Development of mathematical abilities in a child. Development of mathematical abilities in a preschooler

Mathematics is not an easy science, but it is needed always and everywhere; it is not without reason that they say that mathematics is the queen of sciences! What to do if children have difficulty mastering this subject? What does this mean and how can I help my child?

We should not think that mathematical ability is an innate gift, the presence or absence of which we will have to come to terms with. Mathematical abilities, just like others, can and should be developed. Therefore, we can not only teach a preschooler the basics of reading, writing and counting, but also work on developing the so-called mathematical mindset.

What it is? Let's say, if a child counts, adds and subtracts well, can we conclude that we have a future mathematician? In fact, computing ability is only one facet of the world mathematical science.

IN in the generally accepted sense A mathematical mindset is a predisposition to study the exact sciences, a special view of the world in which there is always a place for formulas, diagrams and tables. In addition, a mathematical mindset implies well-developed spatial, abstract and logical thinking. This is what you and I can work on. With the help of various didactic games we can develop important components in a preschooler logical thinking.

How to teach a child to compare. Comparison is expressed in the ability to see the same in the different and the different in the same. You can compare by different parameters and criteria. For example:

• What is the difference between a round table and a square one? (form)
• What is the difference between a wooden door and an iron one? (material)

You can compare objects by color, shape, size, quantity, accessory, function, etc.

Ability to generalize very useful in math lessons at school. Many problems are based on generalization. A preschool child already uses the concepts “square”, “circle”, “triangle” and even “trapezoid” in his speech, but few children are able to name all these concepts in one word. We teach the child to generalize concepts:

• Beets, cabbage, carrots are vegetables.
• Jacket, sweater, trousers - clothes.
• Doctor, teacher, builder - professions.
• Cup, plate, pan - utensils.

You can also play the game in reverse (“limit” the concept, select examples):

• Trees: .... (birch, poplar...)
• Seasons: ....
• Cutlery: ....

Analysis and synthesis. These basic mental operations are present in all areas human activity. When analyzing, the child mentally divides an object or object into its components: a plant - into roots, stems, leaves and fruits; rainbow - 7 colors; fairy tale story- for individual plot twists. Synthesis is the opposite operation of analysis. Preschoolers can guess a hidden object based on its signs, form words from letters, and sentences from words. All kinds of puzzles, including homemade ones (when we cut a picture or a geometric figure and then assemble or glue it), also help to train these skills.

More high level generalization allows the child to master the classification of objects, objects and their properties. Classification- this is the assignment of an object to a group based on species-generic characteristics. To practice this mental operation you can do the following exercises:

• We divide all animals into wild and domestic; figures - “with and without corners”.
• We remove the unnecessary things in the row: apple, pear, ball (the child must explain what is unnecessary and summarize the remaining group of objects).
• We complicate the task: apple, pear, tomato.

There are often cases when in such tasks children give incorrect answers at first glance, but if the child can justify his choice (say, he highlighted the odd one by color), then his option is worth counting.

Using the above methods, we also develop the preschooler’s speech, gradually helping him master verbal and logical thinking. For a young mathematician, the ability to correlate, reason and draw conclusions is a very useful thing.

All kinds logic puzzles, riddles, puzzles and puzzles- all this is very interesting for preschool children and trains logical thinking well. There is always some “catch” in a logical problem, and the child, knowing this, concentrates his attention and is motivated to solve, to find final result. Here are some examples of such problems:

• Masha and Tanya were drawing. One girl drew a house, another a tree. What did Masha draw if Tanya didn’t draw the house?
• Two boys were planting trees, and one was planting a bush. What did Anton plant if Leonid and Anton and Maxim and Anton planted different plants?
• Ira is 5 cm shorter than Katya. Katya is 8 cm taller than Lisa. Who is tallest?

Of course, this kind of developmental activities should not be one-time, but regular. You can entrust the development of mathematical abilities to a specialist by choosing a proven educational center, or you can work with your child yourself. Thus, by training logical thinking, we can prepare a good foundation for the child’s successful mastery of the school curriculum and understanding of mathematics.

Elena Razukhina educational psychologist educational center"Aristotle"

Discussion

Nowadays there are a lot of all kinds of manuals that help teachers and parents arouse a child’s interest in logical thinking, systematization, analysis and mathematics. I started working with both children at about 4 years old. I found appropriate notebooks and activities according to age. The most beloved Peterson, Sycheva, notebooks ed. Dragonfly and the Sunny steps series. Of course, classes are a goal system; the more understandable you make the classes for your child, the greater results you will achieve. For example, we sculpted them with hardening mass for modeling numbers and signs with the children, decorated them, and then “played” with them. They made their “money” and then played balls for completed tasks and good deeds. We started a “shop” with sweets and toys. With this “money” the children then went to this store and bought all sorts of things for themselves. The effect was with different sides: children learned to achieve something systematically, they learned to count, they learned to make choices, etc. Visualization and playful presentation are very important for children, but the latter should not be overdone, as it seems to me. Because no one will play with them at school much, and if your child is accustomed to the fact that an activity is only a game, then later this may disappoint the child when there is no game, but he will have to study and work. Therefore, everything is needed in moderation. Give examples in a language that the child can understand, for example, if a child is interested in Bakugan, then count the Bakugan, if these are Mostrey High dolls, then come up with problems from the series: there were 8 dolls at the party, then 3 girlfriends left, how many are left, etc.
Both of my children, in addition to the fact that they now know and adore mathematics, do many Olympiads with ease, have now also entered rating system best students Russia. I hope everything works out for you too! :-)

useful article. I regularly study at home with my kids. When children become interested, you won’t be able to tear them away from their studies. The most important thing is not to force it, otherwise it won’t do any good.

Thank you, interesting article, I’ll try to use the tips.

On the contrary, it always seemed to me that exactly what is inherent and can be developed

Comment on the article "Development of mathematical abilities in a preschooler: 5 ways"

At this age, the child’s interest and general abilities are important. The level of tasks is such that a capable child can solve them without preparation. Plus music, sports and dancing. This is very important and also develops mathematical abilities.

Discussion

We cook at home, ourselves)) starting at the yard school

I’m surprised by the desire to get a child involved in mathematics as early as possible... and in general the idea that “serious mathematics” is possible from the age of 6-7... Free will, of course, but, in my opinion, this is some kind of global delusion, before all because the child is simply not able to perceive and operate with abstractions...
Specifically, my child became interested in mathematics in the 7th grade, in the 8th grade she went to a club at MCSME, in the 9th grade she entered 179, and then to the Faculty of Mechanics and Mathematics at Moscow State University. Back in the fifth or sixth grade, nothing predicted that she would become a mathematician; I remember very well how annoyed I was that she was confused in simple fractions... School teacher she hasn’t changed since the 5th grade, so it’s not her fault, it’s just that the child’s brain has matured to a different level of understanding, and it became interesting.

Developing mathematical abilities in a preschooler: 5 ways. The other day I was sorting out another stack of books to prepare for school, and made a list of textbooks that I recommend buying to prepare your child for school. How to develop a child before school.

Developing mathematical abilities in a preschooler: 5 ways. The other day I was sorting out another stack of books to prepare for school, and made a list of textbooks on How to develop a child before school. And you could write a treatise on preparing for school, there’s so much there.

Discussion

1. See how he solves routine problems: does he see beautiful solutions right away or do them head-on, is there any desire to look for them at all? good solutions or decisions in general as such.
2. See how the “olympiad” solves: what is the percentage of solved, solutions, is there a desire (not in the sense of deciding Olympiad problems for hours - this rarely happens to anyone, probably, but in the sense of finishing what you started, finding a solution).
3. If he participates in olympiads, see what the result is, if at the next one school stage can show something without preparation, there is a reason to talk about abilities.
4. Well, look at how it is with abstract thinking, analysis and synthesis, this can be seen in high school.
Guided by my own criteria, I have come to the conclusion that my youngest child does not have decent mathematical abilities, but his education allows me to really evaluate.

Ehh.. with the ability to do mathematics everything is not easy, we got a little burned out on this.. (a month or so ago there was my heartbreaking post about school 57).

What I would do:
1. You can count on anything, but life makes adjustments.
2. Mathematics is a useful thing in any way, even if it does not become a specialty. It puts your brain in order, yes.
3. Interest is more important than ability. Because they give motivation to study at a difficult age. But I didn’t rely only on mathematics, this is not a specialty.

From my point of view, “learning strategy” can be of 2 types.
A. The child passionately wants to learn something specific (mathematics, physics, biology, even classical philology). It might make sense to get fundamental education(the same Moscow State University and close to this). But. But. Then you will have to complete your studies - either a second education (at whose expense?) or go to work in fact not in your specialty. We don't take geniuses into account.
B. There is a readiness and even a certain interest in some kind of specialty - just so that there is a piece of bread, not sitting on the parents’ necks, and in the future feeding the family. Then education is based on this specialty - well, so that it is not completely disgusting to study this (but this is about studying at a university). Well, it was possible to get minimal training for the Unified State Exam (and sometimes this is nonsense - why does a doctor or psychologist need mathematics??? - only a few people study medical statistics, and even there there is not much to learn).

It seems to me that option “B” is more reasonable, especially taking into account your large number of children. True, I followed option “A” - but then everything changed so quickly that “B” was difficult to implement.

If “B”, then it is NOT SO IMPORTANT whether you have an aptitude for mathematics or not. One thing is important - to understand certain mathematical methods in order to use them meaningfully. They are their own for an engineer, their own for an economist, and third for someone else.
This is the most important thing - DOES the child UNDERSTAND the basic methods he uses?

For example, can one derive the formula for the same roots quadratic equation yourself, without looking at the book? Or prove the Pythagorean theorem? Print the sum of arithmetic and geometric progression? I deliberately take something relatively simple, maybe a little more complicated. But it is obligatory that he taught a year ago or earlier, so he no longer remembers the evidence.

If not, then it’s worth considering how practical mathematics is used in what your son will do. Less important, but also something to consider, is how much there is in the university curriculum.

Well, about choosing a school. It’s good when mathematics is higher than the school curriculum, but super-duper physics lyceum IMHO is not a very good option. But this is ours personal experience, everyone has their own, there are good options.

Mathematical abilities are also abilities; you either have them or you don’t. They usually appear very early or just early, as if the pregnancy was normal and childbirth is also there, if the child is healthy, then it can be developed. A normal teacher is needed.

Discussion

I read an interview with Sergei Rukshin, the head of the St. Petersburg math circle from which the notorious Perelman and Stanislav Smirnov, a Fields Medal winner, came out. He writes that absolutely anyone can be taught, regardless of gender or ability. But he emphasizes that mathematics is a way of life, it requires full dedication.

Are there math genes? Education, development. Child from 7 to 10. Are there math genes? Yesterday I talked to my dad. In my opinion, the child is still too young for anything to be said about his abilities.

Discussion

I doubt something about genes :) we have at least two generations of “mathematicians”, i.e. those who love and understand and she has never caused problems, but our son knows who he is: (somehow it seems to me that at his age mathematics was much easier, maybe, of course, the program was simpler..

I suspect that the atmosphere in the family has a much greater influence. AND math lovers Since childhood, parents have been throwing problems everywhere they can. And those who are gifted in literature learn to speak beautifully. Exactly the same thing in between. And the musicians sing.

It seems to me that 90% of a child’s abilities are determined by genes, but such qualities as perseverance, character and perseverance are determined only by upbringing. Dear parents and psychologists, please express your opinions on how to develop these qualities in children?

Discussion

Real, meaningful things for the child. Yesterday my daughter spent two hours drawing an illustration for a book. She loves to draw, hence the “meaningfulness” - but what is needed for the job is “perseverance” and the list goes on :-)

My opinion is exactly the opposite of yours, but I won’t give the exact percentages. Abilities depend much more on how the child spent his early (very early) childhood, i.e. from the environment. And perseverance, perseverance and character are more genes. This is more determined by the functioning of the nervous system.

At the Olympics they are looking for children with developed abilities- the children with whom we were involved in development, it wasn’t necessary, well, I don’t agree at all about “fading”, mathematical abilities do not disappear anywhere... maybe they don’t become mathematicians (mathematics...

Discussion

I would like to apologize to Sephia for the fact that with my message I diverted the discussion on the proposed topic a little.
It’s simple, everything is so interconnected (primary school -> specific program -> level of teaching -> teacher’s obsession ->
student interest - > result (grade, desire to learn beyond the program).
Mathematics is difficult and very interesting science, and therefore there is something to talk about. Topics cling one after another :-))
“I can’t understand – is this a problem with the school (they don’t teach you to think?), the program (weak?), the child (not capable?), or mine (am I doing it wrong?) Or do I want too much?”
Sephia did not write what program her daughter is studying in, but this program may at the same time be sufficient for other “weaker” classmates, and be a definite inhibitor for her “advanced” girl. And the fact that some teachers replace the ability to think with templates and memorization - this, unfortunately, is the case:-(
This conf is read (some write) very much interesting people. If they do this, then EVERYONE is definitely puzzled by the good
raising their children and the desire to give quality education. Otherwise they wouldn't come here.
So let's try to help our children and ourselves. Whoever can do what.
Who will bring interesting problems, who will share a non-standard solution to the problem. Whoever can. Perhaps we will cope with the problems of our education.

I also wanted to write about a “mathematical” topic, but I still don’t have enough time. My daughter is in 2nd grade. In mathematics a solid A,
There are simply no other assessments. They study according to Morro and Uzorova (30,000 tasks for oral calculation). But it seems to me that this is not enough.
Out of 28 people, only three are excellent students. In 1st grade, at the beginning of the year, the teacher suggested that parents take a course on Heidman in addition to the main course. There were immediately mothers who were categorically against it, citing their heavy workload.
children in English language (special school). That's where we stopped. Me and two other mothers bought a textbook on our own and studied on our own.
At the beginning of the 3rd quarter, my daughter was told that on the weekend she and her classmate would go to the district Olympiad in mathematics.
She comes home on Friday (the eve of the Olympiad) and says that in class they did work, based on the results of which they will select children for the next Olympiad. He says that no one in the class solved one problem. Here is her condition:
There were 15 birds sitting on two bushes. When 2 birds flew from the 1st to the second, and 3 birds flew away from the second, the second bush became 4
There are more birds than in the first one.
How many birds were there on each bush at the beginning?
Let me make a reservation right away that they have not yet gone through multiplication and division. During the summer holidays after 1st grade they were asked to start
learn the multiplication table.
I was surprised by this task, because... in my opinion, it did not correspond to the program they were studying.
But my daughter was interested in how this problem was solved. I told her how to solve it first in one way (15-3=12, 12:2=6, 12 -4= 8,
8:2=4, 4+2=6, 15-6=9), and then she told me how to designate the unknown through X. We solved this problem, and then came up with
a couple more like this. We studied for an hour. My daughter understood everything and liked it.
The next day, after the Olympics, she comes out happy and says that one problem was similar, and she immediately beat it
decided.
So I had a question: is it possible to identify gifted children at the Olympiad in this way?
IMHO, no. This example suggests that certain programs are simply lagging behind. I didn’t tell my daughter the day before about the solution -
and she couldn't. By the way, she then took 3rd place.
It’s a pity that I still can’t get the conditions for all the problems from the Olympiad. I'm very interested in seeing the rest.

Child from 3 to 7. Education, nutrition, daily routine, visiting kindergarten and relationships with teachers, illnesses and I would like not to miss out, if anything... And please share who has any successes (in general, not just mathematical ones) in 3 years...

Discussion

Girls Olya, Irina, Murzya, Gazelle, sorry, but you are not entirely right when you say, “counts to 10, 20,” etc. The child does not count, but names numbers from 1 to 10, 20, etc. Irina correctly said that such “counting” is mechanical and not meaningful.
There is a certain number - 5 fingers, there are the numerals "one", "two".. And there are also symbols - the numbers 1 2 3 4 5... When the child masters all three concepts and combines them into something whole, for example, name "three", show 3 objects or imagine 3 objects in your mind, and then also math. performs the action, then, in my opinion, we can talk about what the child believes.
Olya Your son is a great guy, because... really counts (“you have an apple, they gave you another”), and besides, he moved from the concrete - counting objects, to the abstract - imagining a certain number and adding it up in his mind.

P.S. My son is exactly 4. He started talking early and at the age of 2 he “counted” to 15. For his birthday (2 years old) he was given a toy - a house, the roof is divided into 6 sectors with a hole in the shape of some animal, there are 6 in the walls of the house door different colors with holes in the form of geometric contours. items + animal inserts, geom inserts. bodies. Sasha immediately remembered the new colors - pink, orange.
After I called each one a geom a couple of times. body and hole, two-year-old Sasha remembered a square, cube, circle, ball, prism, triangle, oval. I realized that a child absorbs like a sponge everything he sees and touches. This knowledge just needs to be systematized in your head. It's the same with the score.

Nastya is 2 and 9. She counts up to 20, but can’t go further (she asks what 30, 40, etc. is called, i.e. she asks what 30 is called, and then counts 31, 32...). In the mind he adds and subtracts only up to 5, if more, then on the fingers (if it’s a plus, then count all the fingers, apples, etc. together, and if it’s a minus, then the part needs to be closed :-))). She really likes arithmetic, but it seems to me that this is more training than a manifestation of mathematical abilities...
He has known geometric figures (both flat and three-dimensional) for a very long time, but again more due to the fact that they played a lot with Montessori frames and Nikitin Kradrats, building from various three-dimensional figures.

Svetlana Zubkova
Formation of mathematical abilities: ways and forms

5 areas are defined.

Formation of elementary mathematical performances of preschoolers,

included in educational field "Cognition" and involves the development in children

cognitive interests, as well as intellectual advancement, through

development of cognitive research activities, FCCM.

According to curriculum work in each age group mathematical

development consists of five sections: "Quantity and Counting", "Value", "Geometric

figures", "Orientation in space", "Orientation in time"

Mathematics- one of the most difficult educational subjects but she has

unique developmental effect. Her study promotes memory development, speeches,

imagination, emotions; builds perseverance, patience, creativity

personality.

Children need to be taught not only to calculate and measure, but also to reason.

The potential of a teacher does not lie in the transfer of certain mathematical knowledge And

skills, and in introducing children to material giving food to the imagination,

affecting not only the purely intellectual, but also emotional sphere child.

The teacher's task: do a lesson on femp entertaining and unusual. Want

remind you of the ancient proverb: “I hear - I forget, I see - and I remember, I

I do - and I understand"

The teacher must make the child feel that he can understand and learn not

only private concepts, but also general patterns. And the main thing is to know the joy of

overcoming difficulties.

Full mathematical development is ensured by organized

purposeful activity during which the teacher puts children in front of

cognitive tasks and helps to solve them, and this is both GCD and activities in everyday life

During directly educational FEMP activities are being decided on a number of

software tasks.

1) educational

2) developing

3) educational,

4) speech

When moving from one software task to another, it is very important to constantly

return to the topic covered, which ensures correct assimilation material.

There must be a surprise moment fairy-tale heroes, connection between everyone

didactic games.

The entire lesson on FEMP is based on clarity.

The teacher must remember that visibility is not an end in itself, but a means of learning.

Poorly chosen visual material distracts children's attention and interferes with learning

knowledge, correctly selected increases the effectiveness of learning.

Two types of visuals are used material(Demonstration, handout.)

Both demonstration and distribution material must meet aesthetic

requirements: attractiveness is of great importance in learning - with beautiful aids, children will find it more interesting to study. And the brighter and deeper the children’s emotions, the more complete

the interaction of sensory and logical thinking, the more intensively it takes place

activity, and children acquire knowledge more successfully.

In progress formation of elementary mathematical representations

For preschoolers, the teacher uses the choice of optimal methods training: practical,

visual, verbal, playful.

When choosing a method, a number of factors are taken into account factors: software tasks, solved on

at this stage, age and individual characteristics children, availability of necessary

didactic means.

The leading method is practical method– these are exercises, game tasks,

didactic games, didactic exercises. The child must not only listen,

perceive, but must also participate in the performance of a particular task. Most

educational games are widely used; they are effective means And

method formation of elementary mathematical representations . Game as a method

training involves the use of individual elements in the classroom different types games

(plot, movement, game techniques (competition, search).

Subject and word games are carried out in and outside of class.

And the more the child plays educational games and completes tasks, the more

will learn better material on FEMP.

Didactic tools should change not only taking into account age

features, but depending on the relationship between the concrete and the abstract at different

stages of children's assimilation of software material. Didactic the material must be

artistically issued.

For example: real objects can be replaced by numerical figures, and they

In kindergarten it is widely techniques are used:show (demonstration, instruction,

explanation, clarification, instructions, questions for children.

Modeling is a visual and practical technique, including the creation of models and their

use for the purpose formation of elementary mathematical concepts in

Mathematics is an exact science, and it is necessary for children to learn to express accurately and coherently

your thoughts. Formation correct speech is an integral part of mental

raising a child. The richer the speech, the wider the opportunities for knowledge

reality, full communication, development of correct thinking.

Model of educational activities according to FMEP:

1. The teacher’s competence in the field of educational activities.

2. The teacher’s readiness for direct educational activities.

3. Selection of optimal methods and techniques

4. Correct selection of demonstration and distribution materials material.

5. Grammatically correct speech teacher

Conclusion.

Mathematics- one of the most difficult subjects in school. They talk about this too

parents and teachers and the students themselves. And preschoolers don’t know that mathematics-

difficult discipline. And they should never know about it.

Our task is to teach the child to comprehend mathematics with interest and pleasure and

always believe in yourself.

Publications on the topic:

Relevance Mathematics is one of the most difficult academic subjects. Teacher's potential preschool does not consist in transferring those.

Formation and development of logical and mathematical abilities in preschool children Formation and development of logical and mathematical abilities in children preschool age and the problem psychological readiness to learning.

Abstract of GCD on the formation of elementary mathematical abilities in the senior group “Tsvetik-Semitsvetik” SUMMARY OF NODS IN THE EDUCATIONAL FIELD “COGNITIVE DEVELOPMENT” Formation of elementary mathematical abilities. Integration with others.

“Without play there is not and cannot be full-fledged mental development. The game is a huge bright window through which spiritual world child.

Mathematics manual for flannelgraph. The manual turned out to be multifunctional, so the goals and objectives are varied. This manual contains.

First of all, you should evaluate natural talent trainee. The choice of further teaching methods will depend on this.

Natural affinity for mathematics

There are several important criteria for assessing abilities:

• knowledge of numerical and symbolic symbols;
• ability for logical thinking;
• ability for abstract thinking.

The lack of these abilities does not mean that you should give up learning. Just training should be carried out with a specialist and using special techniques.

Mathematical through testing, both in paper and electronic versions.

Development of mathematical abilities in a child

If you want to develop your child's ability to exact sciences, then you should submit the material to game form and under no circumstances force you to study. Great value has contact with the teacher during the learning process, as well as the teacher’s ability to interest the student.

It should be remembered that children cannot sit in one place for a long time, so trying to force a child to sit and learn the material can only lead to a reluctance to learn. Today, there are special teaching methods for children. And remember that the knowledge base laid down in childhood is the foundation of future abilities.

Ways to develop mathematical abilities

Having assessed the student’s natural abilities, mathematical abilities should be developed in accordance with his capabilities. While pursuing mathematics, a person must follow several rules.

1. Regular brain training, solving problems and examples in the mind, performing calculations without computing devices, solving non-standard tasks, building logical chains help develop mathematical abilities.
2. Studying new products in the field of programming, mathematics, and biographies of famous personalities will help to intensify interest in mathematics.
3. Look for leisure activities that will help develop logic, thinking, and memory. Crosswords and numbers, problems, puzzles, Board games and many other activities make you think, do mental calculations, and memorize numbers.
4. Spend more time walking outdoors.
5. Lead healthy image life: smoking, alcoholism and other bad habits negatively affect brain function.
6. Compliance with the study and rest regime helps to stay in good shape, not get tired and make progress on the path to studying any subjects, including the exact sciences.

When developing mathematical abilities, one should also pay great attention to the process of independently searching for solutions and developing the student’s memory. The age of the child also plays an important role when choosing teaching methods. If preschool children very easily perceive everything new and learn, then an adult is less receptive to new material and remembers worse. Methods preschool development are as efficient as possible; This is not only memorizing numbers, but solving problems on logical thinking, as well as developing the child’s fine motor skills.

It is worth considering the fact that the development of mathematical abilities is also necessary for a child with pronounced humanitarian talents. After all modern man must be comprehensively developed to adapt to living conditions in the world of innovative technologies.

Introduction

The concept of “development of mathematical abilities” is quite complex, comprehensive and multifaceted. It consists of interrelated and interdependent ideas about space, form, size, time, quantity, their properties and relationships, which are necessary for the formation of “everyday” and “scientific” concepts in a child.

The mathematical development of preschoolers is understood as qualitative changes V cognitive activity child, which occur as a result of the formation of elementary mathematical concepts and related logical operations. Mathematical development is a significant component in the formation of a child’s “picture of the world.”

The development of mathematical concepts in a child is facilitated by the use of a variety of didactic games. In the game, the child acquires new knowledge, skills and abilities. Games that promote the development of perception, attention, memory, thinking, development creativity, are aimed at the mental development of the preschooler as a whole.

In elementary school, the mathematics course is not at all easy. Children often experience various kinds difficulties in mastering the school mathematics curriculum. Perhaps one of the main reasons for such difficulties is the loss of interest in mathematics as a subject.

Therefore, one of the most important tasks educator and parents - to develop a child’s interest in mathematics in preschool age. Introduction to this subject in the game and in an entertaining way will help your child learn the school curriculum faster and easier in the future.

1 DEVELOPMENT OF MATHEMATICAL ABILITIES IN PRESCHOOL CHILDREN

1.1 Specifics of the development of mathematical abilities

In connection with the problem of the formation and development of abilities, it should be noted that whole line Research by psychologists is aimed at identifying the structure of schoolchildren’s abilities to various types activities. At the same time, abilities are understood as a complex of individual psychological characteristics of a person that meet the requirements of a given activity and are a condition successful implementation. Thus, abilities are a complex, integral, mental formation, a kind of synthesis of properties, or, as they are called, components.

The general law of the formation of abilities is that they are formed in the process of mastering and performing those types of activities for which they are necessary.

Abilities are not something predetermined once and for all, they are formed and developed in the process of learning, in the process of exercise, mastering the corresponding activity, therefore it is necessary to form, develop, educate, improve the abilities of children and it is impossible to predict in advance exactly how far this development can go.

Talking about math skills as traits mental activity, we should first of all point out several common misconceptions among teachers.

First, many people believe that mathematical ability lies primarily in the ability to perform quick and accurate calculations (particularly in the mind). In fact, computational abilities are not always associated with the formation of truly mathematical (creative) abilities. Secondly, many people think that schoolchildren who are capable of mathematics have a good memory for formulas, figures, and numbers. However, as academician A. N. Kolmogorov points out, success in mathematics is least of all based on the ability to quickly and firmly memorize a large number of facts, figures, formulas. Finally, it is believed that one of the indicators of mathematical ability is the speed of thought processes. A particularly fast pace of work in itself has nothing to do with mathematical ability. A child can work slowly and deliberately, but at the same time thoughtfully, creatively, and successfully progress in mastering mathematics.

Krutetsky V.A. in the book “Psychology of Mathematical Abilities of Preschool Children,” he distinguishes nine abilities (components of mathematical abilities):

1) The ability to formalize mathematical material, to separate form from content, to abstract from specific quantitative relationships and spatial forms and operating with formal structures, structures of relationships and connections;

2) The ability to generalize mathematical material, to isolate the main thing, abstracting from the unimportant, to see the general in what is externally different;

3) Ability to operate with numerical and symbolic symbols;

4) The ability for “consistent, correctly dissected logical reasoning” associated with the need for evidence, justification, and conclusions;

5) The ability to shorten the reasoning process, to think in collapsed structures;

6) Reversibility thought process(to the transition from direct to reverse train of thought);

7) Flexibility of thinking, the ability to switch from one mental operation to another, freedom from the constraining influence of templates and stencils;

8) Mathematical memory. It can be assumed that she characteristics also follow from the peculiarities of mathematical science, that it is memory for generalizations, formalized structures, logic;

9) The ability for spatial representations, which is directly related to the presence of such a branch of mathematics as geometry.

1.2 Formation of children’s mathematical abilities

preschool age. Logical thinking

Many parents believe that the main thing in preparing for school is to introduce the child to numbers and teach him to write, count, add and subtract (in fact, this usually results in an attempt to memorize the results of addition and subtraction within 10). However, when teaching mathematics using textbooks of modern developmental systems (L.V. Zankov’s system, V.V. Davydov’s system, the “Harmony” system, “School 2100”, etc.), these skills do not help the child in mathematics lessons for very long. The stock of memorized knowledge ends very quickly (in a month or two), and the lack of development of one’s own ability to think productively (that is, to independently perform the above-mentioned mental actions on mathematical content) very quickly leads to the appearance of “problems with mathematics.”

At the same time, a child with developed logical thinking always has more chances be successful in mathematics, even if he was not previously taught the elements of the school curriculum (counting, calculations and

etc.). It is no coincidence that last years in many schools working on developmental programs, an interview is conducted with children entering the first grade, the main content of which is questions and tasks of a logical, and not just arithmetic, nature. Is this approach to selecting children for education logical? Yes, it is natural, since the mathematics textbooks of these systems are structured in such a way that already in the first lessons the child must use the ability to compare, classify, analyze and generalize the results of his activities.

However, one should not think that developed logical thinking is a natural gift, the presence or absence of which should be accepted. There is a large number of studies confirming that the development of logical thinking can and should be done (even in cases where the child’s natural abilities in this area are very modest). First of all, let's figure out what logical thinking consists of.

Logical tricks mental actions- comparison, generalization, analysis, synthesis, classification, seriation, analogy, systematization, abstraction - in the literature they are also called logical methods of thinking. When organizing special developmental work on the formation and development of logical thinking techniques, a significant increase in the effectiveness of this process is observed, regardless of the initial level of development of the child.

To develop certain mathematical skills and abilities, it is necessary to develop the logical thinking of preschoolers. At school they will need the skills to compare, analyze, specify, and generalize. Therefore, it is necessary to teach the child to decide problematic situations, draw certain conclusions, come to a logical conclusion. Solution logical problems develops the ability to highlight the essential and independently approach generalizations (see Appendix).

Entertaining tasks contribute to the development of the child’s ability to quickly perceive cognitive tasks and find solutions for them right decisions. Children begin to understand that in order to correctly solve a logical problem it is necessary to concentrate; they begin to realize that such an entertaining problem contains a certain “catch” and in order to solve it it is necessary to understand what the trick is.

Logic puzzles can be as follows:

Two sisters have one brother each. How many children are in the family? (Answer: 3)

It's obvious that constructive activity In the process of performing these exercises, the child develops not only the child’s mathematical abilities and logical thinking, but also his attention, imagination, trains motor skills, eye, spatial concepts, accuracy, etc.

Each of the exercises given in the Appendix is ​​aimed at developing logical thinking techniques. For example, exercise 4 teaches the child to compare; exercise 5 - compare and generalize, as well as analyze; Exercise 1 teaches analysis and comparison; exercise 2 - synthesis; exercise 6 - actual classification by attribute.

The logical development of a child also presupposes the formation of the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build simple conclusions based on cause-and-effect relationships.

Thus, two years before school you can provide significant impact on the development of mathematical abilities of a preschooler. Even if the child is not a sure winner mathematical olympiads, he will not have problems with mathematics in elementary school, and if he does not have them in elementary school, then there is every reason to expect that he will not have them in the future.

2 DIDACTIC GAMES IN THE PROCESS OF MATHEMATICAL DEVELOPMENT OF PRESCHOOL CHILDREN

2.1 The role of educational games

The didactic game as an independent gaming activity is based on the awareness of this process. Independent play activity is carried out only if children show interest in the game, its rules and actions, if these rules have been learned by them. How long can a child be interested in a game if its rules and content are well known to him? This is a problem that needs to be solved almost directly in the process of work. Children love games that are familiar to them and enjoy playing them.

What is the significance of the game? In the process of playing, children develop the habit of concentrating, thinking independently, developing attention, and the desire for knowledge. Being carried away, children do not notice that they are learning: they learn, remember new things, navigate unusual situations, replenish their stock of ideas and concepts, and develop their imagination. Even the most passive of children join the game with great desire and make every effort not to let their playmates down.

In the game, the child acquires new knowledge, skills and abilities. Games that promote the development of perception, attention, memory, thinking, and the development of creative abilities are aimed at the mental development of the preschooler as a whole.

Unlike other activities, play contains a goal in itself; The child does not set or solve extraneous and separate tasks in the game. A game is often defined as an activity that is performed for its own sake and does not pursue extraneous goals or objectives.

For preschool children, play is of exceptional importance: play for them is study, play for them is work, play for them is a serious form of education. A game for preschoolers is a way of learning about the world around them. Play will be a means of education if it is included in a holistic pedagogical process. By directing the game, organizing the life of children in the game, the teacher influences all aspects of the development of the child’s personality: feelings, consciousness, will and behavior in general.

However, if for the student the goal is the game itself, then for the adult organizing the game there is another goal - the development of children, their acquisition of certain knowledge, the formation of skills, the development of certain personality qualities. This, by the way, is one of the main contradictions of the game as a means of education: on the one hand, there is no goal in the game, and on the other, the game is a means of purposeful personality formation.

This is most evident in the so-called didactic games. The nature of the resolution of this contradiction determines the educational value of the game: if achievement didactic purpose will be carried out in the game as an activity that contains a goal in itself, then its educational value will be the most significant. If the didactic task is solved in game actions, the purpose of which for their participants is this didactic task, then the educational value of the game will be minimal.

A game is valuable only if it contributes to a better understanding of the mathematical essence of the issue, clarification and formation of students’ mathematical knowledge. Didactic games and game exercises stimulate communication, since in the process of these games the relationship between children, child and parent, child and teacher begins to be more relaxed and emotional character.

Free and voluntary inclusion of children in the game: not imposing the game, but involving children in it. Children must understand well the meaning and content of the game, its rules, and the idea of ​​each game role. The meaning of game actions must coincide with the meaning and content of behavior in real situations so that the main meaning of game actions is transferred to real life activities. The game should be guided by socially accepted moral standards based on humanism, universal human values. The game should not humiliate the dignity of its participants, including the losers.

Thus, a didactic game is a purposeful creative activity, during which students comprehend the phenomena of the surrounding reality more deeply and clearly and learn about the world.

2.2 Methods of teaching counting and basic mathematics to preschool children through play activities

IN modern schools the programs are quite rich, there are experimental classes. In addition, new technologies are entering our homes more and more rapidly: many families are purchasing computers to educate and entertain their children. Life itself demands knowledge of the basics of computer science. All this makes it necessary for a child to become acquainted with the basics of computer science already in preschool period.

When teaching children the basics of mathematics and computer science, it is important that when they start school they have the following knowledge:

Counting to ten in ascending and descending order, the ability to recognize numbers in a row and separately, quantitative (one, two, three...) and ordinal (first, second, third...) numbers from one to ten;

Previous and subsequent numbers within one ten, the ability to compose numbers of the first ten;

Recognize and depict basic geometric shapes (triangle, quadrangle, circle);

Shares, the ability to divide an object into 2-4 equal parts;

Basics of measurement: a child must be able to measure length, width, height using a string or sticks;

Comparing objects: more - less, wider - narrower, higher - lower;

Fundamentals of computer science, which are still optional and include an understanding of the following concepts: algorithms, information coding, computer, program, control computer, the formation of basic logical operations - “not”, “and”, “or”, etc.

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.

The development of mathematical concepts in a child is facilitated by the use of a variety of didactic games. Such games teach the child to understand some complex mathematical concepts, form an understanding of the relationship between numbers and numbers, quantities and numbers, develop the ability to navigate in the directions of space, and draw conclusions.

When using didactic games, they are widely used various items And visual material, which ensures that classes are fun, entertaining and accessible form.

If your child has difficulty counting, show him, counting out loud, two blue circles, four red, three green. Ask him to count the objects out loud himself. Constantly count different objects (books, balls, toys, etc.), from time to time ask the child: “How many cups are there on the table?”, “How many magazines are there?”, “How many children are walking on the playground?” and so on.

Acquiring skills oral counting helps teach children to understand the purpose of some household items on which numbers are written. Such items are a watch and a thermometer.

Such visual material opens up scope for imagination when carrying out various games. After teaching your baby how to measure temperature, ask him to measure the temperature on an outdoor thermometer every day. You can keep a record of the air temperature in a special “magazine”, noting daily temperature fluctuations in it. Analyze the changes, ask your child to determine the decrease and increase in temperature outside the window, ask how many degrees the temperature has changed. Together with your child, draw up a chart of air temperature changes over a week or month.

When reading a book to a child or telling fairy tales, when numerals are encountered, ask him to put down as many counting sticks as, for example, there were animals in the story. After you have counted how many animals there were in the fairy tale, ask who there were more, who were fewer, and who were the same number. Compare toys by size: who is bigger - a bunny or a bear, who is smaller, who is the same height.

Let the preschooler come up with fairy tales with numerals himself. Let him say how many heroes there are, what kind of characters they are (who is bigger - smaller, taller - shorter), ask him to put it aside during the story counting sticks. And then he can draw the heroes of his story and talk about them, compose them verbal portraits and compare them.

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.

Preparatory work for teaching children elementary mathematical operations Addition and subtraction involves developing skills such as breaking down numbers into their component parts and identifying the previous and following numbers within the top ten.

In a playful way, children have fun guessing the previous and next numbers. Ask, for example, what number is greater than five, but less than seven, less than three, but greater than one, etc. Children love to guess numbers and guess what they have in mind. Think of, for example, a number within ten and ask your child to name different numbers. You say whether the named number is greater than or less than what you had in mind. Then switch roles with your child.

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 necessary to introduce the baby to basic geometric shapes. Show him a rectangle, a circle, a triangle. Explain what a rectangle (square, rhombus) can be. Explain what a side is and what an angle is. Why is a triangle called a triangle (three angles). Explain that there are other geometric shapes that differ in the number of angles.

Let the child make geometric shapes from sticks. You can give it the required dimensions based on the number of sticks. Invite him, for example, to fold a rectangle with sides of three sticks and four sticks; triangle with sides two and three sticks.

Also make shapes of different sizes and shapes with different amounts chopsticks Ask your child to compare the shapes. Another option would be combined figures, in which some sides will be common.

For example, from five sticks you need to simultaneously make a square and two identical triangles; or make two squares from ten sticks: large and small ( small square made up of two sticks inside a large one). Using chopsticks is also useful to form letters and numbers. In this case, a comparison of concept and symbol occurs. Let the child match the number made up of sticks with the number of sticks that makes up this number.

It is very important to instill in your child the skills necessary to write numbers. To do this, it is recommended to carry out a lot of preparatory work with him, aimed at understanding the layout of the notebook. Take a squared notebook. Show the cell, its sides and corners. Ask your child to place a dot, for example, in the lower left corner of the cage, in the upper right corner, etc. Show the middle of the cage and the midpoints of the sides of the cage.

Show your child how to draw simple patterns using cells. To do this, write individual elements, connecting, for example, the upper right and lower left corners of the cell; upper right and left corners; two dots located in the middle of adjacent cells. Draw simple “borders” in a checkered notebook.

It is important here that the child himself wants to study. Therefore, you cannot force him, let him draw no more than two patterns in one lesson. Such exercises not only introduce the child to the basics of writing numbers, but also instill fine motor skills, which will greatly help the child in learning to write letters in the future.

Logic games mathematical content is taught to children cognitive interest, ability for creative search, desire and ability to learn. An unusual game situation with problematic elements characteristic of each entertaining task always arouses interest in children.

Entertaining tasks help develop a child’s ability to quickly perceive cognitive problems and find the right solutions for them. Children begin to understand that in order to correctly solve a logical problem it is necessary to concentrate; they begin to realize that such an entertaining problem contains a certain “catch” and in order to solve it it is necessary to understand what the trick is.

If the child cannot cope with the task, then perhaps he has not yet learned to concentrate and remember the condition. It is likely that while reading or listening to the second condition, he forgets the previous one. In this case, you can help him draw certain conclusions from the conditions of the problem. After reading the first sentence, ask your child what he learned and understood from it. Then read the second sentence and ask the same question. And so on. It is quite possible that by the end of the condition the child will already guess what the answer should be.

Solve a problem out loud yourself. Draw specific conclusions after each sentence. Let your baby follow your thoughts. Let him understand how problems of this type are solved. Having understood the principle of solving logical problems, the child will be convinced that solving such problems is simple and even interesting.

Regular riddles created folk wisdom, also contribute to the development of the child’s logical thinking:

Two ends, two rings, and in the middle there are nails (scissors).

The pear is hanging, you can’t eat it (light bulb).

In winter and summer, one color (Christmas tree).

The grandfather is sitting, dressed in a hundred fur coats; whoever undresses him sheds tears (bow).

Knowledge of the basics of computer science is currently not mandatory for studying in primary school, compared, for example, with the skills of counting, reading or even writing. However, teaching preschoolers the basics of computer science will certainly bring some benefits.

First, the practical benefits of learning the basics of computer science will include the development of abstract thinking skills. Secondly, in order to master the basics of actions performed with a computer, a child will need to use the ability to classify, highlight the main thing, rank, compare facts with actions, etc. Therefore, by teaching your child the basics of computer science, you not only give him new knowledge that will be useful to him when mastering a computer, but you also strengthen some skills along the way general.

There are also games that are not only sold in stores, but also published in various children's magazines. These are board games with a playing field, colored chips and cubes or a top. The playing field usually shows various pictures or even whole story and there are turn-by-turn directions. According to the rules of the game, participants are invited to throw a dice or a top and, depending on the result, perform certain actions on the playing field. For example, when a number is rolled, the participant can begin his journey in the game space. And having made the number of steps that fell on the die, and getting into a certain area of ​​the game, he is asked to perform some concrete actions, for example, jump three steps forward or return to the beginning of the game, etc.

Thus, in a playful way, the child is instilled with knowledge from the field of mathematics, computer science, and the Russian language, he learns to perform various actions, develop memory, thinking, and creativity. During the game, children acquire complex mathematical concepts, learn to count, read and write. The most important thing is to instill in the child an interest in learning. To do this, classes should be held in a fun way.

CONCLUSION

In preschool age, the foundations of the knowledge a child needs in school are laid. Mathematics represents complex science, which may cause certain difficulties during schooling. In addition, not all children are inclined and have a mathematical mind, so when preparing for school it is important to introduce the child to the basics of counting.

Both parents and teachers know that mathematics is a powerful factor intellectual development child, the formation of his cognitive and creative abilities. The most important thing is to instill in the child an interest in learning. To do this, classes should be held in a fun way.

Thanks to games, it is possible to concentrate the attention and attract the interest of even the most disorganized preschool children. At the beginning, they are captivated only by game actions, and then by what this or that game teaches. Gradually, children awaken interest in the subject of study itself.

Thus, in a playful way, instilling in a child knowledge in the field of mathematics, teach him to perform various actions, develop memory, thinking, and creative abilities. In the process of playing, children learn complex mathematical concepts, learn to count, read and write, and in the development of these skills the child is helped by close people - his parents and teacher.

Bibliography

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Application

Exercises to develop mathematical abilities for children five to seven years old

Exercise 1

Material: set of figures - five circles (blue: large and two small, green: large and small), small red square).

Assignment: “Determine which of the figures in this set is extra. (Square) Explain why. (All the rest are circles).”

Exercise 2

Material: the same as for Exercise 1, but without the square.

Assignment: “The remaining circles were divided into two groups. Explain why you divided it this way. (By color, by size).”

Exercise 3

Material: the same and cards with numbers 2 and 3.

Assignment: “What does the number 2 mean on circles? (Two large circle, two green circles.) Number 3? (Three blue circles, three small circles)."

Exercise 4

Material: the same didactic set (a set of plastic figures: colored squares, circles and triangles).

Assignment: “Remember what color was the square that we removed? (Red.) Open the “Didactic Set” box. Find the red square. What other colors are there squares? Take as many squares as there are circles (see exercises 2, 3). How many squares? (Five.) Can you make one big square out of them? (No.) Add as many squares as needed. How many squares did you add? (Four.) How many are there now? (Nine.)".

Exercise 5

Material: images of two apples, a small yellow one and a large red one. The child has a set of shapes: a blue triangle, a red square, a small green circle, a large yellow circle, a red triangle, a yellow square.

Assignment: “Find one that looks like an apple among your figures.” An adult offers to look at each image of an apple in turn. The child selects a similar figure, choosing a basis for comparison: color, shape. “Which figurine can be called similar to both apples? (Circles. They are shaped like apples.).”

Exercise 6

Material: the same set of cards with numbers from 1 to 9.

Assignment: “Put all the yellow pieces to the right. Which number fits this group? Why 2? (Two figures.) What other group can be matched to this number? (A blue and a red triangle - there are two of them; two red figures, two circles; two squares - all options are analyzed.).” The child makes groups, uses a stencil frame to sketch and paint them, then signs the number 2 under each group. “Take all the blue figures. How many are there? (One.) How many colors are there in total? (Four.) Figures? (Six.)".

Development of mathematical abilities in a preschooler

The mathematical development of preschool children is carried out as a result of the child’s acquisition of knowledge in Everyday life(primarily as a result of communication with an adult), and through targeted training in classes to develop basic mathematical knowledge.

In the process of learning, children develop the ability to perceive more accurately and more fully the world, highlight the signs of objects and phenomena, reveal their connections, notice properties, interpret what is observed; mental actions, methods of mental activity are formed, internal conditions for the transition to new forms of memory, thinking and imagination.

There is a reciprocal relationship between learning and development. Education actively contributes to the child's development, but also depends significantly on his level of development.

It is known that mathematics is a powerful factor in the intellectual development of a child, the formation of his cognitive and creative abilities. The success of teaching mathematics in primary school depends on the effectiveness of a child’s mathematical development in preschool age.

Why do many children find mathematics so difficult not only in elementary school, but even now, during the period of preparation for educational activities?

In modern primary school educational programs, important importance is attached to the logical component.

The development of a child’s logical thinking involves the formation of logical techniques mental activity, as well as the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build simple conclusions based on cause-and-effect relationships.

Many parents believe that the main thing in preparing for school is to introduce the child to numbers and teach him to write, count, add and subtract (in fact, this usually results in an attempt to memorize the results of addition and subtraction within 10).

However, when teaching mathematics, these skills do not help the child in mathematics lessons for very long. The stock of memorized knowledge ends very quickly (in a month or two), and the lack of development of one’s own ability to think productively (that is, to independently perform the above-mentioned mental actions based on mathematical content) very quickly leads to the appearance of “problems with mathematics.”

At the same time, a child with developed logical thinking always has a greater chance of being successful in mathematics, even if he was not previously taught the elements of the school curriculum (counting, calculations, etc.).

The school curriculum is structured in such a way that already in the first lessons the child must use the skills to compare, classify, analyze and generalize the results of his activities.

Logical thinking training

Logical thinking is formed on the basis of figurative thinking and is the highest stage of development of children's thinking.

Reaching this stage is active and difficult process, since the full development of logical thinking requires not only high activity of mental activity, but also generalized knowledge about the general and essential features of objects and phenomena of reality, which are enshrined in words.

Around the age of 14, the child reaches the stage of formal logical operations, when his thinking acquires features characteristic of the mental activity of adults. However, the development of logical thinking should begin in preschool childhood. So, for example, at 5-7 years old a child is already able to master elementary level such techniques of logical thinking as comparison, generalization, classification, systematization and semantic correlation. At the first stages, the formation of these techniques should be carried out based on visual, concrete material and, as it were, with the participation of visual-figurative thinking.

However, one should not think that developed logical thinking is a natural gift, the presence or absence of which should be accepted. There is a large number of studies confirming that the development of logical thinking can and should be done (even in cases where the child’s natural abilities in this area are very modest). First of all, let's figure out what logical thinking consists of.

How to teach a child to compare

Comparison is a technique aimed at establishing signs of similarity and difference between objects and phenomena.

By the age of 5-6 years, a child usually already knows how to compare different objects with each other, but does this, as a rule, on the basis of only a few characteristics (for example, color, shape, size and some others). In addition, the selection of these features is often random and does not involve a comprehensive analysis of the object.

While learning the technique of comparison, the child must master the following skills:

1. Identify the characteristics (properties) of an object based on its comparison with another object.

Children 6 years old usually identify only two or three properties in an object, while their infinite set. In order for a child to be able to see this many properties, he must learn to analyze an object from different sides, compare this object with another object that has different properties. By selecting objects for comparison in advance, you can gradually teach the child to see in them qualities that were previously hidden from him. At the same time, to master this skill well means to learn not only to identify the properties of an object, but also to name them.

2. Identify common and features(properties) of compared objects.

When the child has learned to identify properties and compare one object with another, he should begin to develop the ability to identify the common and distinctive features of objects. First of all, you need to teach the ability to conduct a comparative analysis of the selected properties and find their differences. Then you should move on to general properties. In this case, it is first important to teach the child to see common properties in two objects, and then in several.

3. Distinguish between essential and non-essential essential features(properties) of an object, when essential properties are given or easily found.

You can try to show simple examples, how the concepts of “general” attribute and “essential” attribute relate to each other. It is important to draw the child’s attention to the fact that a “general” feature is not always “essential,” but “essential” is always “general.” For example, show your child two objects where their “common” but “insignificant” feature is color, and their “common” and “essential” feature is shape.

The ability to find essential features of an object is one of the important prerequisites for mastering the technique of generalization.

What does it mean to be attentive?

To “be attentive”, you need to have well-developed properties of attention - concentration, stability, volume, distribution and switchability.

Concentration is the degree of concentration on the same subject, object of activity.

Stability is a characteristic of attention over time. It is determined by the duration of maintaining attention on the same object or the same task.

The volume of attention is the number of objects that a person is able to perceive and cover during simultaneous presentation. By the age of 6-7 years, a child can perceive up to 3 objects simultaneously with sufficient detail.

Distribution is a property of attention that manifests itself in the process of activity that requires the implementation of not one, but at least two different actions at the same time, for example, listen to the teacher and at the same time record some fragments of the explanation in writing.

Switchability of attention is the speed of moving the focus of attention from one object to another, moving from one type of activity to another. Such a transition is always associated with volitional effort. The higher the degree of concentration on one activity, the more difficult it is to switch to another.

Do you strive to develop your child's intelligence?

Intelligence is a peculiar way of thinking, unique and exclusive for each person.

It is determined by the ability focus on a cognitive task, the ability to flexibly switch, compare, quickly establish cause-and-effect relationships, draw conclusions, etc.

Development of intelligence, psychological comfort, in the process of mental activity, and the child’s feeling of happiness are very closely related.

At the age of 5-7 years, the child should develop the ability

1. Long hold intense attention on the same object or on the same task (sustainability and concentration of attention). The stability of attention increases significantly if the child actively interacts with the object, for example, examines and studies it, and not just looks. With a high concentration of attention, the child notices much more in objects and phenomena than in a normal state of consciousness.

2. Fast switch attention from one object to another, move from one type of activity to another (switching attention).

3. Subdue your attention to a consciously set goal and the requirements of the activity (voluntariness of attention). It is thanks to the development voluntary attention the child becomes able to actively, selectively “extract” the information he needs from memory, highlight the main, essential, and make the right decisions.

4. Notice subtle but significant features in objects and phenomena (observation).

Observation - one of important components human intelligence. First distinctive feature Observation is that it manifests itself as a result of internal mental activity, when a person tries to cognize and study an object on his own initiative, and not under instructions from the outside. The second feature - observation is closely related to memory and thinking.

By performing intellectual play tasks with your child, you will have a miraculous effect on your child’s development, his self-confidence and your communication with him.

Development games on the go

1. Often count everything you use with your child. everyday life: how many chairs are there near the dining table, how many pairs of socks did you put in the washing machine, how many potatoes do you need to peel to cook dinner. Count the steps in the entrance, the windows in the apartment - children love to count.

Measure different things - at home or on the street with your palms or feet. Remember the cartoon about 38 parrots - a great reason to watch it and check how tall mom or dad is, how many palms will “fit” on your favorite sofa.

2. Buy “sticky” numbers made of foam, stick them on an empty container - from 0 to 10. Collect a variety of objects: one small car or doll, two large buttons, three beads, four nuts, five clothespins. Ask to put them in containers according to the number on the lid.

3. Make number cards from cardboard and sandpaper or velvet. Run your child's finger over these numbers and name them. Ask to show you 3, 6, 7. Now take one of the cards out of the box at random and invite the child to bring as many items as are shown on his card. It's especially exciting to receive a zero card because nothing beats personal discovery.

4. Hunting for geometric shapes. Invite your child to play hunting. Let him try to find something that looks like a circle and show it to you. And now a square or rectangle. You can play this game on the way to kindergarten

5. Place a spoon, fork and plate on the table in a special way. Ask your child to repeat your composition. When he is doing well, put some kind of screen between you and your baby or sit with your backs to each other. Invite him to arrange his items and then explain to you how he did it. You must repeat his actions, following only verbal instructions. Also a good game to pass the time waiting for an appointment at the clinic

6. When your child bathes, give him a variety of cups - measuring cups, plastic jugs, funnels, colorful cups. Pour water into two identical glasses and ask if there is the same amount of water in both containers? Now pour the water from one glass into a tall and thin glass, and the water from the other glass into a wide and short glass. Where is there more, you ask? Most likely the answer will be interesting

7. Play shopping with your child. Buy toy money or draw one yourself. Rubles can be taken from economic games, like "Manager".

Methods of mental action that help enhance the effectiveness of using logical-constructive tasks

Seriation is the construction of ordered increasing or decreasing series based on a selected characteristic.

A classic example of seriation: nesting dolls, pyramids, insert bowls.

Series can be organized by size, length, height, width

Analysis is the selection of the properties of an object, or the selection of an object from a group, or the selection of a group of objects according to a certain criterion.

For example, the attribute is given: “Find all sour”.

First, each object in the set is checked for the presence or absence of this attribute, and then they are isolated and combined into a group based on the “sour” attribute.

Synthesis - connection various elements(signs, properties) into a single whole. For example:

Assignment: “Determine which of the figures in this set is extra. (Square.) Explain why. (All the rest are circles.)”

The activity that actively shapes the synthesis is the construction

For construction, any mosaics, construction sets, cubes, cut-out pictures are used that are suitable for this age and make the child want to tinker with them.

An adult plays the role of an unobtrusive assistant; his goal is to help bring the work to completion, that is, until the intended or required whole object is obtained.

Comparison is a logical method of mental action that requires identifying similarities and differences between the characteristics of an object (object, phenomenon, group of objects).

For example:

Assignment: “Find one that looks like an apple among your figures.”

An adult offers to look at each image of an apple in turn. The child selects a similar figure, choosing a basis for comparison: color, shape. "Which figure can be said to be similar to both apples? (Circles. They are similar in shape to apples.)"

Indicator of reception maturity comparisons will be the child’s ability to independently apply it in activities without special instructions from an adult on the signs by which objects need to be compared.

A child has extraordinary intelligence if he:

Classification - dividing a set into groups according to some criterion, which is called the basis of classification

Classification with preschool children can be carried out:

By name (cups and plates, shells and pebbles, skittles and balls, etc.);

By size (large balls in one group, small ones in another, long pencils in one box, short pencils in another, etc.);

By color (this box has red buttons, this one has green buttons);

In shape (this box contains squares, and this box contains circles; this box contains cubes, this box contains bricks);

According to other signs of a non-mathematical nature: what you can and cannot eat; who flies, who runs, who swims; who lives in the house and who in the forest; what happens in summer and what happens in winter; what grows in the garden and what in the forest, etc.

All of the examples listed above are classifications based on a given basis: the adult communicates it to the child, and the child carries out the division.

In another case, the classification is performed on a basis determined by the child independently. Here the adult asks number of groups to be divided into many objects (objects), and the child independently looks for the corresponding basis. Moreover, such a basis can be determined in more than one way.

Generalization is the presentation in verbal form of the results of the comparison process

Generalization is formed in preschool age as selection and fixation common feature two or more objects.

A generalization is well understood by a child if it is the result of an activity carried out by him independently, for example, classification: these are all big, these are all small; these are all red, these are all blue; these all fly, these all run, etc.

When formulating a generalization, you should help the child construct it correctly, use the necessary terms and verbiage.

For example:

Task: “One of these figures is extra. Find it. (Figure 4.)”

Children of this age are unfamiliar with the concept of a bulge, but they usually always point to this shape. They can explain it like this: “Her corner went inward.” This explanation is quite suitable. “How are all the other figures similar? (They have 4 corners, these are quadrilaterals.).”