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

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

IN preschool age play is of utmost importance in the life of a small child. She is the leading species activities. The game manages to attract attention children to such subjects, which in ordinary cases are not gaming conditions they are not interested in and are very difficult to focus on.

The didactic game makes it possible to solve various pedagogical problems in game form, the most accessible and attractive for children. The need for the game and the desire to play preschoolers it is necessary to use and direct in order to solve certain educational educational tasks. The task facing educators is significantly different from the task of a teacher. schools: it consists in communion children to the material, giving food to the imagination, affecting not only the purely intellectual, but also the excitable sphere.

The most difficult topic for preschool children is mathematics. To develop cognitive interest in mathematical knowledge uses diverse methods and techniques for teaching mathematics, attract with colorful visuals and handouts material, as well as one of the effective means of awakening keen interest in an educational subject are didactic games.

What kind of games are games used to form mathematical concepts in children? Introducing children with numbers, give various games such as “Make a number from plasticine”, "What does the number look like", “Find objects around us that resemble a number”. Children learn to solve riddles mathematical content, learn poems about numbers, get acquainted with fairy tales in which numbers are present. When getting acquainted with any number, children are offered the following tasks: How: name proverbs, sayings, catchphrases, the name of fairy tales, where a number would be present ( "there is safety in numbers", “Measure 7 times and cut once”, "2 Greedy Bears" etc.). A game like this is often used "Draw something using numbers"- here children can draw a person’s face, a pattern, a snowman or some other object that develops imagination children. Children also really like the game "Draw a number". Children show numbers with their fingers, hands, using their bodies, in pairs. In pairs, children enjoy writing on each other's backs or on palm. Lately, children have been really enjoying didactic material called"Voskobovich's Games". Children have great fun assembling various numbers and shapes using rubber bands and nails. This is where the knowledge of numbers and colors is reinforced.

When learning geometric shapes, children love to play game: "A couple of words" = For example: They say children: circle - children call an object similar to a circle - a steering wheel; square – picture; oval is an egg, and vice versa: I name the object, and the children name the shape. Children also enjoy the game “Which figure is extra”- here children not only name and show the extra figure, but also explain why it doesn’t fit, why it’s extra. (For example: 3 volumetric figures, and one planar). These are also used games: "Find a lid for each box", "Pick up a patch", "Columbus Egg", "Tangram", "Dyenes Blocks". Children express figures, both from the model and from memory. When securing geometric shapes, use games: "Geometric Lotto", "Coding Shapes". To develop visual attention, they play game: “Count how many triangles, circles”.

Games with sticks are very often used in OD. First they give simple tasks. For example: lay out the pattern according to the sample, for memory, and then the task became more complicated: they offer to make 2 equal squares from 7 sticks, make a square of two sticks (using the corner of the table). Children are also not indifferent to "Kusener's Sticks", with the help of which it is easy to check, number composition, etc.

Working by section "Measuring Quantity" besides the usual ones known to everyone methods use such games How: measure with steps, fingers with a conventional yardstick, gave children creative exercise: Help me find the answer to non-standard questions:

How to measure the length of a poisonous snake?

How can you measure a person's strength?

How to measure the sound of rain? His strength?

By section "Quantity and check» educational games are also used. For example: "Even-odd", “Name the number one more - less”. The games are interesting “How many of us are missing one”(back check, “What number did I have in mind?”.

When studying the numbers of the second ten, use games: “Who knows, let him keep counting”, "What numbers are missing", "Name the neighbors".

When forming cyclic images, they offer games such as "What's first, what's next", “Color by continuing the pattern”, "Which figure will be the last".

Very often OD tasks are used - jokes are entertaining game problems with mathematical meaning. They should not be solved like ordinary problems, using one or another arithmetic operation. To solve this, you need to show resourcefulness, ingenuity, and an understanding of humor. They encourage children reason, think, find the answer using existing knowledge. Such tasks - jokes are used in carrying out mathematical leisure. TO example: “How many nuts are there in an empty glass?”, “How many paws do two cubs have?”.

With the help of generating learning children will enter the world of mathematics through exciting games, and education They will not find it difficult and boring.

Publications on the topic:

Formation of social and communication skills through play activities in young children Municipal autonomous preschool educational institution “Kindergarten “Rucheyok” “Formation of social and communication skills.

As is known, in childhood the formation of the self-image of a boy (girl) and the acquisition of gender-role experience as a space where.

Formation of the concept of number in the process of teaching children to count The main concept of elementary mathematics in kindergarten is the concept of number. In preschool age, work on developing the concept of number.

In the modern world, mathematics plays a responsible role in the development and formation of an active, independently thinking, ready person.

Methodological material “Theory and methods of teaching interaction and cooperation to preschool children” MADO "Child Development Center - Kindergarten No. 378" Perm Educator: Balabanova L. A. Methodological material "Theory and methods of teaching.

4. Methodology for teaching counting

The assimilation of counting activity and, in the process of its development, a number of concepts does not occur by itself, but as a result of learning organized by adults. In each age group of kindergarten, tasks are outlined for the development of elementary mathematical concepts in children, in particular for the development of counting activities, in accordance with the “Program of education and training in kindergarten.”

The program material of the second junior group is limited to the pre-numerical period of study. Children of this age learn to form groups of individual objects and select objects one at a time: to distinguish between the concepts of “many” and “one”. When comparing two quantitative groups, using the techniques of superposition and application, determine their equality and non-equality by the number of elements included in them. This work is simply necessary before children begin to familiarize themselves with numbers and is aimed at developing ideas about set. Children are taught to compare two sets, compare elements of one set with elements of another, distinguish between equality and inequality of groups of objects that make up the set. Children learn to form a group of homogeneous objects and select one object from it, and correctly answer the question “how many?” This problem is solved mainly through play and practical activities. There are many games in which children learn to identify one object, form a group of objects, and master the terms “one” and “many.” For example: “Bear and Bees”, “Lanterns”, “Train”, “Cat and Mice”, etc. The application method is more complex than the superimposition method, since it requires a clearer differentiation of elements within the set. When teaching applying and applying techniques, children should be taught to apply and apply objects only with their right hand from left to right. The teacher exercises children in reproducing claps and movements by ear (without counting). Unable to count, babies produce many sounds based only on sensory perception: they clap, raise their hands, or knock with hammers as many times as the teacher knocks. At this age, a huge role is played by the inclusion of techniques in which various analyzers are involved. Children should be taught to understand the following expressions and actively use them in their speech: as much - as, equally, more - less, one at a time - many at a time. Learn to coordinate the words “many”, “one”, in gender, number and case with nouns; understand the meaning of the question “How much” and answer it correctly. The middle group program is aimed at further developing mathematical concepts in children. It involves learning to count to 5 by comparing two sets expressed by adjacent numbers. An important task in this section remains the ability to establish the equality and inequality of groups of objects, when the objects are at different distances from each other, when they are different in size, etc. Solving this problem leads children to understand an abstract number. Grouping objects according to characteristics develops in children the ability to compare and carry out logical classification operations. In the process of various practical actions with aggregates, children learn and use in speech simple words and expressions that indicate the level of quantitative ideas: many, one, one at a time, none, not at all, few, the same, the same, the same, equally; as much as; more than; less than; each of..., all, all. Children in the middle group must learn to name numbers in order; relate each numeral to only one subject; at the end of the count, sum it up in a circular motion and name it by the name of the items counted (for example, “One, two, three. Three dolls in total”). When summing up the count, always pay attention to the fact that children always name the number first, and then the object; learn to distinguish the counting process from the counting result; count with your right hand from left to right; during the counting process, name only numerals; teach children to correctly coordinate numerals with nouns in gender, number, case, and give a detailed answer. Simultaneously with learning to count, the concept of each new number is formed by adding a unit. Throughout the entire school year, quantitative counting up to 5 is repeated. When teaching counting, in each lesson, special attention should be paid to such techniques as comparing two numbers, matching, establishing their equality and inequality, overlapping techniques and applications.

Counting by touch, counting by ear, and counting of various movements within 5 are also given. Familiarity with symbols - numbers within 5 - is introduced. In the process of learning to count, it is necessary to simultaneously introduce numbers - the corresponding designations of numbers.

As children become familiar with the first three numbers, they are taught ordinal counting within 5 and the ability to distinguish it from quantitative counting, and correctly answer the questions: “How many in total?”, “Which is in the count?” Ordinal counting is given together with quantitative counting in order to distinguish them. In the first lesson, it is necessary to reveal the meaning of ordinal numbers. The ordinal value of a number can be revealed by comparing it with a quantitative value. Quantitative counting: “How much?” - "one two Three". Ordinal count: “Which?”, “Which count?” - "first second Third".

One of the important tasks in this group is teaching children the ability to count objects. It is advisable to teach counting in a familiar environment for children, where there are fewer distractions. In this case, it is necessary to show children the method of counting, indicate when to pronounce a numeral, selecting objects.

For example, having selected a cube and placing it on the other edge of the table, the child says: “One”, silently selecting another and placing it next to the first, says: “Two”, etc. pronounce the numeral when the practical action of selection has already been completed. It is important to teach children this method, since many people name a numeral when they take an object, and name the next numeral when they put it next to the first one, that is, they count their movements, not the objects. One should learn to count, lay out, and bring a certain number of objects, first according to the model, and then according to the named number. It is easier for children to count and count according to a pattern than according to a given number. The teacher should know this and complicate the tasks gradually: first, offer to work according to a visual example (a sample card with circles is given and the children are asked to find the same number of toys, put each toy on a card circle, then use the named number (number card or number) to find three ducks , put as many cars as there are numbers on the board).

An even more difficult task will be to count items from a larger quantity. At the beginning of training, children are offered three objects that must be arranged in order, then the number of objects is increased to five or more. Good practice in distinguishing quantitative relationships is ensured by children following the teacher’s instructions. For example: bring a lot of hares and one bear; find where there are few pencils and a lot of notebooks; bring one chair and several dolls.

The program for the senior group is aimed at expanding, deepening and generalizing elementary mathematical concepts in children, and further developing counting activities. Children are taught to count within 10 and continue to be introduced to the numbers of the first ten. Based on actions with sets and measurement using a conditional measure, the formation of ideas about numbers up to ten continues.

The formation of each of the new numbers from 5 to 10 is given according to the method used in the middle group, based on a comparison of two groups of objects by pairwise correlating the elements of one group with the elements of another, children are shown the principle of number formation. For example, on a counting ruler two groups of objects are laid out in a row: on the top strip there are five daisies, on the bottom - five cornflowers. By comparing these two groups of objects, children are convinced that they are equal. They are then asked to count the items on the top and bottom stripes. Another chamomile is added. The children find out that there are more daisies and fewer cornflowers. The teacher draws attention to the fact that a new number has been formed - six. It's more than five. The number six came about when one was added to five. Based on this knowledge and skills, children develop their eye.

During exercises on quantitative comparison of groups of objects, the teacher shows children different ways to designate a quantity. To do this, the same number of sticks are laid out to the right of the group of objects, a counting card, a numerical figure, etc. are hung out. Then a graphical way of indicating a number is shown - a number. In the future, it is necessary to provide children with the opportunity to select the desired number, reproduce, and draw the number of objects indicated by the number. In parallel with the demonstration of numbers education, children continue to be introduced to numbers. Correlating a certain number with a number formed by a particular number of objects, the teacher examines the depicted numbers, analyzing it, compares it with already familiar numbers, the children make figurative comparisons (one is like a soldier, eight is like a snowman, etc.).

The number 10 deserves special attention, since it is written with two digits: 0 and 1. Therefore, it is first necessary to introduce children to zero. Children learn the concept of zero by completing the task of counting objects one at a time. For example, children have 9 toys, they remove them one by one and count them, leaving 8, 7, 6, 5, 4, 3, 2, 1. The teacher asks to remove the last toy as well. Explains to the children that there is not a single toy left. Or, as mathematicians say, zero toys. Zero toys are indicated by the number 0. The teacher suggests finding the place of zero in the number series. Children, independently or with the help of a teacher, decide that zero should come before one, since it is one less than one. We return the toys one by one until we get 9 again. The teacher adds another toy, receives the number 10 and shows that it is written in two numbers: 0 and 1.

Throughout the school year, children practice counting within ten. They count objects, toys, count out smaller ones from a larger number of objects, count objects according to a given number, according to a number, according to a pattern. The sample can be given in the form of a number card with a certain number of toys, objects, geometric shapes, in the form of sounds, movements. When performing these exercises, it is important to teach children to listen carefully to the teacher’s tasks, remember them, and then complete them.

An important task in the senior group remains establishing connections between adjacent numbers, understanding their relationships within 10. Which number follows which, which adjacent numbers are greater or less, and how to make them equal. To do this, all numbers studied by children are compared using specific material. For example, two balls are less than three squares. Knowledge is consolidated on different groups of objects so that children are convinced of the constancy of relationships between numbers. 10

Continuing the work begun in the middle group, the teacher must clarify the children’s ideas that the number does not depend on the size of objects, on the distance between them, on the direction of counting. Solving this program problem will allow children to develop an idea of ​​the abstract nature of numbers and will show the independence of numbers from the direction of counting. Children must be taught to count, starting from any specified object in any direction, without skipping objects or counting them twice.

Children are taught to distinguish between ordinal and quantitative counting. When counting objects in order, you need to agree on which side to count from. Since the result of the calculation depends on this. For example, if children count 10 toys from left to right, then the nesting doll will be the third, and if they count from right to left, then the nesting doll will be the eighth. Ordinal counting is used to determine by which count an item is worth. Children are introduced to the quantitative composition of a number made up of units within 10, for example, the number 3: “One doll, and one more matryoshka, and one more fish. Just three items." Be sure to use a variety of visual materials in classes. This task is repeated throughout the school year.

In the older group, children develop the concept that some objects can be divided into several parts: two, four. For example, an apple. Here it is imperative to draw the children’s attention to the fact that the parts are smaller than the whole, and show this with a clear example. Begin dividing objects into equal parts by folding a sheet of paper in half (into 2 parts), then in half again (into 4 parts). When the children have a good grasp of dividing objects by bending, other techniques are used: cutting with a knife, scissors or tearing.

In the pre-school group, at the beginning of the year, it is necessary to check whether all children, and first of all those who came to kindergarten for the first time, can count objects, compare the number of different objects and determine which ones are more (less) or equal, in what way at the same time they use it.

Sample tasks and questions: “How many big nesting dolls are there?” Count out how many small nesting dolls there are. Find out which squares are more numerous: blue or red. (There are 5 large blue squares and 6 small red ones lying randomly on the table.) Find out which cubes are more: yellow or green.” (There are 2 rows of cubes on the table; 6 yellow ones stand at large intervals from one another, and 7 blue ones stand close to each other.) The test will tell you to what extent the children have mastered counting and what questions should be paid special attention to. A similar test can be repeated after 2-3 months in order to identify children’s progress in mastering knowledge.

During the first lessons, it is advisable to remind children how the numbers of the second heel are formed. In one lesson, the formation of two numbers is sequentially considered and they are compared with each other (6 - from 5 and 1; 6 without 1 is equal to 5; 7 - from 6 and 1; 7 without 1 is equal to 6, etc.). This helps children learn the general principle of forming a subsequent number by adding one to the previous one, as well as obtaining the previous number by removing one from the subsequent one (6-1 = 5).

It is useful to begin each lesson devoted to the formation of subsequent numbers by reviewing how the previous numbers were obtained. You can use a number ladder for this purpose. Double-sided blue and red circles are laid out in 10 rows: in each subsequent row, counting from the left (top), the number increases by 1 (“1 circle more”), with the additional circle turned the other side. The numerical ladder is gradually built up as subsequent numbers are received. At the beginning of the lesson, looking at the ladder, children remember how the previous numbers were obtained.

By the time children enter school, they should have developed the habit of counting and arranging objects from left to right using their right hand. But, answering the question “how much?”, children can count objects in any direction: from left to right and from right to left, as well as from top to bottom and bottom to top. They are convinced that they can count in any direction, but it is important not to miss a single object and not to count a single object twice. Particular attention is paid to comparing the numbers of sets of objects of different sizes (long and short, wide and narrow, large and small), differently located and occupying different areas. Children are encouraged to look for ways to count objects more conveniently and quickly, depending on the nature of their location.

Children in the pre-school group consolidate their knowledge of the composition of the number units of the first heel, they study the composition of the number units of the second heel, learn to establish the relationship between one and the number (6 is 1, 1, 1, 1, 1 and 1 more). They use the following techniques: making a group of different objects or toys; compiling a group of homogeneous objects that differ in quality; compiling a group of pictures that depict different objects united by a generic concept (1 chair, 1 stool, 1 armchair, 1 secretary, 1 closet, 1 sideboard - 6 pieces of furniture in total).

New techniques are also used when working with children aged 6-7 years: sketching a certain number of different toys or geometric shapes. (“I drew a total of 5 shapes: 1 circle, 1 oval shape, 1 square, 1 rectangle, 1 triangle.”) Distributing objects into groups according to one of the characteristics, identifying each group as a unit of counting and determining the total number of groups. (“There are 4 groups of flags in total: 1 group of blue flags, 1 more pink flags, 1 more yellow flags and 1 more blue flags.”) By talking each time about how many objects there are and how they are located, children are convinced that the number of objects is not depends on the space they occupy, their size and other qualitative characteristics.

From comparing the numbers of 2 groups of objects that differ in one characteristic, for example size, they move on to comparing the numbers of groups of objects that differ in 2 or 3 characteristics, for example size, shape, location, etc. Children practice sequentially identifying the characteristics of objects (“ What is it? What is it for? What shape? What color? How many?”), in comparing objects and combining them into groups based on one of the selected characteristics, in the formation of groups. As a result, children develop the ability to observe, clarity of thinking, and ingenuity. They learn to identify features that are common to an entire group of objects or only to part of the objects of a given group, that is, to identify subgroups of objects according to one or another characteristic, and to establish quantitative relationships between them. For example: “How many toys are there in total? How many nesting dolls? How many cars? How many wooden toys? How many metal ones? How many big toys? How many little ones? In conclusion, the teacher suggests coming up with questions with the word how many, based on the ability to identify the characteristics of objects and combine them according to a characteristic common to a given subgroup or group as a whole.

Comparing collections of objects, they use techniques for comparing collections of objects (identifying relations of equality and inequality), children master methods of practical comparison of their elements: superposition, application, arranging objects of 2 collections in pairs, using equivalents to compare 2 collections, and finally, connecting objects of 2 collections with arrows. For example, a teacher draws 6 circles on the board, and 5 ovals on the right and asks: “Which figures are there more (less) and why? How to check? What if we don’t count it?” One of the children is asked to connect each circle with an arrow to an oval. Finds out that 1 circle turned out to be extra, which means there are more of them than other figures, 1 oval was not enough, which means there are fewer of them than circles. “What needs to be done to make the figures equal?” etc. Children are asked to draw the indicated number of figures of 2 types themselves and compare their number in different ways. Techniques are widely used to emphasize the importance of methods of practical comparison of elements of populations to identify quantitative relationships. For example, the teacher puts up 7 Christmas trees. The children count them. The teacher asks them to close their eyes. Place 1 mushroom under each Christmas tree, and then ask the children to open their eyes and, without counting the mushrooms, say how many there are. The guys explain how they guessed that there are 7 fungi. Later, when counting and comparison of numbers increasingly becomes a means of establishing quantitative relationships (“equally”, “more”, “less”), practical comparison methods are used as a means of verification, proof of established relationships . Children must understand that there can be an equal number of any objects: 3, 4, 5, and 6. Useful exercises require indirect equalization of the number of elements of 2-3 sets, when children are asked to immediately bring the missing number of objects, for example , so many flags and drums so that there is enough for all the pioneers, so many ribbons so that it is possible to tie bows for all the bears. To master quantitative relationships, exercises in violation of equality are also used, for example: “Make it so that there are more triangles than squares. Prove that there are more of them. What needs to be done so that there are fewer dolls than bears? How many will there be? Why?"

The study of quantitative relationships, determining larger and smaller numbers is combined with training in counting with the participation of various analyzers: counting sounds, movements, counting objects by feeling. Exercises are combined in different ways. For example, children count the same number of toys as the sounds they heard, find a card with the same number of circles as the number of times they raised their hands, or squat as many times as there are circles on the card. They count the buttons sewn on the card by touch and clap their hands the same number of times or 1 time more (less). For example: “Guess how many buttons Seryozha has on the card if he clapped his hands 1 more (less) time. Count how many flags there are. Think about how many times you need to raise your hand to make 1 more (less) movements than the number of flags.” Exercises in establishing equality and inequality of numbers of sets using different analyzers take place in almost every lesson.

In preparing children for the activity of calculation, the development of memory for numbers is of great importance. The teacher places several groups of objects on the table, calls one of the children in turn to count the objects of one or another group, and offers to remember the number of objects. Then he covers everything with a napkin and checks whether everyone remembers how many of certain items there were. You don’t have to personally call any of the children to the table, but invite everyone to count the toys to themselves, gradually complicating the tasks.

Further development of the concept of number is provided by exercises in dividing objects into equal parts. Children learn to see parts in a whole object, identify the relationship between the whole and the part. 6-7 (lessons) are devoted to dividing subjects into equal parts, and then they periodically return to this until the end of the year.

In the first lesson, situations are created in which it becomes necessary to divide an object into 2 equal parts, for example, divide a treat between 2 dolls or 2 children (guests), help 2 greedy bear cubs divide cheese, etc. The teacher shows how to divide objects into 2 equal parts, i.e. in half, emphasizes that he precisely folds and cuts the object in the middle, then compares the resulting parts, placing one on top of the other or applying one to the other. Children count the parts and make sure they are equal. The teacher says that any of 2 equal parts is usually called a half. The teacher deliberately divides the next subject into 2 unequal parts and asks: “Can such a part be called half? Why not?" Children see that objects can be divided into both equal and unequal parts. One of 2 parts can be called half only when the parts are equal. Gradually, children become convinced of how important it is to accurately fold and cut objects so that equal parts are obtained. Having completed the action, they check (by superimposition and application) whether the parts are equal, count them and, joining together, get a whole object, trace its outline and parts with their hand, compare the size of the whole and the parts.

In the second lesson, the teacher expands the range of objects that the children divide in half. You can use cereal and water. They are distributed equally into 2 transparent glasses of the same size. In the third lesson they show how to divide objects into 4 equal parts, i.e. in half and in half again. They establish relationships between the whole and the part: the part is less than the whole, the whole is greater than the part. If many new children have entered the preparatory school group, it is advisable to start by dividing objects into parts by folding. Children receive 2 objects of the same size, which they are convinced of by placing 1 object on top of another. They divide 1 object into 2 equal parts, the other into 4. By connecting the parts together, they get the whole object, count the parts, show 1 of 2 parts, 2 of 2 parts, respectively 1 (2, 3, 4) of 4 equal parts . Compare the size of 1 part and the whole. To generalize knowledge, you can use schemes for dividing an object into equal parts (apple, circle, square, etc.). Looking at the diagram with the children, the teacher asks: “How many equal parts did you first divide the apple into?” How many of these parts did you get? How many equal parts was the apple then divided into? How many parts did you get? What is more and what is less: half or a whole apple? 2 halves or a whole apple? 1 of 4 parts (1/4) or half (1/2)?” etc.

In subsequent classes, exercises are carried out in dividing geometric figures into 2, 4, 8 parts and in composing whole figures from parts, for example: “How should you fold and cut a square to make 2 equal rectangles?

In the preparatory group for school, great attention should be paid to ordinal counting. Children expand their understanding of in what cases people use ordinal counting, when they resort to numbering and for what purpose (they number houses, apartments, kindergartens, seats in the theater, cinema, transport, etc.).

For children to better understand the meaning of ordinal counting, it is constantly compared with quantitative counting, alternating with the questions how many? which one? They continue to teach children to distinguish between questions of which count? which? Which? The latter is aimed at identifying the qualitative characteristics of objects. What problems do children solve during exercises in ordinal counting? Determine the place of an object among others. (“How many flags are there in total? What is the order of the blue flag? What color is the eighth flag?”) They find an object by its serial number, while performing various tasks. (“In place of the fourth nesting doll, place a tumbler. Replace the sixth blue circle with a red one. Turn the third square the other side up. Give flags to the second, fourth and sixth boys.”) Arrange the objects in the specified order and at the same time determine the spatial relationships between them: in front, after, behind, between: “Arrange the toys so that the first is a matryoshka, the second is a tumbler, the third is a bear. Place the doll between the second and third numbers...” They ask questions: “What is the number of dolls? And the bear? How many toys are there in total? Who is standing in front of the tumbler? Which one is the tumbler?” Ball games are advisable. Children line up and are counted. The one to whom the presenter threw the ball calls his serial number. The presenter can call the serial number. For example, he says: “Sixth!” The child standing in sixth place takes a step forward and says: “I’m sixth!” - and catches the ball.

Children aged 6-7 years are introduced not only to connections, but also to the relationships between adjacent numbers (how much one adjacent number is greater or less than another).

From exercises in comparing the numbers of sets of objects expressed by adjacent numbers, they move on to comparing numbers without relying on visual material. This transition is planned from the first lessons. Consolidating knowledge about the formation of numbers on the second heel, the teacher asks the children: “What number will you get if you add 1 to 6?” Or: “How to get 6 items if there are 5 items?” and so on.

Later, children compare groups of objects of different sizes that take up more or less space. For example, children are asked to count, put down toys, clap their hands, raise their hands, jump, etc. 1 time more or less than the number of toys placed, than the number of circles drawn on the card, or the number that the teacher calls: “Clap in the palms are 1 time larger (less) than the nesting dolls I have here. How many times did you clap? Why?" Another option: “How many circles are on the card? How many Christmas trees will you put up so that there are 1 more (less) of them? Why?" A more complex task: “On the top strip of the card, put 1 circle more than mine. Place 1 circle less on the bottom strip than on the top strip. How many circles are on my card? How many circles do you have on the bottom strip? Why do you have the same number of circles on the bottom stripe as I do?” Each time, children explain how this or that number was obtained, compare adjacent numbers, and establish difference relations between them. (“You need to put 7 Christmas trees, because you have 6 circles on the card, and you asked to put 1 more Christmas tree than circles. 7 is more than 6 by 1, and 6 is less than 7 by 1.”) Children’s answers must be reflected reciprocal nature of the relationships between adjacent numbers. As a result of these exercises, you can move on to comparing numbers without relying on visual material. (“Name a number greater than 7 by 1. How much is 8 greater than 7? What number is less than 7 by 1? Explain why you named 6.”) Exercises on difference comparisons of numbers are given at least 2-3 lessons. In the future, this issue should be returned to periodically until the end of the school year.

Exercises in increasing and decreasing numbers by 1 allow children to consolidate their knowledge of the order of numbers. The teacher puts 1 object (a flag, a matryoshka doll) and asks: “What number will I get if I add 1 object? Why?". Exercises with a ladder allow you to consolidate your knowledge of the direct and reverse sequence of numbers in an interesting way. Children walk up and down the steps of the ladder, counting either the number of steps they have already completed, or the number of steps they still have to go, that is, they count either in forward or in reverse order. A number ladder is used to teach children how to count forward and backward. Exercises with a number ladder allow you to consolidate knowledge about connections and relationships not only between adjacent numbers, but also between other numbers in the series.

Conduct a series of exercises with numerical figures. For example, along the board in a row, the teacher places numerical figures with the number of circles from 1 to 10; He places 2 figures out of place, and asks the children to determine which figures are “lost.” A series of numerical figures can be arranged in both forward and reverse order.

It is necessary to ensure that children always name both numbers being compared. This is an important condition for realizing that each number (except 1) is greater than one, but less than another adjacent to it, i.e. understanding the relativity of the meaning of each number. Gradually, children learn that the expression “before” requires the name of a number less than a given one, and the expression “after” requires a number greater than a given one. In terms of preparing children for the activity of calculation, it is necessary to introduce them to the composition of a number from 2 smaller numbers. Children are shown all the options for the composition of numbers within the heel: the number 2 is 1 and 1, 3 is 2 and 1, 1 and 2, 4 is 3 and 1, 2 and 2, 1 and 3, 5 is 4 and 1 , 3 and 2, 2 and 3, 1 and 4. The teacher lays out 3 circles of the same color in a row on a typesetting canvas, asks the children to say how many circles there are, and indicates that in this case the group is made up of 3 red circles: 1, 1 and another 1. “A group of 3 circles can be made in another way,” says the teacher and turns the third circle back. “How is the group composed now?” - asks the teacher. Children answer that the group is made up of 2 red circles and 1 blue circle, and in total - of 3 multi-colored circles. The teacher concludes that the number 3 can be made up of the numbers 2 and 1, and 2 and 1 together make 3. Then he turns the second circle back, and the children tell him that the group is now made up of 1 red and 2 blue circles. Summarizing the children's answers in conclusion, the teacher emphasizes that the number 3 can be composed in different ways: from 2 and 1, from 1 and 2. This exercise clearly reveals the composition of the number, the relationship between the whole and the part, so it is advisable to begin introducing children to the composition of numbers with it .

To consolidate children's knowledge about the composition of a number from 2 smaller numbers, use a variety of exercises with objects and models of geometric shapes. Children are offered story-tasks, for example: “3 swallows were sitting on the top wire, 1 swallow moved to the bottom wire. How many swallows are there in total? How are they sitting now? How can they still sit?” (Swallows on the typesetting canvas are transplanted from wire to wire.)

Familiarity with the composition of a number from 2 smaller numbers provides the transition to teaching children calculation, that is, solving arithmetic problems.

Conclusion

The formation of elementary mathematical concepts in preschool children has very different directions. One of the most important places in it is occupied by quantitative ideas.

The development of counting activity in preschool children occurs in six stages. All work on the development of counting activities in preschoolers takes place strictly in accordance with the requirements of the program content. Each program for training and education in kindergarten defines tasks for the formation of quantitative concepts in children. The work must take place within the system, consistently, taking into account the age characteristics of the children. The main form of implementation of program requirements is classes in kindergarten. Also, to consolidate knowledge and improve skills acquired in numeracy classes, it is necessary to include exercises to develop quantitative concepts in various types of activities. It is necessary to start work from an early age during the pre-numerical period of education (2-3 years). This work is simply necessary before children begin to familiarize themselves with numbers and is aimed at developing ideas about set. Children are taught to compare two sets, compare elements of one set with elements of another, distinguish between equality and inequality of groups of objects that make up the set. At this age, the foundation is laid for the subsequent development of counting activities.

In the middle group of kindergarten, work is aimed at teaching counting to 5 by comparing two sets expressed by adjacent numbers. An important task remains the ability to establish equality and inequality of groups of objects, when the objects are at different distances from each other, when they are different in size, etc.

Work with children aged 5-6 years is aimed at further developing counting activities. Children are taught to count within 10 and continue to be introduced to the numbers of the first ten. Based on actions with sets and measurement using a conditional measure, the formation of ideas about numbers up to ten continues.

In the preparatory group for school, counting skills are improved from 10 to 10, children learn to name numbers in forward and reverse order, become familiar with the numbers 0-9, etc.; with the composition of the numbers of the second heel of ones, they learn to decompose a number into two smaller ones within 10 on a visual basis and make a larger one from two smaller ones, get acquainted with coins and learn to solve simple arithmetic problems; widely use techniques to emphasize the importance of methods of practical comparison of elements of populations to identify quantitative relationships; learn to see connections and relationships between adjacent numbers; improve skills in dividing geometric shapes; constantly compare quantitative counting with ordinal counting, etc.

The work on developing counting activity in preschoolers is especially labor-intensive and requires a lot of attention. It is the basis for further education at school.

Literature

1. Althouse D., Doom E. Color – shape – quantity. M.: Education, 1984. – 64 p.

2. Bondarenko A.K. Didactic games in kindergarten. M., Education, 1985.-175 p.

3. Volina V.V. Holiday of numbers. Moscow: AST – PRESS, 1996. – 304 p.

4. Erofeeva T.I., Pavlova L.N., Novikova V.P. Mathematics for preschoolers. M. Education, 1992.-192 p.

5. Kozintseva E.A., I.V. Pomerantseva I.V., T.A. Terpak. Formation of mathematical concepts. Lesson notes for the senior group. Volgograd: Teacher, 2008. – 175 p.

6. Leushina A.M. Counting lessons in kindergarten. Uchpedgiz, 1963, - 192 p.

7. Leushina L.M. Formation of mathematical concepts in preschool children. M.: Education, 1974. – 368 p.

8. Metlina L.S. Mathematics in kindergarten. M.: Education, 1984. – 256 p.

9. Peterson L.G., E.E. Kochemasova. Playing game: Practical mathematics course for preschoolers. Guidelines. Moscow: Balass, 2001. – 176 p.

10. Sai M.K., Udaltsova E.I. Mathematics in kindergarten. 1990.-96s.

11. Serbina E.V. Mathematics for kids. M., Education, 1992.- 80 p.

12. Taruntaeva T.V. Development of elementary mathematical concepts in preschool children. M.: Education, 1980. – 64 p.

13. Let's play! Mathematical games for children 5-6 years old. Ed. A.A.Stolyar. M.: Education, 1991. – 80 p.

14. Smolentseva A.A. Plot-based didactic games with mathematical content. M.: Education, 1987. – 97 p.

15. Formation of elementary mathematical concepts in preschoolers. Ed. A.A.Stolyar. M., Education, 1988.-303p.

Leushina A.M. Counting lessons in kindergarten. M.: Uchpedgiz, 1963, - 192 p. (p.3).

Leushina A.M. Counting lessons in kindergarten. Uchpedgiz, 1963, - 192 p. (p.3 - 4)

Sai M.K., Udaltsova E.I. Mathematics in kindergarten. M, 1990.-96s. (p.8)

Erofeeva T. I., Pavlova L. N., Novikova V. P. Mathematics for preschoolers. M. Education, 1992.-192 p. (p. 35). Leushina L.M. Formation of mathematical concepts in preschool children. M.: Education, 1974. – 368 p. (69-74 pp.)

Leushina L.M. Formation of mathematical concepts in preschool children. M.: Education, 1974. – 368 p. (69-74 pp.)

Sai M.K., Udaltsova E.I. Mathematics in kindergarten. Ministry of Public Education, 1990.-96p. (p.12)

Erofeeva T.I., Pavlova L.N., Novikova V.P. Mathematics for preschoolers. M. Education, 1992.-192 p. (p. 154)

Sai M.K., Udaltsova E.I. Mathematics in kindergarten. Ministry of Public Education, 1990.-96p. (p.14)

Erofeeva T.I., Pavlova L.N., Novikova V.P. Mathematics for preschoolers. M. Education, 1992.-192 p. (p.156).

Sai M.K., Udaltsova E.I. Mathematics in kindergarten. Ministry of Public Education, 1990.-96p. (p.20)

Formation of elementary mathematical concepts in preschoolers. Ed. A.A.Stolyar. M., Education, 1988.-303p. (p.173).

Representations of preschool children, and this confirms our hypothesis. CONCLUSION The purpose of the study was to study the problem of using game techniques in the formation of elementary mathematical concepts in preschoolers. To achieve it, we analyzed the psychological and pedagogical literature on the research problem, reviewed and analyzed the game method in...

Reading, writing, counting are the basic skills necessary for a child to master knowledge, so they need to be developed from early childhood, and not wait until the child goes to school. By teaching your child to read, write and count, you will make his life in school much easier. Learning to count can be one of the most difficult tasks, but don’t be afraid and give up when you fail: the main thing is patience and work.

Features of training

It is difficult to focus the attention of a small child on something serious. You should start learning in a playful way to interest the baby. It is not necessary to sit with your baby at the table, like at a school desk. You can learn in different ways: by moving, sitting on the floor, even jumping in place.

With preschool children, you can begin more serious activities that require concentration. The time devoted to counting may also increase. For example, it is advisable to exercise with children for 10 minutes about three times a day. With preschoolers - 20 (at best 30 minutes).

• Create a positive atmosphere. You won't achieve anything by shouting, you will only discourage your child from learning. Patience and calm are important factors in this matter.
• Involve surrounding objects in learning, show your child that the ability to count is vital. You can count plates on the table, birds flying in the park, children on the playground, fruits, cars, toys, steps in the entrance and much more.
• Don't demand more from a small child than he can. All children are individual in their development, each new skill comes in its own time.

If your baby doesn't succeed, don't get annoyed. Wait, return to the task after some time (for example, after a week, a month).

• When learning, try to follow three steps. First, let your baby get used to the names, terms, and the process itself. Then ensure that he understands the essence of what is being studied. Simple memorization is irrational; it is necessary that the child learns to understand and realize the essence of each phenomenon. When the information is understood by the baby, he can retell it and explain it, then he can move on to memorization.
• Don't forget that when getting acquainted with mathematics, you should pay attention not only to counting. Also teach your baby to recognize geometric shapes and navigate in space so that he can show where “up”, “down”, “right”, “left” are. By about three years old, the baby should be able to determine which object is shorter, longer, higher, lower, and in which direction it is going.

Considering age

Children learn new things much easier than adults. The need to acquire new knowledge arises in children by the age of two. Fresh information is given to kids without effort, so they quickly learn some actions. But when teaching counting, you should take into account the child’s age:

• You can start learning to count at 2 years old. During this period, children are able to master counting from 0 to 3. By the age of 2.5-3 years, they can teach counting up to 10. All this must be done with visual aids, objects, and improvised means (for example, using cubes, sticks).

• At 3-4 years old a child is able to learn to count to 20. At this stage, clarity is still needed: it is worth using cards with numbers, objects that need to be counted.
• If your child has a mathematical mind, at 4-5 years old he can learn to count to 100. The main thing is to explain the principle of forming numbers from digits. Do not despair if at this age your child cannot count with tens. You can resume education at age 6.
• Aged 5-6 years you need to move from visualization to mental arithmetic. During this period, the child must learn to count without the help of sticks, fingers, or cards. You need to practice counting backwards, and also call numbers in a chaotic order.

Addition and subtraction

The ability to add and subtract is usually developed by the age of five. First, this should be done with the help of various objects, then practice solving simple examples in your head. When learning to count, you need to gradually introduce simple examples of addition and subtraction. It’s still too early to solve examples in a column, but adding single-digit numbers can be taught.

It is necessary to do mathematics with your child in such a way that he does not lose interest. Therefore, no boring examples like “3+5=? " it can not be. We teach, engaging, visually. Possibly in a humorous way.

You need to start simple. For example, add one to each known digit and subtract it. It is worth using objects that are interesting to the child or important to him. It’s better to present an example in the form of a question: “You have two cookies. You will share one with your mother. How much will you have left? "And everything in the same spirit.

To move on to subtraction, make sure your child has mastered addition well. Use examples of addition and subtraction not only in class, but also while walking, in the store, at lunch, or when cleaning your room. Let the child say the condition of the problem after you. Use special manuals and teaching materials with simple exercises. Pay attention to the presence of bright illustrations. Don't forget - the child needs to be lured.

To easily add and subtract, the baby needs to learn the composition of numbers. He must learn that 5 consists of the numbers 2 and 3, 1 and 4, 10 - from the numbers 1 and 9, 2 and 8, and so on. Before learning to count correctly in the head, a child must be good at solving problems with visual materials or on his fingers. It is better to start learning to count silently from the age of 4, not earlier. From this age, time spent on addition and subtraction affects overall development.

It is important to understand the concepts of “more” and “less”. While flipping through educational books, you can ask which animals are more on the page, which colors are smaller. You also need to learn the term “equally.” It is imperative to explain to the child that changing the places of the terms does not change the sum.

You should not miss the opportunity to ask your child to count in his head. This can be done anytime, anywhere and with anything: you can count houses, benches, flowers, chairs.

Impact on development

At the age of 5-6 years, most preschool children can already count decently to 20, or even to 100. Teaching counting specifically and mathematics in general contributes to the intellectual development of the child as a whole. Mental arithmetic stimulates the brain and makes it tense. Memorizing numbers and their composition develop memory.

When solving simple problems where you need to count, add or subtract any objects, the baby uses his imagination, drawing various images in his head. By speaking the terms of the task out loud, the child trains his speech. Therefore, it is important that adults pronounce the text correctly, because the baby will repeat it.

Knowing numbers will give the child the opportunity to participate to some extent in the lives of adults: he will be able to help set the table, knowing how much cutlery is needed, carry out small tasks for his parents, which will teach him responsibility, and much more. This is good preparation for school. Already in the first grade, a child will be able to count how many children are present at the lesson, name the date, and will know what it means to “prepare two pencils for work.”

Quick techniques

Training should be done gradually. First you need to learn numbers from 0 to 10. But even this can be difficult for a child. Therefore, split the ten, for example, into two fives and learn in stages. For learning, you can use various teaching aids, include entertaining material (games, fairy tales, counting rhymes), make lessons fun, avoiding tedious memorization.

You can easily diversify your learning process at home:

• learn to count on your fingers;
• choose tasks in the form of games;
• connect counting rhymes;
• show pictures, asking how many of certain objects are depicted;
• watch educational programs with your baby;
• Teach your child poems and fairy tales with quantitative and ordinal numbers;
• constantly count everything that comes your way.

The following methods and rules for teaching counting to preschool children are proposed. You can choose the method that is most suitable for your child. It's better to combine several.

Methodology of Sergei Polyakov

According to this method, you need to start teaching your child to count when he shows interest. As soon as parents notice that the baby is interested in numbers, training should begin. Not later than. Sergei Polyakov does not recommend using the method of teaching counting, in which you need to add one at a time. This slows down the learning process and prevents the child from developing.

He does not recommend starting training with counting on sticks, fingers and a ruler. It also does not promote intellectual development. According to Polyakov, classes are based on teaching mental arithmetic. First, the baby lists everything that catches his eye (toys, books, steps), then he tries to count silently, including adding and subtracting.

At the first stage, the child works with numbers within 10. To solve simple examples in your head, your child needs to remember the composition of the numbers. At the second stage, the child solves examples with two-digit numbers. At the same time, he does not retrieve ready-made solutions from memory, as happens at the first stage, but comes to understand and remember methods of addition and subtraction.

When learning, the child must learn the concepts of “more”, “less”, “equally”. Lessons using the Polyakov method are accompanied by various games. For example, at the first stage they use cubes and games with them “Putting numbers on the cubes”, “Gnomes in the house”, “Divide in half”. Others can be used.

Peterson technique

Lyudmila Georgievna Peterson’s method teaches children to think logically. The method is not limited to learning to count; it includes many interesting game tasks that develop ingenuity. This technique is popular in preschool institutions and primary schools. The learning system is a cycle called the “layer cake principle.”

Traditional teaching methods follow a linear concept: in the first grade we learn addition and subtraction, in the second we learn the times tables, division and multiplication, in the third we learn fractions, and so on. It turns out that if a child was sick for a long time in second grade and missed the main points of the topic, it will be difficult to catch up with them. Following this method, Every year the same thing is studied, but with different depths of complexity. For several years in a row, the themes are repeated, with each one appearing again and again in a new aspect.

This system involves a large number of games. Toddlers, for example, love the number beam. The baby is faced with the task of finding out how much 3+2 is. The child stands at mark 3, takes two steps forward (you need to add) and stops at mark 5. If you need to subtract, the child takes 2 steps back. This is how the baby gradually remembers the composition of single-digit numbers.

At home, you can develop your baby’s logic by playing. Lay a row of cubes: 2 red-2 blue, 2 red-2 blue. Tell your child to continue the row so that the sequence is not broken. If the baby takes, for example, a yellow cube instead of a red one, you suggest that this is how the row changes, but it should be preserved.

Another interesting game. Draw a large blue square on a piece of paper. Give your child the task of drawing a figure that differs from yours in only one way. Your child draws a small blue square. Then you draw a small blue circle. He is a small yellow circle. And so on ad infinitum until you get bored.

It is appropriate to use tasks that identify more and less objects. In two squares located opposite each other, you need to draw, for example, hearts - 6 and 5. The child needs to determine which is bigger. Of course, he will immediately rush to count hearts. But you can show him another way.

Show that the hearts are combined in pairs: connect one heart from the left square with a line to the heart from the right square. There are more of them in the square where the heart is left without a pair. Here you can enter the “greater than” and “less than” signs. It happens that there is not enough time to work with the baby and draw tasks for him himself.

Using this method, many printed notebooks are produced with interesting tasks that can keep a child occupied.

Training according to Zaitsev

Nikolai Aleksandrovich Zaitsev developed several games and sets of visual materials to facilitate learning mathematics. For example, the game “One Hundred Count”. It includes a set of cards with numbers up to 100. This game will help develop a child.

Each card shows one number. In addition to numbers, geometric figures are depicted in the number of tens and units of numbers. For example, the number 75. Under the seven there is a row of seven rectangles, each of which has ten sticks (7 tens), and under the five there is 1 with five sticks (5 units).

Gradually, the child needs to be introduced to each card; you can place them on the wall in the nursery. Using the same cards you can learn to add and subtract. Zaitsev’s methodology also includes games such as “I’m cramped in a hundred” (studying numbers up to a thousand), “Platonic Solids” (geometric skills), “A Thousand Plus”, etc.

Soroban School

Mental arithmetic Soroban is a school of mental arithmetic. These are official institutions located in several cities of Russia that teach children under this program. The Soroban school organizes classes so that both hemispheres of the brain are involved. At the same time, various skills and abilities are formed:

• speech;
• imagination;
• creative thinking;
• analytical thinking;
• memory;
• Creative skills;
• attention;
• intuition.

Learning takes place on the abacus. The emphasis is on seeing and remembering the picture in motion. Then the child himself creates moving images and comes up with associations. This technique creates conditions for rapid perception of information, teaches you to synthesize and analyze information, and promotes quick mental calculations.

This program can be used by children from 5 to 11 years old.

The Soroban school’s operating technique is based on three basic principles:

• regularity;
• exciting learning process;
• strong motivation.

Until recently, the Soroban school method worked well only with gifted children. The classes didn’t work with kids of average development level; they seemed too difficult.

In recent years, the school has developed a program suitable not only for “prodigies”, but also for children with average abilities, which allows them to learn something more and develop average abilities to high results.

Using any chosen method, you can and should teach counting backwards. First, you should use visual material for this (the same cubes, cards, toys). Then it is important to teach counting backwards out loud, but without improvised objects. Let's not forget about ordinal counting.

Teaching can be done by telling a fairy tale. For example, “Teremok” (“The mouse came first, the frog came second...”, etc.). Then you need to ask questions to the baby (who was first, second, third). You can ask him to retell the fairy tale using ordinal numbers.

Nowadays it is common practice in schools to build combined lessons with interdisciplinary connections. For example, in a mathematics lesson you can use material from history, literature, geography and other academic subjects. When teaching counting at home, you can also use other disciplines.

In a biology textbook, say, for an older brother or sister, it would be nice to count the organs in the human body; on a world map - the number of continents (connection with geography). You can sing songs with numbers (connection with music), read syllables in words (connection with the Russian language).

After a series of home activities with your child, give him a short test in the form of a test. And depending on how he copes with it, reward him with a small prize. There should always be a stimulating component to learning. Don't forget about counting in everyday life.

Which method is better?

The most effective method is one that suits the child, taking into account his individual characteristics. You may have read or heard about some super-effective technique, but it does not bear fruit with your baby. Don't torture yourself and your child: try something different, less complicated. In the learning process, you need to face the truth - Not all children develop quickly, not all of them are gifted, tasks for each need to be chosen according to their strengths.

In any method, use games to maintain your baby's interest and connection with everyday life.

Preschoolers need to be taught in such a way as to prepare them for school. And these are not only numbers, counting 1, 2, 3, 4, addition and subtraction. Preschoolers need to develop logic and analytical thinking. They must learn to think, look for a solution to a problem on their own, make assumptions, and not just retrieve a ready-made memorized answer from memory. Although in many situations you can’t do without it.

By the beginning of first grade, a child should know how to count to at least 20 (preferably up to 100), and be able to work in his head with single and double digit numbers. Must know where “right”, “left”, “top”, “bottom” are, what “more”, “less”, “equal” means.

There should be no counting on fingers. It is important that actions are carried out only in the mind. Therefore, choose the appropriate method. Any of the above will do.

Despite the importance of achieving results, Do not shout, scold or punish your child during class, if some task is beyond his strength. In this case, you will not return the desire to work, and everything will collapse.

The child should enjoy the activities. It will be good if they evoke joy during the wait before they begin, and not the horror of the upcoming torture.

Good afternoon, dear readers! How much effort adults have to put in to teach a child to count within 10 and 20. And not only count, but also solve examples, subtract and add! At the same time, doing this is not as difficult as it seems at first glance. We offer you non-standard game techniques on how to teach your child to count examples within 20.

Where to begin?

Stage 2

If you have learned how to count, get acquainted with the graphic representation of the numbers. For this purpose, we use cubes with numerical images and cards.

Stage 3

The next stage is very important: it prepares the basis for quick mental arithmetic. This is the study of the composition of a number. If the baby knows exactly how numbers are laid out, he will easily solve addition and subtraction examples.

The study of the composition of numbers is traditionally carried out using so-called “houses”. Draw a house on checkered paper. There are always 2 cage rooms on one “floor”. The number of storeys of a house is determined depending on the number of numerical pairs into which the number can be decomposed.

For example, 4 can be decomposed into 3 and 1, 2 and 2. This means that the number 4 lives in a two-story house, etc. We will write it on the roof. The example clearly shows how to correctly create houses for the numbers 3, 4 and 5.

The child will have to memorize the distribution of “tenants” by floor. Start with small numbers. Ask your little one to carefully look at who lives with which neighbor, and then “populate” the numbers yourself.

When two and three are mastered, move on to more complex numbers. This technique gives the most consistent results. Tested from my own experience.

Here you can download this table and use it to master the number composition technique:

Stage 4

When the houses are completed, it is the turn of examples within 10. In the first grade, these examples will have to be solved in the first half of the year, so it is better to prepare in advance. Now all that remains is to place + or - signs between the “settlers”, having previously explained their purpose to the baby.

First, present addition or subtraction as a game. For example, from a four, a one left the floor. Which neighbor will remain on the floor? Answer: three. Such exercises will help the baby quickly get used to mathematical examples. Gradually we change the words “left” and “came” to “plus” and “minus”.

This is how we mastered counting within 10 with our child. As you can see, the technique is very simple, but it requires time and patience to work. Try to force your baby to count in his head first: written exercises slow down thinking.

Along the way, train the concepts of “more and less” (first use objects, placing them on different sides, then compare the numbers), neighbors of a number (write a series of numbers with missing digits and ask the baby to complete the series, placing the neighbors correctly).

Go ahead…

The time has come to introduce the baby to the second ten. To overcome arithmetic difficulties, we suggest the following training algorithm:

Part 1

We introduce the concept of ten. To do this, lay out 10 cubes in front of the child and add one more. We explain that it is eleven. We say that the ending of the word “dtsat” means “ten”. To form the number from 11 to 19, you just need to add the number to the ending “twenty” and put the preposition “na” between them.

Part 2

Since the baby is already familiar with the concept of ten, we introduce the units digit and operate with these concepts when adding. For example, 13+5. First we add the units: 3+5=8. Now add the remaining ten and get 18.

Part 3

Now let's move on to the negative examples: we act in exactly the same way. Subtract the ones, then add the tens.

Part 4

The most difficult stage is subtraction, in which the first unit is less than the second: 13-6. In this example, we cannot subtract six from 3. You have to deal with dozens. One way is to subtract three from six, subtract the remaining number from ten, i.e. 6-3=3, 10-3=7. After a few practices, your baby will be able to do subtraction in his head.

The child must clearly master the described skills: in 2nd grade he will need this to solve examples with two-digit numbers.

To brighten up the learning process, you can use various aids:

• cubes;
• magnets;
• pictures (learning with pictures is especially varied: you can simply count them, use coloring books with examples to reinforce counting skills);
• any items at hand;
• counting sticks;
• abacus, etc.

The more imagination you show, the sooner you will interest your child in mathematics.

We have looked at the sequence of teaching your little one to solve examples within 20 in stages. If the article was useful to you, leave a comment or share the article with your friends on social media. networks.

See you soon, dear friends!

Where to start learning mathematics with children?

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

At what age should children start learning mathematics?

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

Development of numeracy skills

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

How to explain to a child what a number is?

One, two -

Let's go get some firewood

One two Three -

Look at mom.

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

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

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

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

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

Games for teaching counting

Balls and buttons

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

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

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

How far is it?

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

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

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

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

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

Mosaic

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

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

Learning to count on fingers "Fingermatics"

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

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

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

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

Squirrels

One two three four five

The squirrels came to play. (Show five fingers)

One has disappeared somewhere, (Hide your hand behind your back)

Four squirrels left. (Show four fingers)

Now look quickly (Hide your hand behind your back)

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

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

We only have two left. (Show two fingers)

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

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

Then say:

While you and I were counting,

The squirrels ran away from us.

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

Five teddy bears

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

One little bear at the table was devouring a cutlet,

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

There were two of them.

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

But another one came running and ate all the cutlets.

There were three of them.

Three stupid little bears wanted to close the door,

But the door opened and another beast burst in.

There were four of them.

Four little bears found a swarm of bees,

Another little bear ran in and started a loud howl.

There were five of them.

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

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

This house has five floors:

On the first floor lives a family of hedgehogs,

On the second floor lives a family of bunnies,

On the third - a family of red squirrels,

On the fourth a tit lives with its chicks,

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

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

On the fifth owl,

On the fourth tit,

Squirrels on the third,

Bunnies - second,

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

Two bears

Two bears were sitting

On a thin branch.

One stirred the sour cream,

Another was kneading flour.

One "kuku", two "kuku"

They both fell into the flour!

Nose in flour, mouth in flour.

Ear in sour milk!

Five fingers

There are five fingers on my hand

Five grabbers, five holders.

To plan and to saw,

To take and to give.

One two three four five!

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

Naughty counting rhyme

How many fingers do we have?

Shall we count?

That's it!

Are we bending?

That's two!

Shall we continue?

Three four...

Where is the fifth?!

Wow - look!

Let's continue to the next one:

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

Bang-bang oh-oh-oh!!!

Yes, the ninth is like that!

How many fingers are there in total?

Exactly ten! Oh-ho-ho!!

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

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

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

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

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

Counting on fingers

One two three four five!

Finger went for a walk,

I ate a big bun with poppy seeds.

This fat gentleman

Thumb with number one!

This finger went into the forest

I found honey in a large hollow.

Barely escaped from the bees

Nice finger number two!

This finger goes to sea

On a humming ship.

In a storm on deck, look!

Brave finger number three!

This finger is our strongman:

Like a light children's ball

He's throwing weights!

Thumb with number four!

And the last one is a cute little one,

He sits quietly by the window,

Junior finger number five!

One two three four five!

Sing along, sing along:

Ten birds are a flock.

This bird is a nightingale,

This bird is a sparrow.

This bird is an owl

Sleepy little head.

This bird is a waxwing,

This bird is a crake,

This bird is a starling,

Gray feather.

This one is a finch.

This one is a swift.

This one is a cheerful little siskin.

Well, this one is an evil eagle.

Birds, birds go home!

(Bend or stroke your fingers)

My brother will soon be five.

But he doesn't want to study.

Then I came up with a thing.

I say: give me your hand,

One two three four five.

These fingers are rabbits.

The first one hid somewhere.

Bend your finger - once.

How many of them do we have now?

Brother spread his palm

And he suddenly answered: “four.”

Well done. A capable boy.

Bend your finger again.

How many are there now - look?

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

The third hare suddenly disappeared:

The prankster ran away into the forest.

Our bunny barely disappeared,

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

We left everything

How many fingers? —

One. —

And then this bunny

He lay down on his side in bed.

We bend the fifth finger,

Now what remains?

The brother looks slyly and laughs:

- What remains is... a fist.

Little bunny

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

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

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

That's how big we are

Raises the child's hands up.

Not tiny

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

Like this, like this

Stands up, raising the baby's hands up.

These are the little ones.

The dragonets were flying

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

The dragons were flying and eating donuts.

How many donuts did the dragons eat?

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

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