techniques
Famous children's teacher Maria Montessori She raised little geniuses according to a special system. Under her leadership, even one-year-old children mastered the alphabet and counting. Moreover, this was knowledge at a very deep level.
Still Many kindergartens use the Maria Montessori system, based exclusively on the “carrot method”, and children who study it show brilliant success in learning to count.
The secret of the technique is that teachers talk to children as equals and try to understand their language, instead of imposing their own.
Counting sticks have not lost their popularity for many decades. They help the child understand that there are real objects behind the numbers, and it is easy to master basic manipulations with them - addition and subtraction.
Counting on fingers The good thing is that it can be used everywhere - you are walking with your baby or watching a TV show. You can “bend your fingers” at red cars or commercial breaks between cartoons. This calculating tool is always at hand.
Counters and chants help you remember the sequence of numbers. For example: “One girl has exactly two braids, and three boys have four bows to go with them,” and so on.
Folk tales and fables. There are usually three characters in them (heroes, a swan, a crayfish and a pike, three sisters), and in “Turnip” or “Teremka” the number of characters grows to five or six.
By associating each character with a number, it is also easier for the child to remember the plot of the fairy tale, so using the “mathematical-literary method” you kill two birds with one stone.
Pretend you don't know. When your child asks you to count a large number of items, say that you forgot the count and you need to deal with it together.
Don’t cause your child to panic – gently guide him to the correct answer.
Trainings on TV. Many video baby monitors in specialized programs do an excellent job of teaching children the alphabet, counting, or even a foreign language.
Program “Underwater Account” – TV channel “Carousel”
Learning to count to 10
Turn numeracy lessons into a game. This could be playing economist or salesman: “Give me six apples” or “Count out ten napkins.”
The child can use abacus and sticks during this game, make notes in a notebook. But if he is capricious and categorically refuses to perform actions related to the score, do not put pressure on him.
Repeat the numbers with your baby all the time - even when tying your shoelaces: one shoelace is tied, two shoelaces are tied, three buttons are fastened, one hat is on.
Repetition is the mother of learning. Gradually, the baby himself will begin to pronounce simple rhymes and identify them with objects.
Counting table from 1 to 10 - Umachka Internet channel
Learning to count to 100
The child’s selective memory remembers only what is interesting to the baby. If there is a humanist in the family, don’t expect to count to one hundred in the early stages; it’s better to try “letter riddles.”
The easiest way to learn counting up to 100- this is to take ten times ten. If the child knows how to count to ten well, then 21 will be 2 and then 1 (not a plus, but then - immediately explain the difference between number and addition).
Don't forget to explain what zero is and why he turns two into 20, and three into thirty. This can be one of the hardest parts of counting to one hundred. Don't scold your child if he doesn't immediately figure out what's what.
By the way, at a subconscious level, knowledge about the correct counting is still stored, and if at first the child stubbornly does not want to count to one hundred, perhaps he will do it later, already at school.
Remember that children's brains are complex!
If the child copes with the task - for example, remembers coins up to 20 - give him a “prize fund”. Gradually build up to 100 coins and let your child buy anything as a reward for learning.
Let's sum it up
Be sure to encourage your baby for correctly performed actions. If he brought the correct number of spoons to the table or correctly named the number of light bulbs in the chandelier - don’t skimp on praise or even candy.
Which, by the way, can also be given by number from 1 to 10 - let the child say at random. So gradually he will understand that the number 10 is the largest.
And remember that you yourself were little. It was just as difficult for you to understand how a five differs from a six, and why an inverted six is already a nine.
Was it difficult for you? It’s just as difficult for a child now.. Support him on the path to mastering counting, and perhaps a new Perelman or a new Marie Sklodowska-Curie will grow up in your family.
Quite often, parents are faced with the task of teaching their child to count. It may seem that there is nothing complicated in this, but for small child Sometimes it can be very difficult to learn to count. Children, as a rule, tend to remember only what is interesting to them, so adults need to try to interest the baby first, then the process of acquiring new knowledge will be much easier.
If you present arithmetic as a dry, boring activity, it will be difficult to interest your child in it
The optimal age to start teaching a child to count
The best time to start teaching children to count is when their brains are actively developing. This usually occurs before the age of 6-7 years. It is important for parents to begin developing their child’s counting skills even before entering school.
The children are already in early age As soon as they start talking, they show interest in counting. Parents need to maintain this interest with the help of special educational games.
Basic rules for teaching counting
If you want to teach your child to count, you must adhere to the following basic teaching rules:
- The amount of information a child receives. Exercises should be performed three times a day, the duration of each of which should not exceed 10 minutes. In this way, the child will not become tired of the abundance of information, and interest in new knowledge will not disappear.
- Do not repeat the material covered every day. It is better to remember it only in cases when the accumulated knowledge is required to solve more difficult tasks.
- Do not give your child too difficult tasks. You should not scold your child if he fails to achieve the desired result. Perhaps it is actually difficult for him to cope with the task. Select tasks for your child that he can solve.
- Consolidate the acquired knowledge in everyday life. More often, work with your child to count everything that is around: cars, birds on a tree, the number of plates on the table, buses on the road, etc.
- Follow the order of the steps. According to psychologists, the process of acquiring new knowledge in a child consists of three stages: the adaptation stage, the stage of understanding the information received, and memorizing the material.
The most important thing is not to rush the baby. Be patient, communicate with your baby more often, compare objects when talking, talk about numbers, provide support and help in gaining knowledge.
You can teach your child to count on a walk, where you come across remarkable interesting objects Baby teaching methods
To teach a child correct mental arithmetic, you must use the following methods:
- Fingers. This method is one of the most popular among parents. Its essence lies in counting fingers. The method helps develop the baby’s visual memory, hand motor skills, and also promotes rapid learning to count objects.
- Material for counting. Ideal for teaching your child to count examples. Ordinary toys or certain educational sets are suitable as materials. When choosing such a set, give preference to the brighter and more colorful ones, make sure that they are made from environmentally friendly and safe materials.
- Educational children's books (we recommend reading:). Currently, stores offer a huge range of interesting books for the development of preschool children. Try to choose a textbook written in simple and understandable language for your child, so that in your absence he can continue to learn to count objects on his own.
Make sure your child's brain doesn't overload during activities. Too much information can tire a child and will not bring the desired result. At the beginning of classes, teach him to count examples up to 10, spend no more than 10-15 minutes on this, in the future you can work with your baby for up to 30 minutes. During each new lesson, review previously covered material.
Learning to count to 10
You can start teaching your child how to count to 10 as early as two or three years old. First, he must learn to count to 5, and then to 10. At this age, kids already know that they have two legs and that means they need to put on two socks. At 3-4 years old, you can give your child more complex tasks. The most important thing is that the child begins to understand the meaning of the words “equally”, “more”, “less”. You can give him simple examples: “Masha had three tangerines, and Katya had two. Which girl has more fruit and which girl has less?”
To make it easier for your child to master counting to 10, invite him to count his fingers. Give the baby the task of adding 2+1, let him raise one finger on his left hand and two on his right, and then count the total number of fingers raised.
The same manipulations can be carried out so that the baby learns to subtract: the child bends several fingers, and then counts the number of those remaining in the raised position. The same can be done with various objects: pencils, pens, etc.
Learning to count to 20
When your child learns to count to 10, move on to learning to count to 20. Cars on the streets are a good material for counting. On the way to kindergarten, you can offer to count their number. When your child has mastered the lesson well, try counting the cars in reverse order.
A child may find it quite difficult to add numbers from 1 to 20, so lessons should be conducted with a playful focus. For example, you can say: eight decided to add three to itself. She first took a two from a three and turned into a ten. Three became one. How much will it be if eight adds three to itself?
Your baby's brain needs daily exercise. If a child begins to practice mental arithmetic at an early age, he will have well-developed mental abilities.
Mental arithmetic training
When your child turns 5 years old, try to wean him from using counting materials, including your fingers. Let him learn mental arithmetic. If at first this helped him a lot, then in the future it will only interfere with the process of acquiring new knowledge.
After five years, children must be taught to add and subtract numbers up to 10 on an automatic machine, i.e. You need to ensure that the baby remembers the results of calculations. To achieve these goals, the use of mathematical chains helps well. Do not forget that the process of acquiring knowledge must maintain a playful nature. For large numbers there are separate techniques.
Learning to count in 1st grade
For every child there comes an important moment in life - he goes to 1st grade. This is the time when the basis of all knowledge about the future is formed. In the first grade, a child’s activity changes, but the ability to learn everything through games does not disappear. The child takes on the role of a student and develops self-organization skills. He needs to master the skills of planning his work, monitoring and evaluating his actions, communicating with peers and the teacher.
First-graders pay a lot of attention to oral work. To teach first-graders mental arithmetic and consolidate previously acquired knowledge, teachers use some methods with a playful twist:
- Zaitsev's cube method. It is a very common gaming method, the purpose of which is to quickly learn counting. Kids gain knowledge with great interest using cubes. The essence of the method is to use several tables, with the help of which children learn to add and subtract numbers in their heads much easier and faster. This method can also be used by parents during developmental activities with their child in preschool age. The set of Zaitsev's cubes includes a teaching aid and a CD with songs, which makes the process of acquiring new knowledge very interesting and simple.
- Glen Doman method. This method involves children learning to count using special cards with dots on them. The method allows you to develop the baby’s visual memory and the ability to count the number of objects.
Teachers may also use other methods of teaching numeracy in their practice, so it is advisable for parents to clarify in advance how the learning process will take place at school. To achieve high results, experts advise not to use different teaching methods - this may not have the best effect on the child.
The Doman technique can also be used at an early age, but during preparation for school it is especially effective Learning to count in 2nd grade
The next important test for the child is entering second grade. Some teachers follow only the school curriculum and do not pay due attention to the learning process of their students. It turns out that the child seems to know how to add and subtract, but at the same time he is unable to understand why one number turns into another.
In mathematics, it is very important to follow the sequence of actions and regularly train your memory. Only in this case will the baby be able to confidently count two-digit numbers in his head.
If parents are faced with the problem of their child’s poor performance at school, teachers advise working with him more at home. Examples for home practice:
- Add two-digit numbers 30+34 in your head. You can invite your child to break 34 into 30 and 4. This will make it easier for the child to perform addition. Train your visual memory as often as possible while performing everyday tasks.
- Perform addition 40+35. Some children find it much easier to do backwards addition. To do this, you need to round the smaller number to the nearest ten: 40+40. Then simply subtract the extra part: 80-5=75.
- Practice adding and subtracting simple examples in your head. For example: 2+3 or 2+2. Then start complicating the problems: 3+7=10, 10-2=8, 10-8=2. If your child is good at solving simple problems, then tasks with two- and three-digit numbers will not be difficult for him.
- If your child has a rich imagination, you can invite him to count objects or animals in his mind. Each baby is individual, so parents must choose the most suitable teaching method based on its characteristics.
Mental counting will be easier for a child who is a dreamer to master, who will replace boring numbers with animals or toys. Don’t think that the desired result will be achieved quickly, be patient. It is not as easy for a child to learn to count as it might seem at first glance.
Experts advise adhering to the following recommendations:
- During classes, monitor how the baby reacts to the learning process. If he is bored and uninterested, it is better to try another technique.
- Do not force your baby to study against his will. This way you will not achieve the desired result.
- Do not be nervous during classes and do not scold your baby.
- Regularly review the material you have already studied.
- Praise your child for every achievement.
Teaching a child to count quickly is not that difficult (we recommend reading:). Parents just need to approach this with full responsibility, show love, patience and understanding to the baby, then the result will not be long in coming.
Clinical and perinatal psychologist, graduated from the Moscow Institute of Perinatal Psychology and Psychology of the Reproductive Sphere and the Volgograd State Medical University clinical psychologist by specialty
It would seem that there is nothing complicated in counting, but kids completely refuse to understand why after ten there is eleven, and after twenty there is twenty-one. They switch numbers or skip them altogether, driving their parents to despair. “It seems like he’s not a stupid boy, but he can’t understand such little things! What will happen next?
The thing is that a baby’s memory is very selective. Children learn only those things that interest them, delight them, surprise them, or somehow frighten them. It is unlikely that they will quickly remember something that they consider uninteresting, even if adults insist on it. Therefore, parents need to interest the baby so that he himself wants to count. In this case, little fidgets won’t even notice how easy it is to count.
Linguists have long noticed that when learning languages, people most easily master numerals. If learning writing and the alphabet requires special conditions, then learning to count does not require sitting at a table with a pencil and a book. You can count everywhere: at home, in transport, while walking.
How to teach counting to 10?
The child is already two years old, which means it’s time to start learning to count. First, teach him to count to five. While walking, study the number of trees, children on the playground, entrances to the house, cars. Absolutely everything can be counted. When dressing your baby, draw his attention to the fact that there are only one tights, and always two socks, one hat, two boots, and so on. When returning from a walk, be sure to look through all the shoes in the hallway. Let your son or daughter think for themselves about how many people can wear four shoes.
When reading a book, do not skip the illustrations. Let the child tell you the number of drawn balls, puppies, kittens, and so on. Also remember that good poems for teaching counting are small poems with rhymes.
Among other things, the baby must realize that he learns to count for a reason - he benefits from it. Thus, he now knows how to divide the candies equally. When setting the table, ask your child for help, let him give you a certain number of spoons, because this number of people will be dining, and not vice versa, for example: “There will be four people for lunch, because there are four spoons on the table.”
Before you go to the store, tell your child: We need to buy so many things... Remember: onions, beets, carrots, potatoes, bread - only five purchases. Remind me, please, otherwise I might forget something.” When listing purchases, bend your fingers, and then ask your child to repeat the list. When shopping in a store, if your child forgets to tell you what to buy, ask him yourself: “Do you by any chance remember what we need to buy?” After your purchases are made, be sure to count them. If suddenly something is missing, check everything with your child again. The baby, realizing that his mother cannot cope without him, will try to concentrate, and thereby train his counting skills and auditory memory. If your child remembers the entire shopping list, be sure to praise him. Next time the task needs to be made more difficult.
Playing shop will help strengthen counting skills. It will be easier to play with kids without money. Three-year-olds, by the way, are more interested in the payment process. At the same time, you can play without using real money, but using “family currency”: candies, candy wrappers or buttons. You can reward the “clever guy” for correct calculations. For example, invite him to divide five sweets among three people, and let him keep the extra ones.
Digital alphabet
If your child has learned to count, you can proceed directly to learning numbers. Usually, kids simply memorize numbers from one to ten. The main thing is that the baby understands that the numbers indicate the number of certain items. Whether it is three kittens, three apples or three balls, it is always indicated by one number. Kids really like magnetic numbers and various “Velcro books” that are attached to the refrigerator, tiles or to a special board. If the child always has numbers in front of his eyes, he will learn them even without his noticing.
When the baby learns the numbers from one to ten, then introduce the concept of “zero”. To do this, you can invite your child to count what is not there. “If we have candies, then we can count them, and if we ate all the candies and there is nothing left, then we have “zero candies.” The word “zero” means that “there is nothing.”
Older children (four to five years old) can be taught how numbers are formed. Place ten counting sticks in a row - in ancient times ten was called "twenty" for short. Place one stick on top (preferably it should be a different color). Thus, “one” by “twenty” becomes “eleven”. Add one stick at a time to the top row and gradually reach twenty. Then explain the formation of tens: two tens is “twenty”, and three tens is “thirty”, etc.
The exception is the number forty, which in ancient times meant “very many” and ninety, meaning “nine to a hundred.”
How to teach counting from one to one hundred?
When teaching your child to count objects from one to one hundred, you don’t need to require instant memorization. It is best to move step by step, for example, increasing your knowledge by ten every week. The next day, before starting to study new numbers, you should repeat what was covered yesterday. You can move on only if he has mastered the previous material well. In this way, he will gradually learn to count from one to one hundred. It is necessary to remember that the baby must understand the count, and not memorize it. Mathematics is based on finding patterns and understanding. The child needs to figure out exactly what principle the numbers are arranged in this way and not otherwise.
Reinforcing the material you have learned, offer your preschooler the following task:
What number is before the numbers 5;9;21;46;85;100.
Name the number after the numbers: 8;16;26;57;82;99.
Name the number between numbers 5 and 7; 11 and 13; 45 and 47.
Find the missing number: 5,6,7,9,10.
If counting to one hundred is not difficult for your child, then you can start learning how to count backwards. It is best demonstrated on the fingers, bending them, or on counting sticks. It's worth starting with five. Here, a lot depends on the characteristics of the baby, namely on what kind of thinking he has better developed: imagination or spatial thinking. It happens that a baby easily makes quite complex mathematical calculations, but counting backwards turns out to be difficult for him. Don't push! Show him the countdown with visual examples, for example, when going down in an elevator.
Applied Mathematics
These days, first graders can use a computer and a calculator, but they have a hard time doing mental math. The brain, just like muscles, needs regular training. And mental arithmetic, studied from early childhood, is good for the development of mental abilities.
Some parents are sure that their children, especially those under 5 years old, are not yet ready to engage in mental arithmetic. But readiness for mathematical studies does not just suddenly appear, it is formed. If such readiness is not developed, then it may not even manifest itself by the age of ten. Already from the age of three, along with numbers, you can teach your child the first lessons in mathematics. You will be convinced that the results will exceed all your expectations.
You should explain to your daughter or son what “more or less” means. While reading a book, draw your child's attention to the drawing. Invite him to count the images on it: flowers, butterflies, and so on. For example, is there enough flower for each butterfly? Who are more present here: flowers or butterflies? When playing dice, be sure to count them. Let the child demonstrate which cubes are more numerous: small or large, yellow or red, wooden or plastic. At first, it may be difficult for a child to distinguish between concepts such as “a small cube and a large one” and “which cubes are there more,” but there is nothing to worry about.
Main training
To explain to your child the concept of “equally,” use examples such as: “Lena has two dolls and Masha also has two. Who has more dolls? No one has! Because there are equal numbers of them.” Invite your child to divide four apples equally among two people, six among three, and so on. Then move on to simple logic problems. For example, there are four squirrels sitting on a branch, each with one nut. How many nuts are there in total?
Has everything started to work out? It's time to start mastering basic mathematical operations: minus, plus, equal. “You have two apples, they gave you another one. Thus, we got three apples.” It is better to learn to count to 10 on your fingers - it is also useful gymnastics. To add two and four, you need to raise two fingers on one hand and four on the other and count how many fingers are “open” in total. The same can be done with candy, toys and counting sticks. It is useless to insist that the child simply remember that five plus three equals eight. The child needs to understand the mechanism of counting: first, he needs to find out how much there was, then how much was added, and then how much became. Explain subtraction in the same way: we calculate how much there was, then how much needs to be subtracted, then how much is left. Here you need to remember the following: when adding, you always get more than it was, and when subtracting, on the contrary, it becomes less.
Explain to your child that no matter what order he puts the objects in, the result will be the same. For example, if you first put three apples on the table, then two more pears, then there will be five fruits on the table. And if you first put two pears, and then two apples, you will still get five fruits. With this you will explain to your child the primary law of addition: “The sum does not change by changing the places of the terms.”
Today there is a large selection of manuals and books on early childhood development on sale. However, before purchasing them for your baby, study them yourself very carefully. You should avoid examples that contain phrases such as “try to guess how much you get” or “determine without counting.” Because this is a flawed approach to math classes. Mathematics, as we know, is an exact science; it does not guess, but calculates. You cannot teach children to count using questions such as “guess”, “guess”, since they have ambiguous answers and the child may think that the correct answer can simply be guessed and not calculated.
Often, parents of first-graders complain that their children have a humanitarian mindset and lack the ability to do mathematics. However, to do mathematics you do not need to have special abilities. Mathematical calculations themselves help to increase mental abilities, develop memory, ingenuity, and help develop logical thinking. The sooner you start training your baby’s brain using mathematical calculations, the faster your efforts will bring good results.
When a baby grows out of diapers and begins to run, talk and be interested in everything, loving parents think about how to teach their child to count. These skills are very useful for a little person, and the sooner he masters them, the better it will be.
Next, we’ll talk about how to introduce your baby to numbers and numbers up to 100.
When should you teach your child to count?
No one can name the exact dates, but it has been scientifically proven that at 2-3 years a child has the strongest need for new knowledge and obtaining information. Now the baby is ready to learn everything, he absorbs knowledge like a sponge, reaches out to the unknown and generally provides an ideal soil for cultivating certain abilities.
That is why it is better to start introducing numbers to your child between the ages of two and three. However, you can do this earlier. Already at the age of one, children are able to understand that one and two are different things, although they are not yet able to fully understand the quantitative states of objects.
How to teach counting to 10?
Counting to 10 is the main task that a parent of a small child needs to set. But it can be difficult for a baby to master 10 numbers at once, so first teach your baby to count to 5.
To do this, you can resort to the following methods, which are easy to implement at home.
- There are five fingers on the hand - starting from this, introduce the little one to the “names” of the numbers.
- Show cards with objects depicted on them (from one to five) - remember, it is better not to show the image of the numbers themselves to the baby for now.
- Educational cartoons and programs - they can be found on the Internet.
- Abacus and other educational toys.
- Poems and nursery rhymes.
- Counting in everyday life.
It’s very good if you introduce your baby to household chores while teaching him to count. For example, you can instruct your little one to wash five cups. At the same time, ask your child to count: one cup, two cups. Or before going to the store, ask your child to remember five items from the grocery list. Your child should remind you of what you need to buy. At the same time, you can bend your fingers so as not to lose count. This will allow both to teach the child to count in his head and to take care of the development of his memory.
Exercises with cards will be useful. Such manuals are sold in all bookstores and online stores for children. First, show the cards sequentially, then alternate - let the child answer how many objects are shown on the card (remember that we are not teaching writing numbers yet!)
But try not to bore your child with your “math.” Do everything unobtrusively and easily, in a playful way, so that your child does not prematurely feel like a student in a school class.
This activity is similar to when you want to teach a child to read syllables and gradually introduce him to letters and sounds. Take your time and make sure your child has thoroughly mastered the information before moving on to the next stage of learning.
How to teach a child to write numbers?
After the first 10 numbers have been learned, you can show your child how to write them. It’s better not to overload your baby’s memory and study one written number a day.
Dedicate your whole day to digital:
- write it on a piece of paper and hang it in a visible place;
- Together with your child, fashion a number out of plasticine;
- watch a program that talks about this figure;
- Give examples using a calendar. For example, “On the 2nd we will go to grandma.”
Such a simple and everyday object as a watch will help your child write numbers. The child has probably seen it many times, so the numbers on the dial will not be new to him.
How to teach counting to 20?
The next stage of a child's mathematical education at home will be counting to 20. You should start classes only when the baby has already mastered the numbers from 1 to 9 and the number 10 well.
- Explain that each subsequent number (beyond 10) will consist of two digits. In other words, each number is divided into tens and ones. The first digit is tens, the second is units.
- Use two boxes. Place ten objects (balls, cubes, etc.) in one and one (2, 3, 4) in the other; this visual example will help the baby understand what’s what.
- Say that all the numbers in the ones position come one after another, that is, after 11 comes 12, then 13, 14, etc.
- When your child understands the essence of counting to 20, you can give him a small task. For example, ask your child to put 16 sweets (candies, balls) into an empty box. In this case, the baby must count out loud.
How to teach counting to 100?
By the age of 4-5, when the baby is already counting from 1 to 20, you can introduce him to numbers up to 100. This requires some patience and time; learning to count is a rather long and labor-intensive process.
- First of all, tell us that there are 9 tens in the number series up to 100. Name the numbers - 10, 20, 30, 40, 50, 60, 70, 80, 90. But make a reservation that between these numbers there are still units, that is, these the numbers don't go one after another.
- After this short overview lesson, encourage your child to learn 10 new numbers per day. Start with the third ten (21, 22, 23...). Before going to bed, ask your baby to tell you what he has learned. At the same time, you can repeat the material covered by counting any objects.
- When your child has learned several dozen numbers, play a game with him: show him a number line with a missing number in the middle. The kid must find and insert the lost element.
- Praise your child for correct answers and rejoice at his success. Motivate your child to learn.
How to teach addition and subtraction?
Basic operations such as addition and subtraction will be useful to your child even before school. The ability to count objects in everyday life will give the baby self-confidence and also give impetus to the development of intelligence. But where to start?
First of all, remember - no math lessons! Just a game and an interesting pastime.
- Prepare visual materials: apples, candies, cubes - something that will be interesting for your baby to operate with.
- First, parse a prime number (for example, 3). You can get a total of 3 by adding two candies and one. Ask your child to show how much he understands the explanation.
- Continue adding until your child understands what's what, and only then move on to subtraction.
Why do I call my method easy and even surprisingly easy? 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” (site) 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 a complete description of my method of teaching 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 the automatic retrieval of ready-made solutions from memory, but the understanding and memorization of addition and subtraction methods 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 his subsequent 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 must be developed at an early age, which is facilitated by mental calculation.
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 children will return to fish, birds, dolls, ladybugs and other objects and creatures 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 be intimidated by the 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 their own child, parents can easily start elementary lessons using this method from the age of two.
First stage.
Teaching counting within the first ten (lessons No. 1 - No. 40).
Initial lessons of the first stage (No. 1 - No. 5). 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 (see Figure 1 of Appendix 1). 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 on thick paper, 200-250 g/m2, Figure 2 of Appendix 1, and then cut out cube blanks from it, glue them in accordance with the instructions, fill them with any filler, for example, some kind of cereal, and paste them over outside with tape. It is also necessary to make a box to place these five cubes in a row. It is just as easy to glue it from Figure 3 of Appendix 1 printed on thick paper and cut out. At the bottom of the box there are five squares drawn according to the size of the cubes; the cubes should fit in it freely. And the numbers 1, 2, 3, 4, 5 need to be cut out from Table 1 of Appendix 2 printed on thick paper.
You have already understood that learning to count at the initial stage will be done with the help of 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 a child sees at once, alternately place different numbers of cubes in a box and ask: “How many cubes are in the box? Don't count, say it right away. Well done! And now? And now? You are 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 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 little 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.
Lesson #2
In the second lesson, children who, when tested in lesson No. 1, were able to immediately say, without counting, that there are two cubes in the box, can join the games. If there are many such children, it is advisable to divide them into groups of three children. Take turns playing with the children.
1. Game “Putting numbers to dice” with three dice.
Place three cards with the numbers 1, 2 and 3 on the table. Place a box on the table and put two cubes into it. Ask your child how many cubes are in the box. After he answers “two,” ask him to put the number 2 next to the box (he already knows the numbers 1 and 2). Add a third 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 three cubes in the box, show him and call the number 3 and ask him to remove the number 2 from the box and put the number 3 in its place. Then remove two cubes from the box and ask how many cubes are left. After the child answers “one,” ask him to remove the number 3 from the box and put the number 1 in its place. Repeat this game several times. Very soon the child will remember what three cubes look like and will begin to name this number immediately, without counting. At the same time, he will remember the number 3 and will now know the numbers 1, 2, 3 and move the number corresponding to the number of cubes in it to the box.
2. Game “Dwarfs in the House” with three dice.
Play the same way as in lesson No. 1 (see lesson No. 1, p. 2), but this time the gnomes will come to the house and leave it, one and two at a time. Start the game with an open box, and then make a roof by covering the box with your palm. Play through with each child all possible addition and subtraction options within three. You can also ask: “And if three leave, how many will remain?” When the child answers that there are none left, tell him that “not a single one” is another name for zero. Show him the number 0, which can also be cut out from Table 1 of Appendix 2 for this purpose. Each time after the child answers, remove the roof-palm and allow the child to add or remove cubes himself and make sure his answer is correct. You always need to remove the last cubes, counting them from left to right of the child.
3.Playing “Cards” with numbers 1, 2 and 3.
Throw cards randomly to your child with the numbers 1, 2, 3. If you name it correctly, you win; if you make a mistake, you name the number correctly, take it for yourself, and after one turn give it to the child again. When everyone wins, ask him to add the numbers in a column in order.
Play games 1, 2 and 3 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. Note. Do not move on to the next lesson if, after lesson No. 2, the child does not want to immediately say, without counting, that there are three cubes in the box. To help such a child overcome the habit of counting with his finger, repeat the games of lesson No. 2 with him for some time.
Lesson #3
In the third lesson, children who, when tested in lesson No. 1, were able to immediately say, without counting, that there are three cubes in the box, can join the games. If there are many such children, it is advisable to divide them into groups of three children. Take turns playing with the children.
1. Game “Putting numbers to dice” with four dice.
Place four cards with the numbers 1, 2, 3 and 4 on the table. Place a box on the table and put three cubes in it. Ask your child how many cubes are in the box. After he answers “three,” ask him to put the number 3 next to the box (he already knows the numbers 1, 2 and 3). Add a fourth 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 four cubes in the box, show him and call the number 4 and ask him to remove the number 3 from the box and put the number 4 in its place. Then remove two cubes from the box and ask how many cubes are left. After the child answers “two,” ask him to remove the number 4 from the box and put the number 2 in its place. Then remove another cube and ask how many cubes are left. The child has already understood the meaning of this game. He will say that there is one cube left in the box, move away the number 2 and move the number 1 towards the box. Repeat this game several times. Very soon the child will remember what four cubes look like and will begin to name this number immediately, without counting. At the same time, he will remember the number 4 and will now know the numbers 1, 2, 3, 4 and move the number corresponding to the number of cubes set in it to the box.
2. Game “Divide in half” with four dice.
Place four cubes in a box and ask your child to divide them equally between you and him so that everyone has the same number of cubes. When the child takes two cubes and gives you the same number, ask him to say how many cubes he has and how many you have.
3. Game “Dwarfs in the House” with four dice.
Play the same way as in previous lessons, but this time the gnomes will come to the house and leave it one, two, and three at a time. Start the game with an open box, and then make a roof by covering the box with your palm. If, with the box covered, it is still difficult for the child to guess how many gnomes there will be in the house after two or three more are added to the ones already there, place these two or three cubes next to the covered box. This will make it easier for the child to mentally add some cubes to others. And if, with the box covered, it is difficult for him to guess how many gnomes will remain in the house after two or three leave, take these two or three cubes out of the box so that it is not visible how many cubes are still left in the box, and place them next to in a box. For example, there were four gnomes in the box, but three left. The child has not yet forgotten what those four looked like, and, looking at the three cubes that you took out from under your palm and placed next to them, without any explanation, he will guess that there is only one left under the roof in the house. Play through all possible addition and subtraction variations within four with each child. You can also remind that there are zero cubes in an empty box. Start the game by placing all four dice, cover the box and ask: “How many gnomes are in the house now? That's right, four. And if two leave, how many will remain?” If the child cannot answer immediately, remind him how he just divided four in half: he took two cubes for himself and gave two to you.
When adding, first add the smaller number to the larger number, and immediately after that, on the contrary, add the larger number to the smaller number. Do this first with the box open and clearly show the child that if, for example, one comes to three gnomes, then there will be four of them, and if three come to one, then there will also be four. Do not demand that the child understand and assimilate this explanation the first time. It will come to him gradually.
Each time after the child answers, remove the roof-palm and allow the child to add or remove cubes himself and make sure that his answer is correct (you always need to remove the last cubes, counting them from left to right of the child).
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