Where to start learning mathematics with children?

It is necessary to begin studying mathematics with the development of counting skills.

At what age should children start learning mathematics?

As early as six months, you can start learning mathematics with your child.

Development of numeracy skills

The basis of the fundamentals of mathematics is the concept of number. However, number, like almost any mathematical concept, is an abstract category. Therefore, difficulties often arise in explaining to a child what a number is.

How to explain to a child what a number is?

One, two -

Let's go get some firewood

One two Three -

Look at mom.

Long before your baby tells you he has three beads, he will be able to recite these nursery rhymes. He learns to pronounce the names of numbers and learns their group characteristics before he encounters the true meaning of the numbers.

To parse numbers, you can use counting sticks. Ask your child to place two chopsticks on the table. Ask how many chopsticks are on the table. Then spread the sticks on both sides. Ask how many sticks are on the left and how many are on the right. Then take three sticks and also lay them out on two sides. Take four sticks and have your child separate them. Ask him how else you can arrange the four sticks. Let him change the arrangement of the counting sticks so that there is one stick on one side and three on the other. In the same way, sequentially sort out all the numbers within ten. The larger the number, the correspondingly more parsing options.

It is very useful to compare pictures that have both similarities and differences. It’s especially good if the pictures have a different number of objects. Ask your child how the pictures differ. Ask him to draw a different number of objects, things, animals, etc.

Draw your child’s attention to what is happening around him: on a walk, on the way to the store, etc. Ask questions, for example: “Are there more boys or girls here?”, “Let’s count how many benches there are in the park,” “Show me which one is the tree is tall, and which is the lowest,” “How many floors are there in this house?” Etc.

Try not only to name numbers, but also, if possible, introduce elements of addition and subtraction. For example, there are 4 flights of stairs in the entrance, you are on the top floor. Accompany the passage of each floor with the words - we have 4 stairs, we have passed 2, 2 are still left... 3 have passed - we have left...

Games for teaching counting

Balls and buttons

Concepts of spatial arrangement are easily learned in playing with a ball: ball above your head (above), ball at your feet (below), throw to the right, throw to the left, back and forth. The task can be complicated: you throw the ball with your right hand to my right hand, and with your left hand to my left. In action, the baby learns many important concepts much better.

It is much more difficult for him to correctly place objects on a plane. For this exercise, take any flat shapes (for example, a square to start with) and flat buttons. Place a square of thick paper on the table, give the baby a few buttons (5 large and 8 small). Let him, according to your instructions, put the buttons in the right place. For example: “Put a large button in the middle, another one under the square in the middle, another one above the square in the middle, one on the right in the middle, one more on the left in the middle.”

If the child has completed this task, move on to the next task. Now you need to arrange the small buttons. One - in the upper right corner (we explain what a corner is on the right, from above), the second - in the upper left corner, etc. If this task is completed without errors, we proceed to an even more complex one. “Place the small button on top of the large button that lies above the card (under the card).” Options: to the right of the large button, which lies on the right side of the card; to the left of a large button, which lies to the left of the card, etc. The difficulty increases gradually, from lesson to lesson, but in no case during one lesson! If the child begins to experience difficulties, return to a simpler task: this is a temporary situation.

How far is it?

While walking with your child, choose an object not far from you, for example, a staircase, and count how many steps there are to it. Then select another object and also count the steps. Compare the distances measured in steps - which is greater? Try to guess with your child how many steps it will take to get to some close object. You can walk to a place with normal steps, then turn around and see how many fewer steps it takes you if you walk back with giant steps.

In mathematics, it is not the quality of objects that is important, but their quantity. Operations with numbers themselves are still difficult and not entirely clear to children. However, you can teach your child counting using specific subjects. The child understands that toys, fruits, and objects can be counted. At the same time, you can count objects “in between times.” For example, on the way to kindergarten, you can ask your child to count the objects you meet along the way.

It is known that children really like doing small housework. Therefore, you can teach your child to count while doing homework together. For example, ask him to bring you a certain amount of any items needed for the business. In the same way, you can teach your child to distinguish and compare objects: ask him to bring you a large ball or a tray that is wider.

It is very important to teach a child to distinguish the location of objects in space (in front, behind, between, in the middle, on the right, on the left, below, above). For this you can use different toys. Arrange them in different orders and ask what is in front, behind, next to, far, etc. Consider with your child the decoration of his room, ask what is above, what is below, what is on the right, on the left, etc.

The child must also learn concepts such as many, few, one, several, more, less, equally. While walking or at home, ask your child to name objects that are many, few, or one object. For example, there are many chairs, one table; There are many books, few notebooks.

Mosaic

Of course, a child at the age of three is not yet able to use a mosaic for its intended purpose - to lay out patterns or pictures according to a model - and yet he is quite capable of playing with a mosaic. First, show your child how to use it - this is not so easy for a two-year-old. Let him lay out the pieces in any order until he gets bored (this is a great exercise for developing his hands).

The next task may be more difficult: arrange the mosaic elements on the same line or at a certain interval between them. This requires not only finger dexterity, but also an eye (the model is set by an adult). Several such lines can be laid out so that they differ in color: after all, even if the child does not yet name the colors, he is able to select one of them and match it with other objects of the same color (in this case, mosaic elements). Completing this task will help develop fine motor skills of the fingers, the eye, and the ability for basic analysis and synthesis. Along the way, the baby will learn to name and remember colors faster. But be careful: the mosaic pieces are very small and can be dangerous for the baby, so do not leave him alone even for a minute, and after playing, carefully put everything in the box.

Learning to count on fingers "Fingermatics"

The most universal aid for teaching mathematics is fingers. To introduce a child to counting, nothing could be simpler.

Every evening, after the usual evening bath, when the mother begins to dry, treat and prepare the child for bed, the “helper” should show numbers on his fingers and loudly and joyfully call them: “One!”, “Two!”, “Three!” etc.

Usually the child stops tossing and turning, being capricious, without looking up, follows the “finger numbers” and smiles. The mother is extremely pleased and puts the baby to sleep without interference within a few minutes.

The path of humanity to the decimal system, in which you and I and the baby will count, comes precisely from the human digits. Start with one handle. Count your fingers, hide a few and count how many are left. Hide everything and become familiar with the concept of zero. Separate some fingers from others and find out that five is one and four, two and three. Then start adding the second handle. One finger of the left hand came to visit the fingers of the right - and there were six fingers. Then another one came to them, and there were seven of them, etc. Or let two or three fingers come at once, and you find out how many there are.

Squirrels

One two three four five

The squirrels came to play. (Show five fingers)

One disappeared somewhere (Hide your hand behind your back)

Four squirrels left. (Show four fingers)

Now look quickly (Hide your hand behind your back)

There are already three of them left. (Show three fingers)

Well, well, what a pity, (Hide your hand behind your back)

We only have two left. (Show two fingers)

This news is so sad (Hide your hand behind your back)

There is only one squirrel left. (Show one finger)

Then say:

While you and I were counting,

The squirrels ran away from us.

Talk to your child about where the squirrels could go to take a nap, look for food, and so on.

Five teddy bears

Read a poem. After reading the first line, raise one finger. Raise the next finger every time another bear appears during the action.

One bear at the table was devouring a cutlet,

But then, out of nowhere, another suddenly came running,

There were two of them.

He began to take the cutlet away, he also wanted to eat,

But another one came running and ate all the cutlets.

There were three of them.

Three stupid little bears wanted to close the door,

But the door opened, and another beast rushed in.

There were four of them.

Four little bears found a swarm of bees,

Another little bear ran in and started a loud howl.

There were five of them.

The bees sting in earnest and all the bears ran away.

On the last line, hide your hand behind your back.

This house has five floors:

On the first floor lives a family of hedgehogs,

On the second floor lives a family of bunnies,

On the third - a family of red squirrels,

On the fourth a tit lives with its chicks,

On the fifth, the owl is a very smart bird.

Well, it's time for us to go back down:

On the fifth owl,

On the fourth tit,

Squirrels on the third,

Bunnies - second,

On the first hedgehogs, we will come to them later.

Two bears

Two bears were sitting

On a thin branch.

One stirred the sour cream,

Another was kneading flour.

One "kuku", two "kuku"

They both fell into the flour!

Nose in flour, mouth in flour.

Ear in sour milk!

Five fingers

There are five fingers on my hand

Five grabbers, five holders.

To plan and to saw,

To take and to give.

One two three four five!

(Rhythmically clench and unclench your fists. When counting, alternately bend the fingers on both hands.)

Naughty counting rhyme

How many fingers do we have?

Shall we count?

That's it!

Are we bending?

That's two!

Shall we continue?

Three four...

Where is the fifth?!

Wow - look!

Let's continue to the next one:

Here's the sixth, seventh, eighth....

Bang-bang oh-oh-oh!!!

Yes, the ninth is like that!

How many fingers are there in total?

Exactly ten! Oh-ho-ho!!

(Arms bent at the elbows, fingers spread out and twisting the hands in different directions.

We bend the fingers on the other hand with one hand. On the fifth finger we show the sign “Wow!” (fingers in fist, thumb bent).

We move to the other hand and bend it again, starting from the little finger. When we bend the eighth finger, we get a “pistol” from which we shoot.

Very small ones bend their fingers with the other hand, and those who succeed, bend their fingers without help.

The last lines are the same as the first line).

Counting fingers

One two three four five!

Finger went for a walk,

I ate a big bun with poppy seeds.

This fat gentleman

Thumb with number one!

This finger went into the forest

I found honey in a large hollow.

Barely escaped from the bees

Nice finger number two!

This finger goes to sea

On a humming ship.

In a storm on deck, look!

Brave finger number three!

This finger is our strongman:

Like a light children's ball

He's throwing weights!

Thumb with number four!

And the last one is a cute little one,

He sits quietly by the window,

Junior finger number five!

One two three four five!

Sing along, sing along:

Ten birds are a flock.

This bird is a nightingale,

This bird is a sparrow.

This bird is an owl

Sleepy little head.

This bird is a waxwing,

This bird is a crake,

This bird is a starling,

Gray feather.

This one is a finch.

This one is a swift.

This one is a cheerful little siskin.

Well, this one is an evil eagle.

Birds, birds go home!

(Bend or stroke your fingers)

My brother will soon be five.

But he doesn't want to study.

Then I came up with a thing.

I say: give me your hand,

One two three four five.

These fingers are rabbits.

The first one hid somewhere.

Bend your finger - once.

How many of them do we have now?

Brother spread his palm

And he suddenly answered: “four.”

Well done. A capable boy.

Bend your finger again.

How many are there now - look?

The brother counts: - one... two... three...

The third hare suddenly disappeared:

The prankster ran away into the forest.

Our bunny barely disappeared,

My brother is already shouting to me: “two!”

We left everything

How many fingers? —

One. —

And then this bunny

He lay down on his side in bed.

We bend the fifth finger,

Now, what remains?

The brother looks slyly and laughs:

- What remains is... a fist.

Little bunny

Mother and child stand facing each other, holding hands. The adult says to the baby: “Show how big you are.” Carefully pulls his hands up. “That’s how big it is!

Now show how small the bunny (any toy) is (sits down and pulls the child down by the arms). Little bunny."

Repeats the same actions, reading a poem by N. Pikuleva.

That's how big we are

Raises the child's hands up.

Not tiny

Squats with the child, pointing with his hands low above the floor.

Like this, like this

Stands up, raising the baby's hands up.

These are the little ones.

The little dragons were flying

Two people are playing. Standing face to face, they stretch their arms forward so that one of the palms of each is between the two palms of their partner. The players take turns pronouncing a word of the verse, clapping their partner’s palm in time with each word:

The dragons were flying and eating donuts.

How many donuts did the dragons eat?

The one who gets the turn to answer calls out any number, for example, three, along with a clap. The partner starts counting: “One!” (clap) - “Two!” (response clap) - “Three!” When the last number is called, the one whose hand is currently “under attack” must remove it as quickly as possible so that the clap does not reach the target.

The given exercises at first glance are quite primitive, but, firstly, they are designed for children from six months to two years. And secondly, it is precisely such simple rhymes that are easier for children to remember and give them a lot of pleasure.

Deep learning in mathematics is somewhat different from the usual: “One, two, three.” If you want your child to come to school thoroughly prepared, read the review of methods on the topic of how to teach your child to count. Who are the authors of these systems? How do benefits work? Are they effective, and which one should you choose? You will find out all this right now.

A little preface: early mathematics yes or no?

Perhaps someone will be surprised to see familiar names in the subheadings - Montessori, Doman, Zaitsev and the Nikitin family. Of course, they appear as innovative authors who offered the world fundamentally different reading methods or teaching methods, like Maria Montessori.

However, each of these people invented something that deserves close attention - non-standard techniques for teaching mathematics. Please note - no counting, no addition and subtraction, namely mathematics. Each method is valuable. They have no contraindications or special limiting recommendations. They have a lot in common. They can be used in a way that your child likes or seems rational to you: all together, one at a time, part of the technique, or the whole technique at once.

Nikitin family: teaching counting by dots

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

It is necessary for the child to learn to organize the cards: first by color, then by quantity and numbers. The following is a standard set of mathematical tasks, selected specifically to teach a child to count:

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

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

Nikitin table “Hundreds” - a way to overtake peers

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

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

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

Zaitsev’s “No!”: teaching mathematics not up to ten, but up to a thousand...at least

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

Nikolai Alexandrovich thought and invented a technique as innovative as cubes, but under the name “Hundred Counting”. The author himself warned that one hundred is a minuscule amount that the brain of a five-year-old child is capable of. Having swapped the types of activities, Zaitsev determined that mental arithmetic is more important and primary, and only then come written calculations.

“Stoschet” is a set of manuals in which, again, the theme of numbers and geometric shapes is played out. Figures are necessary to quantitatively illustrate a figure.

The tape “Hundred Counting” introduces children to all types of mathematical operations with numbers. Children who have mastered the tape algorithm easily go beyond hundreds, reach thousands, and even step beyond this threshold. The child learns mental calculation as if unnoticed. Plus, he's passionate, and that's worth a lot.

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

The “Hundred Count” table consists of the same chips, but they are placed in a rectangle. The tasks created by the author for children are structured in such a way that children do not solve, but search. During the game, they master the composition of numbers, learn to count and compare, and all this without poring over a notebook until 23.00.

The genius of Glenn Doman: teaching math

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

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

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

How to teach a child to count using Doman? Is learning using the author's math cards suitable for ordinary children? How to form the perception of numbers at the level of intuition (without counting units) - yes. But as a separate method, it leaves many blind spots in a person’s mathematical thinking.

Maria Motessori - a rich set of techniques for teaching mathematics

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

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

Montessori Math Aids to Ten

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

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

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

An effective and efficient means of learning mathematics is Montessori's golden asset. With it, parents do not have a headache, which is called how to teach a child to count correctly. By playing with beads, 4-5 year old children learn numbers on an intuitive level. The manuals, specially constructed from “golden” beads, reveal the concept of number.

The same beads, but in different configurations, tables, boards of a special design, three-dimensional chips with examples of addition, “Fractions” materials, an abacus of an original design - this is a small list of Maria Montessori’s materials for comprehensive teaching of mathematics.

Montessori materials convincingly illustrate mathematical formulas. With gold beads supported by digital cards, you won't have a problem teaching your child how to count with a column. By sorting sets by rank and matching numbers to them, children will understand the relationship between mathematical concepts and actions in a playful way.

Interesting facts about columnar calculations

Having prepared the child for school, later we invariably ask the question: where do the two come from? Why can’t a schoolchild who solves problems well at home be able to tell the answer to the teacher?
As banal as it may be, this only means that in his “mathematical building,” where every brick must be in its place, there is a defect. Most often these are problems such as: ignorance of the composition of a number, the multiplication table, the principle of dividing a number into digits.

Despite the effectiveness of the described methods, they should all lead to a theory. That is, a student, having mastered numbers figuratively, should be able to answer all program questions. Definitely, you will have to cram. However, this is only for the good. The Russian program provides the most clear algorithm for teaching a child to count in a column. Parents whose children studied in foreign schools told us about this.

It turns out that traditional notation with transferring or borrowing bit units gives an excellent result, provided that it is supported by theoretical knowledge.

Early methods - excellent mathematics

Separately, I would like to comment on the negative point of view regarding methods of early teaching of mathematics. If a child wants to know, then this knowledge must be given to him. Moreover, the authors do not suggest seating children at a desk. All classes are conducted “in passing” in a manner that is friendly to children’s health. And this is an excellent alternative, given the pre-school fever, when the child is urgently seated at the desk, given a textbook and counting sticks and told to get ready for school.

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

Vanzha Irina Nikolaevna
Job title: teacher
Educational institution: MADOU" Kindergarten No. 20 "Cinderella"
Locality: Nefteyugansk city, Tyumen region
Name of material: Article
Subject:"Teaching backward counting for children of senior preschool age"
Publication date: 10.10.2017
Chapter: preschool education

Teaching children of senior preschool age to count backwards

For the mental development of children, the acquisition of

mathematical

ideas,

formation

mental

actions,

necessary

knowledge

the surrounding world and solving various kinds of practical problems, as well as

for successful learning in junior high school.

Formation of counting activities in preschool children

were engaged

teachers

Y.A. Komensky,

Pestalozzi,

K.D. Ushinsky, F. Frebel, M. Montesori, L.V. Glagoleva, E.I. Tikheyeva,

F.I. Blecher,

humanist thinker

Y.A. Komensky in the guide to raising children before school “maternal

school" included in the program on arithmetic and basic geometry the assimilation

within

dozens

discrimination

determining the greater and lesser of them, comparing elective items,

geometric shapes, study of measurement measures.

I.G. Pestalozzi - Swiss democratic educator and founder

theories of primary education, pointed out the shortcomings of existing methods

training, which is based on rote learning, and recommended teaching children

counting specific objects, understanding operations with numbers, ability

determine time.

Russian teacher - democrat K.D. Ushinsky proposed teaching children

individual

items

actions

addition

subtraction,

to form an understanding of ten as a unit of counting.

The great Russian thinker L.N. Tolstoy published the ABC in 1872,

one of the parts of which is “Account”. He suggested teaching children to count

forward and backward within a hundred, learn numbering based on children's

practical experience gained in the game.

Counting is one of the leading concepts in mathematics. People learned to count

deep

antiquities.

development

primitive peoples. With the emergence of civilization, the need for counting and

The ability to perform arithmetic operations has increased sharply.

Preschool pedagogy also did not ignore education

counting. In kindergarten, preschoolers become familiar with counting. Mathematical

exercises

logically

expand

representation

surrounding

Education

kindergarten is a necessary component in preparing for school.

Premature learning of counting activities inevitably leads to

to the fact that the idea of ​​number and counting acquires a formal character.

education

begins

preceded

preparatory work: numerous and varied exercises with

sets of objects in which children, using application techniques and

overlaps, compare aggregates, establish “more than” relationships,

“less”, “equal”, without using numbers and counting.

Children of the sixth year of life still have visual-figurative thinking,

but with a special system of education and training they begin to develop

verbal thinking. Memory and attention begin to acquire strong-willed

direction.

descriptiveness,

prudence,

express your thoughts. Children of this age are looking for active communication, both with

peers and adults, they are proactive figures, “natural

tateli”, assistants in any affairs and endeavors of an adult. They tend to

the desire to complete a task and receive a positive assessment for it.

Thus, the children of the older group have already started the second stage

in teaching counting, which began in the middle group, its basis for

preschoolers

active

usage

recalculation

comparison of sets. It is carried out based on the definition of a number as

characteristics of the class of equivalent sets, that is, their common property,

regardless of the nature of the objects included in them.

The senior group program is aimed at expanding, deepening and

generalization

elementary

mathematical

ideas,

further development of account activities. Children are taught to count within 10,

continue to introduce the numbers of the top ten. Based on actions with

sets

measurements

conditional

continues

formation of ideas about numbers up to ten.

Learning to count begins with practical operations with sets,

crushing

elements,

comparisons

sets.

activities can be conditionally divided into separate stages, namely

the counting process and the result, in connection with which the correlated and the final are distinguished

check. By the process of counting, i.e., correlated counting (naming numbers), children

master faster. The result of the count is much more difficult to digest.

Constructing a model of a natural series of numbers, possibly after

children will become familiar with the process of establishing a one-to-one correspondence

between a set of objects, its numerical characteristics and digital

designation of this quantitative characteristic.

As more and more numbers and counting activities are learned,

the count is entered in direct order and the reverse name of the numbers, first with support

digital

designation,

notice

call numbers in reverse order, as many teaching methodologists believe,

is basic for teaching a child the process of counting, therefore

it is necessary to develop such a skill, but the task should be formulated in

form: “Say the numbers in reverse order.” (And not “count it”). Same

The tasks are formulated in this way: “Name the numbers from 9 to 5,” etc.

Pin

following

allow

exercises in increasing and decreasing numbers by 1. The teacher puts 1

object (flag, matryoshka), asks: “What number will be obtained if I

Why?".

interesting

secure

reverse

sequences

allow

exercises

ladder Children walk up and down the steps of the ladder, counting either

the number of steps they have already climbed, or the number of steps

which they still have to go through, i.e. they count first and then backward

ok. To exercise children in forward and backward counting, use

number ladder. Number ladder exercises help reinforce

knowledge about connections and relationships not only between adjacent numbers, but also

between the other numbers in the series.

Conduct a series of exercises with numerical figures. For example, along

boards in a row, the teacher arranges numerical figures with the number of circles from

places

offers

determine which figures are “lost.” A series of numerical figures can be

arranged in both forward and reverse order.

Necessarily

called

compared numbers. This is an important condition for realizing that each number

(except 1) more than one, but less than another adjacent to it, i.e. understanding

the relativity of the meaning of each number. Gradually children learn that

the expression “before” requires you to name a number less than the given one, and the expression “after”

More given.

In the older group, tasks are gradually becoming more complex and further

development of counting activities.

quantitative and ordinal numbers, groups of 2-3 subjects,

naming the total number of items.

In the senior group, you can vary the placement of recalculated

items.

learn

objects,

posted

circle, in the form of a number figure. It is important to pay attention to the fact that

skip

Multiple

exercises

lead children to the conclusion that you can start counting with any object,

The main thing is not to miss a single one.

In the older group, the nature of counting tasks involving

auditory analyzer. If in the middle group children counted only sounds, then in

the older group can combine the counting of sounds and sequential counting

objects, compare sounds and objects by quantity.

senior

preschool

age

available

which consist of several specific tasks. Games “Who knows, let

are being formed

representation

sequences

placement

natural

understanding

reciprocal

relationships between numbers within 10.

The teacher offers the children a number ladder

How many steps are there on the number ladder?

Which number is the smallest?

Which number is the largest?

What number comes after?

Children's understanding of the relationships between adjacent natural numbers

individual

items

introduced

education

groups, i.e. training based on changing the basis.

Thus,

mastering counting activities and the process of its development

is being done

result

adult-organized learning. In every age group of children

kindergarten, tasks for the development of elementary mathematical skills in children are outlined.

ideas,

in particular

development

activities,

in accordance with the “Program of education and training in kindergarten”.

Bibliography

1.White-haired

Preschool

formation

primary

submissions

natural

numbers/A.V. Beloshistaya,//Preschool

upbringing. – 2002 No. 8. pp. 20-24.

2.Volkova

Stolyarov

Development

six year olds

mathematics. / S.N. Volkova, N.N. Stolyarova // Primary school – 1990. - No. 7

– P.35 – 39.

3.Danilova

Mathematical

Preparation

preschool

institutions. M.: INFRA - M. 2004. - 154 p.

4. Karpova E.V. Didactic games in the initial period of learning. - M.:

Education, 2008. - 294 p.

5.Kozintseva

Pomerantseva

Formation

mathematical

representations.

Notes

Volgograd: Teacher, 2008. – 175 p.

6.Kolesnikova

Program

"Mathematical

steps."

Kolesnikova – M.: TC Sfera, 2007. – 64 p.

7. Komarova L.D., How to work with Cuisenaire rods? Games and exercises

on teaching mathematics to children 5-7 years old. / L.D. Komarova - M.: Publishing house

GNOM and D, 2007. – 64 p.

Counting is an activity with finite sets. Counting includes structural components: goal (to express the number of objects by number); means of achievement (a counting process consisting of a number of actions reflecting the degree of mastery of an activity); result (total number): it seems difficult for children to achieve a counting result, that is, a total, a generalization. Developing the ability to answer the question “how much?” words a lot, a little, one two, the same amount, equally, more than... speeds up the process of children understanding the knowledge of the final number when counting.

The methodology for teaching counting to children of middle preschool age is aimed at the further formation of mathematical concepts in children. One of the main program objectives of teaching children of the fifth year of life is to develop their ability to count, develop appropriate skills and, on this basis, develop an idea of ​​number.

Teaching counting within 5. Teaching counting should help children understand the purpose of this activity (only by counting objects can you accurately answer the question how many?) and master its means: naming numerals in order and relating them to each element of the group. It is difficult for four-year-old children to learn both sides of this activity at the same time. Therefore, in the middle group, it is recommended to teach counting in two stages.

AT THE FIRST STAGE, based on a comparison of the numbers of two groups of objects, the purpose of this activity is revealed to children (to find the final number). They are taught to distinguish groups of objects into 1 and 2, 2 and 3 elements and name the final number based on the teacher’s count. This “cooperation” takes place in the first two lessons.

Comparing 2 groups of objects located in 2 parallel rows, one below the other, children see which group has more (fewer) objects or there are equal parts in both. They denote these differences with numeral words and are convinced: in groups there are equal numbers of objects, their number is indicated by the same word (2 red circles and 2 blue circles), they added (removed) 1 object, there were more (fewer) of them, and the group became be designated by a new word.

Children begin to understand that each number represents a certain number of objects, and gradually learn the connections between numbers (2 > 1, 1< 2 и т. д.).

By organizing a comparison of 2 sets of objects, one of which has 1 more object than the other, the teacher counts the objects and focuses the children’s attention on the final number. He first finds out which objects are more (less), and then which number is greater and which is less. The basis for comparing numbers is children’s differentiation of the numbers of sets (groups) of objects and naming them with numeral words.

It is important that children see not only how to get the next number (n+1), but also how to get the previous number: 1 from 2, 2 from 3, etc. (n - 1). The teacher either increases the group by adding 1 item, or reduces it by removing 1 item from it. Each time, figuring out which items are more and which are less, he proceeds to comparing numbers. It teaches children to indicate not only which number is greater, but also which is less (2>1, 1<2, 3>2, 2<3 и т. д.). Отношения "больше", "меньше" всегда рассматриваются в связи друг с другом. В ходе работы педагог постоянно подчеркивает: чтобы узнать, сколько всего предметов, надо их сосчитать.

Focusing the children's attention on the final number, the teacher accompanies naming it with a generalizing gesture (circling a group of objects with his hand) and names it (i.e. pronounces the name of the object itself). During the counting process, numbers are not named (1, 2, 3 - only 3 mushrooms).

Children are encouraged to name and show where 1, where 2, where 3 are objects, which serves to establish associative connections between groups containing 1, 2, 3 objects and the corresponding numeral words.

Much attention is paid to reflecting in children’s speech the results of comparing sets of objects and numbers. ("There are more nesting dolls than cockerels. There are fewer cockerels than nesting dolls. 2 are more and 1 is less, 2 are more than 1, 1 is less than 2.")

AT THE SECOND STAGE, children master counting operations. After children learn to distinguish between sets (groups) containing 1 and 2, 2 and 3 objects, and understand that the exact answer to the question is how many? It is possible only by counting objects, they are taught to count objects within 3, then 4 and 5.

From the first lessons, learning to count should be structured so that children understand how each subsequent (previous) number is formed, i.e. general principle of constructing a natural series. Therefore, the demonstration of the formation of each next number is preceded by a repetition of how the previous number was obtained.

Consecutive comparison of 2-3 numbers allows you to show children that any natural number is greater than one and less than another, “neighboring” (3< 4 < 5), разумеется, кроме единицы, меньше которой нет ни одного натурального числа. В дальнейшем на этой основе дети поймут относительность понятий "больше", "меньше".

They must learn to independently transform many objects. For example, decide how to make the number of items equal, what needs to be done so that there are (remaining) 3 items instead of 2 (instead of 4), etc.

In the middle group, counting skills are carefully practiced. The teacher repeatedly shows and explains counting techniques, teaches children to count objects with their right hand from left to right; during the counting process, point to objects in order, touching them with your hand; Having named the last numeral, make a generalizing gesture, circle a group of objects with your hand.

Children usually find it difficult to coordinate numerals with nouns (the numeral one is replaced with the word once). The teacher selects masculine, feminine and neuter objects for counting (for example, colored images of apples, plums, pears) and shows how, depending on which objects are counted, the words one, two change. The child counts: “One, two, three.” The teacher stops him, picks up one bear and asks: “How many bears do I have?” “One bear,” the child answers. “That’s right, one bear. You can’t say “one bear.” And you have to count like this: one, two...”

A large number of exercises are used to strengthen counting skills. Counting exercises should be included in almost every lesson until the end of the school year. To create the prerequisites for independent counting, they change the counting material, the classroom environment, alternate group work with independent work of children with aids, and diversify the techniques. A variety of game exercises are used, including those that allow not only to consolidate the ability to count objects, but also to form ideas about shape, size, and contribute to the development of orientation in space. Counting is associated with comparing the sizes of objects, distinguishing geometric shapes and highlighting their features; with determination of spatial directions (left, right, ahead, behind).

Children are asked to find a certain number of objects in the environment. First, the child is given a sample (card). He is looking for which toys or things are as many as there are circles on the card. Later, children learn to act only on words. (“Find 4 toys.”) When working with handouts, we must take into account that children do not yet know how to count objects. The tasks are first given those that require them to be able to count, but not count.

Learning to count is accompanied by conversations with children about the purpose and use of counting in different types of activities. In an effort to deepen children's understanding of the meaning of counting, the teacher explains to them why people think and what they want to learn when they count objects. Advises children to see what their mothers, fathers, and grandmothers think.

So, in the middle group, under the influence of training, counting activity is formed, the ability to count various sets of objects in different conditions and relationships.

28. Tasks of pre-mathematical preparation of preschoolers.

Pre-mathematical preparation, carried out in kindergarten, is part of the general preparation of children for school and consists of developing their elementary mathematical concepts. This process is connected with all aspects of the educational work of a preschool institution and is aimed primarily at solving the problems of mental education and mathematical development of preschool children. Its distinctive features are its general developmental orientation, connection with mental, speech development, play, household, and work activities.

When setting and implementing tasks for pre-mathematical preparation of preschoolers, the following are taken into account:

Patterns of formation and development of cognitive activity, mental processes and abilities, the child’s personality as a whole;

Age-related capabilities of preschoolers in acquiring knowledge and related skills and abilities;

The principle of continuity in the work of kindergarten and school.

In the process of pre-mathematical preparation, teaching, educational and developmental tasks are solved in close unity and interconnection with each other.

By acquiring mathematical concepts, the child receives the necessary sensory experience of orientation in the various properties of objects and the relationships between them, masters the methods and techniques of cognition, and applies the knowledge and skills formed during training in practice. This creates the prerequisites for the emergence of a materialistic worldview, connects learning with the surrounding life, and cultivates positive personality traits. Let us further dwell on the main tasks of pre-mathematical preparation of children in kindergarten.

1. Formation of a system of elementary mathematical concepts in preschoolers. From the content side, the most important in the sense of forming the primary simplest ideas are such fundamental mathematical concepts as “set”, “ratio”, “number”, “magnitude”. These concepts are widely represented in primary education, but not in the literal sense, but from the point of view of propaedeutics of formation only in the idea of ​​them. Figuratively speaking, a child in kindergarten comprehends “science before science,” and naturally this is due to the fact that, in their psychological structure, elementary mathematical concepts have a figurative nature. The gradual complication of knowledge mastered by children consists of an increase in both the volume of quantitative, spatial and temporal representations, and the degree and generalization.

2. Formation of prerequisites for mathematical thinking and individual logical structures necessary for mastering mathematics at school and general mental development. The assimilation of initial mathematical concepts contributes to the improvement of the child’s cognitive activity as a whole and its individual aspects, processes, operations, and actions. The formation of logical structures of thinking - classification, ordering, understanding of the conservation of quantity, mass of volume, etc. acts as an important independent feature of the general mental and mathematical development of a preschool child.

3. Formation of sensory processes and abilities. The main direction in teaching young children is to implement a gradual transition from specific, empirical knowledge to more generalized ones. Empirical knowledge, formed on the basis of sensory experience, is a prerequisite and necessary condition for the mental and mathematical development of preschool children.

4. Expanding children's vocabulary and improving coherent speech. The process of forming elementary mathematical concepts involves the systematic assimilation and gradual expansion of vocabulary, improvement of grammatical structure and coherence of speech.

5. Formation of initial forms of educational activity. Pre-mathematical preparation also plays an important role in the development of initial forms of educational activity. Children develop the ability to listen and hear, act in accordance with the instructions of the teacher, understand and solve educational and cognitive problems in certain ways, use didactic material for their intended purpose, express in verbal form the methods and results of their own actions and the actions of their comrades, control and evaluate them, draw conclusions and generalizations, prove their correctness and other skills and abilities of educational activities. The child masters mathematical concepts mainly in classes, being in a group of peers, thereby expanding the scope and experience of collective relationships between children. In the process of forming mathematical concepts, preschoolers develop organization, discipline, arbitrariness of mental processes and behavior, activity and interest in solving problems arise.

The noted tasks of pre-mathematical preparation of preschoolers take place in each kindergarten group, but are specified taking into account age and individual characteristics. For its correct formulation and implementation, it is necessary for the teacher to know the program for the development of elementary mathematical concepts not only of the group with which he works; the use of means, methods, forms and methods of organizing work that are adequate to the tasks and level of development of children; systematic work on the implementation of tasks both in classes on the formation of mathematical concepts, and in everyday life.

Problems are solved not in isolation, but comprehensively, in close connection with each other. Being mainly aimed at the mathematical development of children, they are combined with the implementation of tasks of moral, labor, physical and aesthetic education, i.e., the comprehensive development of the personality of preschoolers. An integrated approach to their implementation is the most effective way to teach young children. Objectives determine the content of pre-mathematics training in kindergarten.

In children, visual-figurative thinking predominates. The problem is that most mathematical concepts are abstract and difficult for younger students to grasp or remember. Therefore, any mathematical operations must be based on practical actions with objects.

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

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

Let's look at each of them.

Preparing to teach mental arithmetic

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

• 3 - three little pigs;
• 4 - ninja turtles;
• 5 — fingers on the hand;
• 6 — heroes of the fairy tale “Turnip”;
• 7 - gnomes, etc.

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

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

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

Oral counting based on the composition of the number

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

Without knowledge of the appropriate tables, a child is unlikely to be able to learn to divide numbers in his head. Constant practice in the use of tables significantly improves the speed of obtaining results when performing mental calculations.

Use of computational techniques for oral counting

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

So, for example, one of the first ways to teach a child to count mentally in the 1st grade is the method of counting and “jumping.” Children quickly understand that adding 1 results in the next number, and subtracting 1 results in the previous number. Then you need to offer to meet number 2’s best friend - a frog who can jump over a number and immediately name the result of adding or subtracting 2.

The principle of performing these mathematical operations with the number 3 is explained in a similar way. The example of a bunny who can jump further away - after two numbers at once - will help with this.

Children also need to demonstrate the following techniques:

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

The counting process is facilitated by the ability to apply combinational and distributive laws. For example, 11 + 53 + 39 = (11 + 39) + 53. At the same time, children should be able to see the simplest way to count.

How to learn to count quickly in your head as an adult

An adult can use more complex algorithms for mental counting. The most convenient way to quickly count in your head is to round numbers and then add them. For example, the example 456 + 297 can be calculated like this:

• 456 + 300 = 756
• 756 - 3 = 753

Subtraction is done in the same way.

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

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

There are rules for computing operations with decimals, calculating percentages, and exponentiation.

You can learn these techniques at school or find material on the Internet, but in order to learn how to quickly count in your head based on them, you need to practice and practice again! During the training process, many results will be remembered by heart, and the child will name them automatically. He will also learn to operate with large numbers, breaking them down into simpler and more convenient terms.