Children's mathematical abilities. Child's mathematical abilities

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 intellectual development child, the formation of his cognitive and creative abilities. From the effectiveness of a child’s mathematical development in preschool age the success of teaching mathematics depends on primary school.

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 is given a logical component.

Development logical thinking for a child involves the formation of logical techniques of 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 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. For example, at the age of 5-7 years, a child is already able to master at an 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 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 there are an infinite number of them. 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 carry out comparative analysis 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 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 performing not one, but at least two different actions at the same time, for example, listening to the teacher and at the same time recording in writing some fragments of the explanation.

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.

The development of intelligence, psychological comfort in the process of mental activity, and the child’s sense 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 of voluntary attention that 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 the important components of 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.

Doing intellectual activities with your child game tasks 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. More often, together with your child, count everything that you use in everyday life: how many chairs are there near dining table how many pairs of socks did you put in 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 from foam, stick them on an empty container - from 0 to 10. Collect various items: 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 cards with numbers 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 geometric figures. 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.).”

Topic 6.

DIAGNOSTICS OF MATHEMATICAL ABILITIES OF SENIOR PRESCHOOL CHILDREN

There is a significant variety of types of giftedness that can manifest themselves already in preschool age. Among them is intellectual giftedness, which largely determines a child’s aptitude for mathematics and develops intellectual, cognitive, and creative abilities.

Children with intellectual giftedness are characterized by the following features:

highly developed curiosity, inquisitiveness; the ability to “see” yourself, find problems and the desire to solve them, actively experimenting; high (relative to age-related capabilities) stability of attention when immersed in cognitive activity (in the area of ​​his interests); early manifestation of the desire to classify objects and phenomena, discover cause-and-effect relationships; developed speech, good memory, high interest in new, unusual; the ability to creatively transform images and improvise; early development sensory abilities; originality of judgment, high learning ability; desire for independence.

The main areas of work with children with a penchant for mathematics include: determining the child’s aptitude, developing individual programs for the development of the child’s abilities, and additional education.

I want to focus on the first stage - determining the child’s aptitude for mathematics.

In view of the implementation of the Federal State Educational Standard in the educational process of preschool educational institutions, the issue of monitoring the quality of preschool education has become especially acute. It is necessary to competently approach the issue of diagnosing the levels of development of children. In the modern sense, pedagogical diagnostics is a system of methods and techniques, specially developed pedagogical technologies, test tasks that allow you to determine the level professional competence teachers, level of development of a preschool child. Its main purpose is to analyze and eliminate the causes that give rise to shortcomings in work, accumulate and disseminate teaching experience, stimulate creativity and pedagogical skill.

Purpose of diagnosis: tracking achievements in a child’s mastery of the means and methods of cognition, identifying gifted children in the field of mathematical development.

Form of organization: problem-game situations conducted individually with each child.

We have proposed several diagnostic situations: “Enter the hut”, “Let’s restore the ladder”, “Correct the mistakes”, “Which days are missed” and “Whose backpack is heavier”.

Diagnostic situation “Enter the hut”

Goal: identification practical skills children 5-6 years old in composing numbers from 2 smaller ones and in carrying out search actions.

On three huts located in a row, the numbers (6, 9,7 respectively) indicate the number of gold coins. Traces lead to the huts. Only the one who opens the door can take the coins. To do this, you need to step on the left and right footprints together as many times as the number shows. (Mark with pencil).

Teacher: Which hut did you choose? What tracks will you step on? If you want, then enter other huts?

Diagnostic situation “Correct the mistakes and name the next move”

The goal is to identify children’s ability to follow the sequence of moves, offer options for correcting mistakes, reason, and mentally justify the course of their actions.

The situation is being organized without practical action. The child watches the adult’s progress, comments on his own move, and corrects mistakes.

Teacher: Imagine that you and I are playing dominoes. Some of us made mistakes. Find them and fix them. The first move was mine (left).

As errors are discovered, the child is asked the question: “Which of us made mistakes? How can I fix them using additional chips?”

As a result, generally low results were obtained for the group. At first school year the use of these methods turned out to be inappropriate. The knowledge of most children is not sufficiently formed, the ability to reason and justify actions is poorly expressed. In addition, the proposed situations are not enough to diagnose all areas of children’s mathematical development.

After the diagnosis, teachers were given the following recommendations:

1. Analyze the subject-game development environment

2. Initiate creativity cognitive activity individual children (teacher’s personal participation in children’s activities, creation of play communities, motivation)

3. Select games and gaming materials necessary for independent mastery of the actions necessary in a given period (knowledge of the dependencies between numbers, quantities in the conditions of a serial series)

4. Practice organizing and conducting leisure activities, children's games, projects, and joint events with parents.

5. Develop your own pedagogical creative potential. (accompanied by slide)

To carry out repeated diagnostics in September, the author’s diagnostic methods of Anna Vitalievna Beloshistaya were chosen, since it was her developments, in my opinion, that are most accessible, feasible and understandable to children and teachers. Positive aspects of these diagnostic techniques are their simplicity, a small amount of and handouts, which significantly speeds up the diagnostic procedure, especially since all types of diagnostics must be carried out during scheduled moments, and most of them, according to the instructions, are carried out individually. The author focuses on aspects of developmental learning and the personal-activity successive approach.

1. Diagnostic situation of analytical-synthetic activity

(adapted technique)

Goal: to identify the maturity of the analysis and synthesis skills of children aged 5-6 years.

Objectives: assessment of the ability to compare and generalize objects based on characteristics, knowledge of the shape of the simplest geometric figures, the ability to classify material according to an independently found basis.

Presentation of the task: the diagnosis consists of several stages, which are offered to the child one by one. Conducted individually.

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

diagnostic situation

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

Material: the same as for No. 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.).”

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

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

Assignment rating:

Slide with a photo of a child

2. Diagnostic situation “What is unnecessary”

(methodology)

Purpose: to determine the development of visual analysis skills in children aged 5-6 years.

Option 1.

Material: drawing of figurines-faces. (slide “Faces”)

diagnostic task

Assignment: “One of the figures is different from all the others. Which? (Fourth.) How is it different?”

Option 2.

Material: drawing of human figures.

diagnostic task

Assignment: “Among these figures there is an extra one. Find her. (Fifth figure.) Why is she extra?”

Assignment rating:

Level 1 – task completed completely correctly

Level 2 – 1-2 mistakes made

Level 3 – task completed with the help of an adult

Level 4 – the child finds it difficult to answer the question even after prompting

3. Diagnostic situation for analysis and synthesis

for children 5 – 7 years old (methodology)

Goal: to determine the degree of development of the skill of isolating a figure from a composition formed by superimposing some forms on others, to identify the level of knowledge of geometric figures.

Presentation of the task: individually with each child. In 2 stages.

Material: 4 identical triangles. (slide)

diagnostic task

Assignment: “Take two triangles and fold them into one. Now take the other two triangles and fold them into another triangle, but of a different shape. What is the difference? (One is tall, the other is low; one is narrow, the other is wide.) Is it possible to make a rectangle out of these two triangles? (Yes.) Square? (No.)".

Material: drawing of two small triangles forming one large one. (slide)

diagnostic task

Assignment: “There are three triangles hidden in this picture. Find them and show them."

Assignment rating:

Level 1 – task completed completely correctly

Level 2 – 1-2 mistakes made

Level 3 – task completed with the help of an adult

Level 4 – the child did not complete the task

4. Diagnostic test.

Initial mathematical representations(methodology)

Purpose: to determine children’s ideas about relationships more than; less by; about quantitative and ordinal counting, about the shape of the simplest geometric figures.

Material: 7 any objects or their images on a magnetic board. Items can be either the same or different. The task can be offered to a subgroup of children. (slide “Yula”)

diagnostic task

Method of execution: the child is given a sheet of paper and a pencil. The task consists of several parts that are offered sequentially.

A. Draw as many circles on the sheet as there are objects on the board.

B. Draw 1 more squares than circles.

B. Draw 2 less triangles than circles.

D. Draw a line around 6 squares.

D. Color in the 5th circle.

Assignment rating:

Level 1 – task completed completely correctly

Level 2 – 1-2 mistakes made

Level 3 – 3-4 mistakes made

Level 4 – 5 mistakes were made.

During diagnostics, visual material can be provided to children in a multimedia version or on a magnetic board, if the instructions for conducting it do not require practical actions with it. The material should be colorful, age-appropriate, aesthetically designed, appropriate for the number of children.

The proposed methods No. 1 – 2 are carried out in September, as one of the stages of initial monitoring. Methods No. 3-4 – in May, to determine the result of children’s mathematical development.

Only after carrying out several diagnostics is a conclusion drawn up about the maturity of the child’s knowledge, skills and abilities, the results of which are entered into the table: (slide of an empty table)

As a result of the work carried out over the year in accordance with these recommendations for teachers to enrich the group environment in the field of mathematical development, as well as thanks to the diagnostic methods selected in accordance with the tasks of the educational educational institution in May, we came to the following results: (tables)

		Analysis-synthesis	Concept of form	Initial mat. representation
	Total for the group

As can be seen from the above data, the level of knowledge, both individually and in the group as a whole, has increased significantly. During the diagnostic process, gifted children were identified who easily coped with the situations proposed by the teacher and quickly and accurately found the right solutions.

In order to further develop the mathematical abilities of gifted children, teachers were asked to continue working with these children individually: in special moments, in joint targeted activities with the teacher in the field of mathematical development.

Bibliography:

1. Monitoring in kindergarten. Scientific and methodological manual. – SPb.: PUBLISHING HOUSE “CHILDHOOD-PRESS”, 2011. – 592 p.

2. Management of the educational process in preschool educational institutions. Toolkit/ , . – M.: Iris-press, 2006. – 224 p.

3. Formation and development of mathematical abilities of preschoolers. Toolkit. / . – M.: Arkti, 2004.

· Make sure that the child is emotionally positive about communication.

·Tasks are offered in strict accordance with the instructions.

· An assessment of a child’s mathematical development is made based on the results of several diagnostics.

· The choice of a specific diagnostic technique is made in accordance with the basic and basic general education program of the preschool educational institution.

· When summing up, one should take into account the results of short-term observations of the child, his behavior in conditions new game, in a creative or problematic situation.

Mathematics ability is one of the talents given by nature, which manifests itself already from early age and directly related to the development of creative potential, the desire to understand the world around the baby. But why is learning maths so difficult for some children, and can these abilities be improved?

The opinion that only gifted children can master mathematics is wrong. Mathematical abilities, like other talents, are the result of a child’s harmonious development, and must begin from a very early age.

In the modern computer world with its digital technologies, the ability to “make friends” with numbers is extremely necessary. Many professions are based on mathematics, which develops thinking and is one of the most important factors influence on the intellectual growth of children. This exact science, whose role in the upbringing and education of a child is undeniable, develops logic, teaches one to think consistently, determine the similarities, connections and differences of objects and phenomena, makes the child’s mind fast, attentive and flexible.

For mathematics classes for children five to seven years old to be effective, a serious approach is needed, and the first step is to diagnose their knowledge and skills - to assess at what level the child’s logical thinking and basic mathematical concepts are.

Diagnostics of mathematical abilities of children 5-7 years old using the method of Beloshistaya A.V.

If a child with a mathematical mind has mastered mental calculation at an early age, this is not yet a basis for one hundred percent confidence in his future as a mathematical genius. Mental arithmetic skills are only a small element of an exact science and are far from the most complex. The presence of a child’s ability in mathematics is evidenced by a special way of thinking, which is characterized by logic and abstract thinking, understanding of diagrams, tables and formulas, ability to analyze, ability to see figures in space (volumetric).

To determine whether children from primary preschool (4-5 years old) to primary school age have these abilities, there is an effective diagnostic system created by Dr. pedagogical sciences Anna Vitalievna Beloshista. It is based on the creation by a teacher or parent of certain situations in which the child must apply this or that skill.

Diagnostic stages:

1. Testing a 5-6 year old child for analysis and synthesis skills. At this stage, you can evaluate how the child can compare objects of different shapes, separate them and generalize them according to certain characteristics.
2. Testing figurative analysis skills in children aged 5-6 years.
3. Testing the ability to analyze and synthesize information, the results of which reveal the ability of a preschooler (first grader) to determine the shapes of various figures and notice them in complex pictures with figures superimposed on each other.
4. Testing to determine a child’s understanding of basic mathematics concepts – we're talking about about the concepts of “more” and “less”, ordinal counting, the shape of the simplest geometric figures.

The first two stages of such diagnostics are carried out at the beginning of the school year, the rest - at the end, which makes it possible to assess the dynamics of the child’s mathematical development.

The material used for testing should be understandable and interesting for children - age-appropriate, bright and with pictures.

Diagnosis of a child’s mathematical abilities using the method of Kolesnikova E.V.

Elena Vladimirovna created a lot teaching aids for the development of mathematical abilities in preschoolers. Her method of testing children 6 and 7 years old has become widespread among teachers and parents different countries and complies with the requirements of the Federal State Educational Standard (GES) (Russia).

Thanks to Kolesnikova’s method, it is possible to establish as accurately as possible the level of basic indicators of the development of children’s mathematical skills, find out their readiness for school, and determine weak sides to fill gaps in a timely manner. This diagnosis helps to find ways to improve the child’s mathematical abilities.

Developing a child’s mathematical abilities: tips for parents

It is better to introduce a child to any science, even something as serious as mathematics, in a playful way - this is exactly what will happen the best method training that parents should choose. Listen to the words of famous scientist Albert Einstein: “Play is the highest form of exploration.” After all, with the help of the game you can get amazing results:

– knowledge of yourself and the world around you;

– formation of a mathematical knowledge base;

– development of thinking:

– personality formation;

– development of communication skills.

You can use various games:

1. Counting sticks. Thanks to them, the baby remembers the shapes of objects, develops his attention, memory, ingenuity, and develops comparison skills and perseverance.
2. Puzzles that develop logic and ingenuity, attention and memory. Logic puzzles help children learn better spatial awareness, thoughtful planning, simple and backward counting, and ordinal counting.
3. Mathematical riddles are great way development of the main aspects of thinking: logic, analysis and synthesis, comparison and generalization. While searching for a solution, children learn to draw their own conclusions, cope with difficulties and defend their point of view.

The development of mathematical abilities through play creates learning excitement, adds vivid emotions, and helps the child fall in love with the subject of study that interests him. It is also worth noting that gaming activities also contribute to the development of creative abilities.

The role of fairy tales in the development of mathematical abilities of preschool children

Children's memory has its own characteristics: it records vivid emotional moments, that is, the child remembers information that is associated with surprise, joy, and admiration. And learning “from under pressure” is an extremely ineffective way. In the search for effective teaching methods, adults should remember such a simple and ordinary element as a fairy tale. A fairy tale is one of the first means of introducing a child to the world around him.

For children, fairy tales and reality are closely connected, magical characters are real and alive. Thanks to fairy tales, a child’s speech, imagination and ingenuity develop; they give the concept of goodness, honesty, broaden horizons, and also provide an opportunity to develop mathematical skills.

For example, in the fairy tale “The Three Bears,” the child unobtrusively gets acquainted with counting to three, the concepts of “small,” “medium,” and “large.” “Turnip”, “Teremok”, “The Little Goat Who Could Count to 10”, “The Wolf and the Seven Little Kids” - in these tales you can learn simple and ordinal counting.

Discussing fairy tale characters, you can invite the baby to compare them in width and height, “hide” them in geometric shapes that are suitable in size or shape, which contributes to the development of abstract thinking.

You can use fairy tales not only at home, but also in school. Children really love lessons based on the plots of their favorite fairy tales, using riddles, labyrinths, and fingering. Such classes will become a real adventure in which the kids will take personal part, which means the material will be learned better. The main thing is to involve children in the game process and arouse their interest.

Method of express diagnostics of intellectual abilities of children 6-7 years old (MEDIS)

E. I. SHCHBLANOVA, I. S. AVERINA, E. N. ZADORINA

Currently, a large number of schools have appeared in which education is conducted according to accelerated programs, with in-depth study of any subjects, according to special programs for gifted children, etc. In this regard, the problem of selecting students capable of such learning arose. Unfortunately, the solution to this problem is often arbitrary, without any psychological and pedagogical justification.

As a rule, an experienced teacher can quite competently determine a child’s readiness to enter the first grade of school and distinguish normally developed children from children with one or another developmental delay. The issue of children's readiness for school education is covered in sufficient detail in the literature.

The problem of selecting capable and gifted children requires a completely different approach to be solved. This approach should first of all take into account the complexity and versatility of the phenomenon of giftedness itself, which includes both cognitive (intellectual and creative abilities) and non-cognitive (motivational and personal characteristics) factors of development.

Therefore, first of all, it is necessary to clearly formulate the objectives of the training program for which children are being selected, and the requirements that are presented to children within the framework of this program. When making such a selection, the main attention should be paid to the interests of the child: whether studying at a given school will be optimal for his development. To resolve this issue among many other factors great importance has a definition of the level of intellectual development of the child.

Diagnosis of the level of intellectual development of children requires a thorough and comprehensive analysis by a qualified specialist - a psychologist. However, the practical implementation of such an individual examination of each child upon admission to school is not possible. At the same time, even to make an approximate judgment about the intelligence of children, it is necessary to have a methodology that would allow one to meet a number of conditions required for diagnosing intelligence.

Among them, first of all, it is necessary to mention the standardization of tests, which allows, to a certain extent, to avoid subjectivity in the selection of tasks and ensure equal opportunities for all children. The tasks in the methodology must be selected in such a way that it is possible to evaluate different sides the child’s intelligence and at the same time reduce the influence of his training (“training”). In addition, the technique must be sufficiently reliable and valid with comparative ease of use and little time consumption.

The development of this methodology was carried out on the basis of well-known foreign tests cognitive abilities- KFT 1-3 K. Heller and co-workers. KFT tests 1-3, developed at the University of Munich and intended for gifted first-graders.

Each MEDIS form consists of 4 subtests with 5 tasks of increasing complexity. Before completing each subtest, two tasks similar to the test ones are performed in training. During this training, performing tasks together with the experimenter, the child must understand what he must do and find out everything that is not clear to him. Training tasks can be repeated if necessary.

MEDIS tasks, as in foreign tests, are presented in the form of pictures, which makes it possible to test children regardless of their reading ability. When completing tasks, the child is only required to choose the correct answer (cross out the oval under it) from several proposed ones. Before presenting the tasks, the child is shown an image of an oval, a crossed out oval under the selected picture, and a training exercise is carried out in crossing out the oval on command. All instructions and explanations are given orally by the experimenter.

First subtest aims to identifygeneral student awareness, their vocabulary. Among five to six images of objects, you need to mark the one named by the experimenter. The first tasks include the most common and familiar objects, such as "boot", and the last - rarer and lesser-known objects, such as "statue".

Second subtest provides an opportunity to assess the child's understandingquantitative and qualitative relationshipsbetween objects and phenomena: more - less, higher - lower, older - younger, etc. In the first tasks these relationships are unambiguous - the largest, the farthest, while in the last tasks the child needs, for example, to choose a picture where one object more than another, but less than a third.

The third subtest reveals level of logical thinking, analytical and synthetic activity of the child. Moreover, in tasks to eliminate the superfluous, both images of specific objects and figures with different numbers of elements are used.

Fourth subtestsent for diagnosismathematical abilities. It includes mathematical tasks for intelligence, in which various materials are used: arithmetic problems, tasks on spatial thinking, on identifying patterns, etc. To complete these tasks, the child must be able to count to ten and perform simple arithmetic operations (addition and subtraction).

Thus, the variety of tasks in MEDIS makes it possible to cover different aspects of a child’s intellectual activity in minimal periods of time and obtain information both about his ability to learn in primary school and about the individual structure of his intelligence. This gives grounds for using MEDIS as the main part of a battery of methods for determining the readiness of children to learn in schools with educational programs of increased difficulty.

MEDIS can be used individually and in groups of 5-10 people. When examining children in groups, the experimenter needs the help of an assistant. The environment during testing should be calm and serious, without unnecessary tension. Each test taker must have his own test book, on the cover of which his first and last name must be indicated. During testing, monitoring of children is of great importance. In group testing, this task is performed primarily by the experimenter's assistant. This observation allows you to avoid cases of misunderstanding by the child of instructions and at the same time receive Additional information about the readiness of children to study at school and the individual characteristics of their behavior.

It should be taken into account that the group testing environment may be extremely unfavorable for some children: those with increased anxiety, confused by the new environment, etc. In such cases, it is recommended to repeat the testing using a different form of test or supplement it with an individual psychological and pedagogical examination.

All MEDIS tasks are completed without a time limit. The pace at which the experimenter reads the tasks should depend on the speed at which the children complete the tasks; it may differ in different groups. At the same time, children should not be forced to complete the task at a certain pace. Children who work quickly need 15 seconds to complete each task. Children who work slowly may need 20-25 seconds. The speed of reading tasks should not remain constant when moving from one task to another in different test parts.

When planning testing, it is important to take into account not only the time required to complete the tasks of the corresponding part of the methodology, but also the time required to distribute test materials, explain how to perform the test, and work with children on the training examples given at the beginning of each subtest. The total test time is on average 20-30 minutes.

When interpreting the results of this technique, it should be taken into account that, like any other test, MEDIS cannot serve as the only criterion for making decisions about the level of intellectual development of a child, about his selection for training in special programs, about the profile of his abilities. Test results should be considered in conjunction with other indicators: data from an interview with the child, information from parents, indicators of the child’s interests, etc.

Instructions: All test tasks spoken no more than 2 times!

Task 1 - awareness.

1- show the rodent (correct answerin the 5th picture),

2- acrobat (4),

3- edible (2),

4- plane (2),

5- biceps (4).

Task 2 - mathematical abilities.

1- show the bed where the flowers were planted before everyone else (3),

2- a picture in which the girl stands closer to the tree than the boy and the dog (4),

3- a picture in which a duck flies the lowest, but fastest (2),

4-degree thermometer, in which the temperature is higher than the lowest, but lower than all the others (4),

5- picture where the boy runs fast, but not faster than everyone else (1).

Task 3 - logical thinking.

In all tasks it is necessary to show the “extra”.

(right answers- 3, 4, 2, 2, 5).

Task 4 - quantitative and qualitative relationships.

1- find a rectangle in which there are more than 6 sticks, but less than 12 (3),

2- We drew a row of dominoes, but forgot to draw one. Which domino do you need to take on the right to continue this row? (2),

3- choose a cube that has one more point than this cube on the left (4),

4- count the sticks in the cubes on the left. Which cube has more sticks? Show how much more (1)

5- show the plate on which the least amount of cake was eaten (3).

FULL NAME. ___________________________________________________________

Research Date ________________________________________________

MEDIS subtests

5- high

4- above average

Parents who want to teach their child mathematics are faced with the question of what exactly needs to be taught to the child. What abilities can and should be developed in preschool age to ensure successful completion of the school curriculum.

What abilities are considered mathematical in children under 7 years of age?

You should not think that mathematical abilities only mean the ability to count quickly and accurately. It's a delusion. Mathematical abilities include a whole range of skills aimed at creativity, and logic, and counting.

The speed of counting and the ability to memorize a large array of numbers and data are not genuine mathematical abilities, since even a slow and thorough child who studies thoughtfully can successfully comprehend mathematics.

Mathematical abilities include:

1. Ability to generalize mathematical material.
2. The ability to see what different objects have in common.
3. The ability to find the main thing in a large amount of different information and exclude what is not necessary.
4. Use numbers and signs.
5. Logical thinking.
6. The child's ability to think in abstract structures. The ability to distract yourself from the task at hand and see the resulting picture as a whole.
7. Think both forward and backward.
8. The ability to think independently without using templates.
9. Developed mathematical memory. Ability to use acquired knowledge in various situations.
10. Spatial thinking – confident use of the concepts of “up”, “down”, “right” and “left”.

How are mathematical abilities formed?

All abilities, including mathematical ones, are not a predetermined skill. They are formed and developed through training and reinforced by practice. Therefore, it is important not only to develop this or that ability, but also to improve it through practical exercises, leading to automation.

Any ability goes through several stages in its development:

1. Cognition. The child gets acquainted with the subject and learns the necessary material;
2. Application. Applies new knowledge in independent play;
3. Consolidation. Returns to classes and repeats what was previously learned;
4. Application. Using fixed material when playing independently;
5. Extension. There is an expansion of knowledge about the subject or ability;
6. Application. The child supplements independent play with new knowledge;
7. Adaptation. Knowledge is transferred from the game situation to life.

Any new knowledge must go through the application stage several times. Give your child the opportunity to use the received data in independent play. Children need some time to comprehend and consolidate every minor change in knowledge.

If a child cannot master the acquired skill or knowledge through independent play, there is a high probability that it will not be consolidated. Therefore, after each lesson, let your baby go out to play or take a break and play with him. During the game, show how to use new knowledge.

How to develop mathematical abilities in a child

Start off mathematical development It should be in the form of a game and use things that will interest the baby. For example, toys and household items that he encounters every day.

From the moment the child shows interest in a particular object, the parent begins to show the child that the object can not only be examined and touched, but also performed with it. different actions. By focusing on some features of an object (color, shape), in an unobtrusive manner, you can show the difference in the number of objects and introduce the first concepts of plurality and spatial position.

After the child learns to separate objects into groups, you can show that they can be counted and sorted. Pay attention to geometric features.

The development of mathematical abilities must go simultaneously with the basics of number operations.

Any new knowledge should be presented with the child’s clear interest in learning. If there is no interest in the subject and its study, the child should not be taught. It is important to maintain a balance in your child's learning to develop a love for mathematics. Almost all problems associated with studying the foundations of this discipline have their origin in the initial lack of desire to know.

What to do if your child is not interested

If your child gets bored every time you try to teach him the basics of mathematics, then you need to:

• Change the form of presentation of the material. Most likely, your explanations are too complex for the child to understand and do not contain game elements. Preschool children cannot perceive information in the classical form of a lesson; they need to be shown and told new material during a game or entertainment. Dry text is not perceived by a child. Use it in teaching or try to involve the child directly in teaching;
• Show interest in the subject without your child's participation. Children younger age are interested in everything that interests their parents. They love to imitate and copy adults. If the child does not show interest in any activity, then try to start playing with the selected objects in front of the child. Talk out loud about what you are doing. Show your own interest in the game process. The child will see your interest and join;
• If the child still quickly loses interest in the subject, you need to check whether the knowledge and skills that you want to instill in him are too difficult or easy;
• Keep in mind the length of classes for different ages. If a child under 4 years old loses interest in a subject after 5 minutes, then this is normal. Since at this age it is difficult for him to concentrate on one subject for a long time.
• Try introducing one element at a time into your lesson. For children 5-7 years old, the duration of classes should not exceed 30 minutes.
• Don't be upset if your child doesn't want to study on a particular day. You need to try to involve him in training after some time.

The main thing to remember:

1. The material must be adapted to the age of the child;
2. The parent must show interest in the child’s material and results;
3. The child must be ready for class.

How to develop mathematical thinking

The order of teaching a child mathematical thinking consists of interconnected activities that are presented in order of increasing complexity of the material.

1. You need to start learning with concepts about the spatial arrangement of objects

The child must understand where right is left. What is “above”, “below”, “before” and “behind”. Having this skill allows you to perceive all subsequent activities easier. Orientation in space is fundamental knowledge not only for the development of mathematical abilities, but also for teaching a child to read and write.

You can offer your child the following game. Take a few of his favorite toys and place them at different distances in front of him. Ask him to show which toy is closer, which is further, which is to the left, etc. If you have any difficulty choosing, please tell me the correct answer. Use in this game various options words that determine the location of objects relative to the baby.

Use this approach to learning and repetition not only in class, but also in everyday life. For example, ask your child to determine the spatial arrangement of objects on the playground. More often in everyday life, ask for something, orienting the baby in space.

In parallel with spatial thinking, they teach generalization and classification of objects according to their external signs and functional accessories.

2. Explore the concept of set of objects

The child must distinguish between the concepts many - few, one - many, more - less and equally. Offer toys different types in different quantities. Offer to count them and say how many or few there are, which toys are fewer and vice versa, also show the equality of toys.

A good game to reinforce the concept of set is “What’s in the Box.” The child is offered two boxes or drawers containing different numbers of items. By moving objects between boxes, the child is asked to make the number of objects more or less, to equalize. Under the age of 3 years, the number of objects should not be large so that the child can clearly assess the difference in objects without counting.

3. It is important to teach a child simple geometric shapes in early childhood.

Teach your child to see them in the world around them. It is good to use applications from mathematical forms. Show your child a drawing of an object with clear contours (house, car). Offer to make an image of an object from prepared triangles, squares and circles.

Show and explain what the angle of the figures is, invite the child to guess why the “triangle” has such a name. Invite the child to familiarize himself with the figures big amount corners

Consolidate geometric knowledge by drawing the studied material, folding different figures from other objects (sticks, pebbles, etc.). You can use plasticine and other materials to create different shapes.

Ask them to draw a series of shapes different types, count them with your child. Ask which figures are many and which are few.

When walking with your child, pay attention to the shape of houses, benches, cars, etc. Show how combining different shapes can create new and familiar objects.

4. The ability to navigate in space and classify objects allows you to teach measuring the size of an object

Early learning to measure length with a ruler and using centimeters is not recommended, as this will be difficult to understand material. Try measuring objects with your child using sticks, ribbons and other materials at hand. This training does not involve the measurement itself, but the principle of its implementation.

Most teachers advise teaching your child to measure using counting sticks. They justify this by convenience for the child and teaching him to use special material. These sticks will come in handy when learning units of counting. They can also be used as visual material when working with books (putting a stick aside according to the number of characters), studying geometric shapes (a child can lay out the desired shape with chopsticks), etc.

5. Quantitative measurements

After learning basic math concepts, you can move on to quantitative measurements and studying numbers. The study of numbers and their written notation occurs from an early age according to a certain system.

6. Addition and subtraction

Only after mastering quantitative measurements and numbers should you introduce addition and subtraction. Addition and subtraction are introduced at the age of 5-6 years and are the simplest one-step operations with small numbers.

7. Division

Division in preschool age is introduced only at the level of shares, when the child is asked to divide an object into equal shares. The number of such parts should not exceed four.

Examples of activities with a child to develop mathematical abilities

To solve this problem, you don’t need any sophisticated methods, you just need to make some additions to your everyday life.

• When walking outside, invite your child to count any items or objects (tiles, cars, trees). Point to many objects, ask to find a generalizing feature;
• Encourage your child to solve problems to find the correct answer by guiding him. For example, Masha has 3 apples, and Katya has 5, Lena has one more apple than Masha and one less than Katya. The problem can be simplified by asking what number is between 1 and 3;
• Clearly explain to your child what addition and subtraction are. Do this on apples, toys or any other objects. Let your child touch objects and show these simple operations by adding or subtracting an object;
• Ask your child what the differences between objects are;
• Show what scales are and how they work. Explain that weight can not only be felt by holding an object in your hands, but can also be measured in numbers;
• Teach how to use a clock with hands;
• Please pay attention Special attention spatial arrangement of objects;
• You can study shapes not only on cards, but also look for them in objects around;
• Show your child that mathematics is in everything around him, if you just look closely.

What additional materials will help teach your child mathematics?

• Cards and pictures with different numbers of objects, with numbers and mathematical symbols, geometric figures;
• Magnetic or chalk board;
• Clock with hand and scales;
• Counting sticks;
• Construction sets and puzzles;
• Checkers and chess;
• Lotto and dominoes;
• Books that contain counting and allow you to carry out mathematical operations;
• Methodological aids for the development of logic and other abilities according to the child’s age.

Tips for parents who want to teach their child the basics of mathematics

1. Encourage your child to find answers. Help him find them by reasoning. Don't scold for mistakes or laugh at incorrect answers. Each child’s attempt to draw a conclusion or solve a problem trains his abilities and allows him to consolidate knowledge;

2. Use your playtime to develop essential skills. Focus on what has been studied previously, show how new and already learned material can be used in practice. Create situations in which the child will need to use knowledge to achieve a certain result;

3. Do not overload your child with a large amount of new information. Give him time to comprehend the acquired knowledge through free play;

4. Combine the development of mathematical abilities with spiritual and physical development. Introduce counting into physical education classes and logic into reading, and role-playing games. Diversified development of the child - way to full development baby. Physically and spiritually developed child comprehends mathematics much easier;

5. When teaching a child, try to use all channels of information absorption. In addition to the oral story, show this on various objects, give the opportunity to touch and evaluate the weight and texture. Use a variety of forms of presenting information. Show how you can use the acquired knowledge in life;

6. Any material should be in the form of a game that will interest the child. Excitement and involvement in the process are good for remembering. If your child is not interested in the material, stop. Think about what was done wrong and correct it. Each child is individual. Find a method that suits your baby and use it;

7. The ability to concentrate on a task and remember the conditions is important for the successful development of mathematical fundamentals. Ask a question about what the child understood from the given task after each condition. Work to improve concentration;

8. Before asking your child to decide on his own, show an example of how to reason and decide. Even if the child has carried out a certain calculation operation more than once, remind him of the procedure. It is better to show the correct course of action than to allow the child to reinforce the wrong approach;

9. Don't force your child to study if he doesn't want to. If the baby wants to play, then give him this opportunity. Offer to study after some time;

10. Try to diversify knowledge in one lesson. The best option it will be if during the day you pay a little attention to a variety of areas of mathematical knowledge than if you memorize the same type of material, bringing it to automatism;

11. The task of a parent in preschool age is not to teach counting and calculations, but to develop abilities. If you don’t teach your child to add and subtract before school, it’s okay. If the child has mathematical thinking and knows how to draw conclusions, he will be able to comprehend any complex operations quickly and at school.

What books help develop mathematical abilities?

The solution to the issue of teaching mathematics to a child under 7 years old with the help of books begins from an early age. For example, the fairy tale “Teremok”. In it, the appearance of various characters occurs as they increase in size. Using this example, you can teach your child the concepts of big and small. Try playing this fairy tale in a paper theater. Invite your child to arrange the figures of the fairy tale characters in in the right order and tell a story. The fairy tale “Turnip” also teaches the child the concepts of more and less, but its plot develops from the opposite (from large to small).

It will be useful from a mathematical point of view to study the fairy tale “The Three Bears” through the concepts of large, medium and small; the child can easily master counting to three.

When choosing books to read to your child, pay attention to the following:

• The presence of an account in the book and the possibility of comparing heroes according to certain criteria;
• The images in the book should be large and interesting. Using them, you can show your child what geometric shapes are used to create different objects (a house is a triangle and a square, the hero’s head is a circle, etc.);
• Any plot should develop linearly and contain certain conclusions at the end. Avoid books with complex plots that do not develop linearly. Teach your child that any action has its consequences and how to draw conclusions. This approach will help you more easily understand the principles of logical thinking;
• Books should be selected according to age.

There are a large number of different publications on sale that allow you to familiarize yourself with most mathematical operations and terms using the examples of heroes. The main thing is to discuss the material read with your child and ask leading questions that will stimulate the development of mathematical abilities.

Buy methodological books for developing your child’s mathematical abilities according to his age. Now there are a large number various materials, which contain tasks for the development of the child’s mathematical abilities. Bring such publications into the game. Remind your child of the tasks he previously completed using this publication to solve new problems.

Developing a child's mathematical abilities is not a difficult task. A child under 7 years old seeks new knowledge on his own and is happy when it is presented to him in a playful way. Find a lesson option that suits your child and have fun learning math basics.