How to teach a child how to count

In just 5-6 months, following the methodology, Doman says, you can teach a small child( starting from 4-6 months) mathematics in the amount of two classes of primary school. The kid will learn very quickly to produce in the mind all mathematical actions, master the elements of algebra and learn to solve equations.

There are two important reasons why children should be taught mathematics. First, mathematical calculations are one of the higher functions of the human brain. Only man has the ability to account. In addition, this skill is very useful in life, as in a civilized society it has to be used almost daily. We count from childhood to old age. Schoolchildren and housewives, scientists and businessmen count.

The second reason is much more important. Children should be taught to count as early as possible, since this will help the physical development of the brain, and consequently, what we call intelligence.

Why can not adults count? The answer to this question is simple. Doman writes that we adults blend the symbol, for example 5, with the very fact of having five objects.

Our difference from children, in his opinion, is that they see things as they really are, while adults see things as they think they should be. If you say "seventy-nine", the adult will be able to present only "79", but not 79 points.

You will not be able to imagine this and especially to perceive it. And small children can.

So that the child understands what one is, and this really is you need to show him just the fact and say: "This is called" one. "

Then you present him another fact:

and say: "This is two."

Then you say "It's three" and show the child:

And so on. This can be done quickly, and the child will take everything perfectly and remember it.

You can teach your child math, even if they themselves are not too capable in this area. In addition, if you do everything right, then both will get pleasure. The whole lesson takes less than 30 minutes a day.

The material used to teach your child the account is extremely simple. He takes into account the immaturity of the children's visual apparatus and promotes its development, as well as the development of the brain.

All mathematical cards can be made from ordinary white cardboard so that they are suitable for repeated use.

So, in order to start, you need to prepare the following.

• White cardboard cards approximately 27x27 cm in size. If possible, use pre-made cards to save time for cutting, especially since everything else will require significantly less effort. You need at least 100 such cards.

• You will also need a large red felt-tip pen with a thick stem.

Points should be red just because the attention of children is most attracted by this color. In addition, it creates a good contrast on a white background, which is very important, given the immaturity of the child's visual apparatus. The very process of contemplation of such points will contribute to the rapid development of visual receptors, so that when you gradually move to the study of figures, it will not be difficult for your child.

So, start with making cards.

• Use a red felt-tip pen to print points on the card - from 1 to 100.

• Draw points in chaotic, not in the form of a square or some other shape.

• The availability of the printer will greatly simplify the operation. Then all the preparation you can do on the computer, and then just print the sheets.

• In all four corners on the back of the card, write down a number corresponding to the number of points on the card with a pencil or pen.

• Do not forget to leave small margins at the edges of the card. It is for them that you will keep the card with your fingers when you begin the learning process.

You can start learning by making cards. As in all previous cases, very soon you will find that your child is learning with astonishing speed. Take an example from him and do not fall behind. The new material should always be at your fingertips. Remember the old truth: children really do not like to return to the material that has already been traversed. If you do not have time to prepare new material, take a break, but do not show the old cards.

The sequence of learning the account is simple and easy, besides it does not change depending on the age of the child. Here are the steps you have to go through.

The first stage The second stage The third stage The fourth stage

The fifth stage

Mastering the concept of "quantity"

Equations

Solving problems

Mastering the concept of "digit", remembering them

Digital equations

At the first stage, you need to teach the child to perceive the actual amount thatthe letter is usually denoted by numbers.

Prepare five cards with images of points from 1 to 5. Show the kid a card with a single point and say aloud: "This is one."Show the cards very quickly, just as long as you need time to call the number. And do not give any explanations. Also show the remaining four cards.

The total duration of the first day's classes is no more than three minutes. During the second day, repeat the main exercises 3 times. Add the second set of five cards( with the number of points from 6 to 10) and also demonstrate it three times. Thus, the total duration of lessons will increase to six minutes.

After this, start shuffling each set, so that before the next show the cards lay completely randomly.

When you get acquainted with a child with the number from 1 to 10, the baby will develop his vision so that it will be easy to distinguish one quantity from another.

Now continue to show two sets of 5 cards, but on the second day of classes, mix them up so that there are cards in one set, for example: 3, 10, 8, 2 and 5, and in the other - all the others. Constant mixing of cards will allow you each lesson to have something new and unforeseen, because the child will never know in advance in what order you will show him the cards. This is very important in order to preserve the novelty necessary for employment.

Continue with the first two sets for five days. On the sixth day, start cleaning up old cards and add new ones. Do it this way: take the two smallest numbers( that is, start with 1 and 2) and add the next by the ordinal number( that is, 11 and 12).So update your sets daily for two cards. Learned cards will be useful for you for the second and third stages.

Never let a child get bored. Too slow classes bore him much more correctly than too fast.

Daily program( starting from the second day of classes)

Number of teaching material

One lesson

Frequency

Image

Duration

New cards

Deleted cards

Duration of use of each

card

principle 2 sets

1 set( 5 cards)

is shown 1 time, each set by

3 times

red dots measuring less than 2 cm 5 seconds.for lesson

2 daily( 1 in each set)

2 daily( two least numbers)

3 times a day for 5 days( 15 times)

always stop before your child wants

In general, you will learnit, using 10 cards daily, dividing them into two sets, every day updating two numbers.

Again, we are forced to remind you of the need to avoid boredom. If the child is bored, then you are doing everything too slowly. If you do everything correctly, you will soon be able to update more than two cards a day. In order to meet the wishes of your

child, update three or even four cards. By this time this game should give you mutual pleasure.

You continue to teach your child with the help of cards until you pass the last one, with the image of 100 points. Now that your child has seen all the cards from 1 to 100, he perfectly mastered the idea of ​​quantity. He will want to go to the second stage even before you finish the first one. Therefore, you can proceed to the second stage after you have mastered the cards from 1 to 20.

After the child has mastered the numbers from 1 to 20, both of you will be ready to put them together and see what happens. In other words, he is ready to master the operation "addition".

It's very easy to start learning this operation. In fact, your child has been ready for this for several weeks. After all, every time you show him a new card, he sees that there is one additional point on it. It becomes so predictable that he will begin to anticipate those cards that have not yet been seen. However, he can not predict or withdraw from somewhere the name of this number - for example, "21".Most likely, he will think that the new card, which we will soon show him, will look exactly like the previous one containing 20 points, except that one extra point will appear on it.

This is called addition. However, he does not yet know what it's called, but already has an embryonic idea of ​​what it is and how it works. It is important to understand that he will come to this idea on his own, even before you show him the operation "addition" for the first time.

The material for this you can prepare very simply: write the equations on the reverse sides of cards from 1 to 20. Before you start, put your cards face down on the lap, one on top of the other, three cards. Say cheerfully and with enthusiasm: "One plus two equals three."While you are saying this, show him the card with the number in question.

Thus, you hold a one-point card in your hand, say "one", then postpone it, say "plus", show a card with two dots, say "two", postpone it and, after the word "equals," show the cardwith three points, saying "three".

The child, without any explanation, understands what the words "plus" and "equals" mean, just as he understands the meaning of the words "mine" and "your" - the meaning of these words he himself derives from the context.

Do it quickly and in the most natural way. The most important thing is to prepare all the cards necessary for a given equation in advance. The child will not sit quietly and watch as you rummage in a pile of cards, picking the right ones.

Choose cards in the evening, on the eve of the day of classes, so that by the time you choose a suitable time for study, they were already at your fingertips. And do not linger on too simple examples with numbers from 1 to 20, go to more complex ones, which even you yourself can not solve quickly in your mind.

Demonstration of each example should take you only a few seconds. Do not try to explain what the words "plus" or "equals" mean. This is not necessary, because by producing actions, you are faster than any explanation to demonstrate the true meaning of these words. That is, your child will see the process itself before hearing an explanation from you.

Yes, he did not need it - all explained the clarity of your actions. This method of training is the best.

If you say to an adult: "One plus two equals three," he mentally sees the following: 1 + 2 = 3, because adults imagine symbols, not facts. But what a child will see:

Children see not symbols, but facts. Telling about examples, always follow the same manner of presentation, using the same terms. Saying once: "One plus two equals three", do not say then: "To one to add two will be three."When you teach the child facts, he draws conclusions and comprehends the rules. If you change the terms, then the child has every reason to think that the rules have also changed.

Each lesson should consist of three examples. There may be fewer, but there should not be more. Remember that your classes should be short-lived. Each of the three daily activities should contain three different equations, so the total number of daily examples will be nine. Do not make mistakes and do not repeat the same examples. Every day they must be new. Stick to the examples of two members - then your classes will go faster and more fun.

After two weeks of classes with nine equations, it's time to subtract, otherwise the addition will just bother your child. You need to learn subtraction exactly the same way. You show cards, call numbers, action and result.

Over the next two weeks, you will successfully cope with the subtraction, parsing with your child about 126 examples. This is quite enough, and now it's time to move on to multiplication.

Multiplication is nothing more than a multiple addition, so it will not be a big discovery for your child. Since your daily set of point-based cards is constantly increasing, you already have enough possibilities for multiplication equations. Prepare all possible examples by writing them on the back of the cards.

Now use three of them and say: "Two times three is six."

The child will understand the word "multiply" as quickly as he understood before the word "plus", "equals", "minus", etc.

Your subtraction tasks will be replaced by multiplication tasks, but they will continue according to the same scheme. At the same time, you continue to teach the child numbers. Ideally, your child will only see the real number, the number in the form of dots on the cards, and will not imagine numbers, even such simple ones as 1 or 2.

The next two weeks you dedicate to multiplication. After two weeks of multiplication, it is time to move on to division. Now that you have passed all the numbers from 0 to 100, you have all the necessary material for the examples for division. Write the appropriate equations on the back of almost all the cards( this is a long job, so you can draw a husband to her).

You just tell the child: "Six divided by two equals three."

And he will perfectly understand the meaning of the word "divide". As before, each lesson will consist of three different equations, and every day - from three classes with daily nine equations your child will cope without any difficulty.

After dedicating two weeks to division, you will finish the second stage and you will be ready to go to the third.

You probably remember our main advice: never expose your child to checks. Children love to learn and do not like to be tested. Instead of testing, you should use the method of identifying abilities.

The purpose of this method is to give the child the opportunity to demonstrate his knowledge, but only if he wants to.

Here is a simple example. You show him two cards with 15 and 32 points and ask: "Where is thirty-two?"

If he correctly points the card, then, of course, you reward him with a kiss. If he was mistaken, then say: "Is not thirty-two - is not this?" - and show him the correct card. You are cheerful, relaxed, full of enthusiasm. If he does not answer your question, then bring him the card a little closer and ask: "That's thirty-two, is not it?"

Regardless of his answers, continue to conduct the classes cheerfully, calmly and with enthusiasm.

The method of identifying abilities can be applied at the end of the session. Thus, there will be a balance between what you give and what you get. In the course of classes, you familiarize him with three examples, at the end you give the opportunity to solve one more example, but only if he himself wants it.

Starting with questions about numbers, you will quickly go to the questions of choosing the right answer when deciding one or another example. This is much more interesting for the child, not to mention you.

Do not ask your child to say the answer, but always give him the option of choosing between the two options.

For this method, you will need the same three cards that you used to demonstrate the examples, and the fourth card is a possible answer.

Young children are just beginning to learn to speak, so it is difficult for them to respond verbally. But even those children who have already begun to talk do not like to respond verbally, especially since this in itself is a test for them.

Remember that you are teaching your child not to speak, you are teaching his math. Choosing between two variants of answers, he will have fun and will easily cope with the task. But he will quickly feel irritated if we make him respond verbally.

Since you have already passed all the numbers and are familiar with the four rules of arithmetic, you can now diversify and complicate your studies in every possible way. Continue to stick to the previous schedule - three lessons per day with three different equations in each lesson. But now there is no need to show all three cards of the equation, show only a card with the answer.

As a result, your classes will be shorter. You just tell the child: "Twenty-two divided by eleven is equal to two" - and show him a "two" card. Your child already knows what is 22 and what is 11, so do not need to show him these cards.

Now your classes will consist of different kinds of equations, for example from the equations for division, addition and subtraction. It's time to move on to equations with three members, and you will see for yourself how they will please your child. But do not delay or slow down the pace, remember that the speed of the material is very important for your child.

Write one or two trinomial examples on the back of each card. This is how it should look.

Notice that your classes continue to be very short. The child learns nine nine-part examples on a daily basis and at the end of each lesson tries to solve one task by choosing the correct answer.

After a few weeks, add another operation, going to the examples with four members.

This stage is very simple. But you will need to make new cards, on which the numbers will be written. They will have the same size - 27x27 cm - and cover the figures from 0 to 100. Write should be a thick red felt-tip pen, the size of the digits is 15 cm in height and 7.5 cm in width. When writing, stick to the same sample. Your child needs a certain standard in perceived visual information - this will help him a lot.

Always mark cards on the back, in the upper left corner, to be sure that when holding them, hold them correctly, not upside down. For the previous cards it did not matter where the top and where the bottom, so you marked all four corners, here you only need to mark the top left corner.

As a result, your cards should look like this:

At this stage, your daily program will consist of three equations, solving problems at the end of each lesson, and three more classes you use to train numbers. Total: six lessons. To learn the numbers you will be exactly the same as before taught cards with dots.

You will need 2 sets of cards with numbers, 5 digits in each set. As before, start with a set from I to 5 and from 6 to 10. First show them in ascending order, but then always mix so that the order of the display was unpredictable. Daily, delete the two smallest digits, replacing them with the two largest digits. Let each set have one new card, and not so that there are two new cards in one set, and not one in the second set.

Demonstrate each set three times a day. Do it as quickly as possible. If you notice that the child began to get bored, accelerate the process of updating the cards: instead of two, replace 3-4 daily.

You might think that three times a day is too often. If your child is willingly engaged in the first two times, but constantly tries to escape from the third, then reduce the number of classes to two.

To study all the numbers from 0 to 100, you need a month, or even less. After that, you can go to the demonstration of larger digits - 200, 300, 400, 500 and 1000. After that selectively familiarize it with such, for example, figures like 210, 325, 450, 586, 1830.

Of course, you do notmust show each digit in order from 0 to 200 or 500 - this will instantly tire your child. You have already laid the foundations of knowledge, so now just a little diversify its digital "diet".

Even when you just passed the numbers from 1 to 20, it's time for "bridging" between the numbers and the number of points. There are many ways for this. One of the simplest is the following: use equalities, inequalities, relations "more" and "less," cards with numbers and dots.

You should constantly monitor the attention of the child, his interest and enthusiasm. This will help you modify the daily program accordingly, adapting it to the ever-evolving needs of your child.

Take a card with 10 points, put it on the floor, then put an inequality sign next to it, and then a card with the number 35. After that say: "10 is not 35".

In the process of working with digital cards, be distracted by the above-described games, as soon as your child has a corresponding desire. Children like to invent and make their own combinations of numbers and numbers.

Learning the numbers is a very simple step for your child. Try to pass it quickly and cheerfully to quickly proceed to the fifth stage.

This stage is a repetition of what you have done before. It includes all the arithmetic operations and mathematical relations with which you have already met.

For him, you will need white cardboard cards measuring 45 cm in length and 10 cm in width. On them you will write digital equations. But now we recommend that you write not red, but a black felt-tip pen and a smaller font - the numbers should be 5 cm in height and 2.5 cm in width.

Your first card will look like this:

And now go back to the second stage and follow the advice that was given there, only this time cards will not have points, but with equations. After completing the second stage, go to the third.

For this you will need additional materials. We need to make cards that do not contain a ready answer. And again, use cards with numbers so that your child can choose the right answer from them. It will be useful for you to write it in the upper left corner on the back of the card with the task that you yourself always remember about it:

25 + 5 = 30

Below are some examples of your training cards with those operations that you have already done on points.

Examples for subtraction:

Examples for multiplication:

Examples for division:

Continue using numbers 5 cm high long enough to make sure your child is comfortable with it. And only gradually make them more and more small. If you reduce the figures too quickly and too much, you risk losing your child's attention.

Gradually you will reduce the height of the digits to 2 cm, or even less. Thus, your card will have more space for longer and more complex equations. At this stage, your child may want to make up his own equation using the known numbers and symbols( =, +, -, x,:) and demand that you decide it yourself.

So, your child has learned to count.

First, he has mastered the quantity, that is, is able to distinguish one quantity from another.

Secondly, he can add these quantities, subtract, multiply and divide. Thanks to this, hundreds of different combinations are opened before it, which can be done with different quantities.

Third, he understood what symbols are and that they are used to refer to different quantities.

And, last but not least, he understood the difference between the real number and the symbols, one of which must be chosen correctly to denote the given number.