Methods of teaching ordinal counting in kindergarten (description). Do-it-yourself didactic manual for teaching counting in kindergarten
Types of account: quantitative and ordinal account
Hello dear friends!
So, the fourth lesson of the first topic.
How did you accomplish homework with your child? How is his progress? Have you mastered all the material? Were you able to work with him in math? If the child has not yet comprehended everything, then do not despair and do not scold him! Nevertheless, you need to persistently stir up questions on the topic - inadvertently, as if playing! I hope you do so! If you have any questions for me, write in the comments. I and hopefully other parents will answer you!
Did you take the Family Drawing Test with your child? What are the results? Are you satisfied or do you have something to think about? If there are problems, solve them immediately! Write in the comments.
And today we move on to the next subtopic "Quantitative and ordinal counting". The child must know the names "quantitative account" and "ordinal account" and their difference. And they differ in the question they answer.
In quantitative counting, we answer the question "how much?"(The child should know this by heart. You need to check it like this: “What question do we answer when we count quantitatively?” Ask often and make sure that the child gives a complete answer, as written).
For example, How many toys? (Five). How many blue sticks? (Three). As you can see, before that we only dealt with quantitative counting, in which you only need to know the total number of items - How many their? So it doesn't matter what order the items are counted in. And this child has no problems, he easily names the number of objects.
The condition is important:
Do not skip a single item when counting or do not count any item twice.
Unobtrusively and non-instructively explain this to the child. For example, such a game situation.
Look, what beautiful birch trees. How many?
I counted seven. Did you count correctly?
Yes, six.
Oops, I'm to blame. I counted the same birch twice. You have to be very careful when counting.
With an ordinal account, we answer the question "which counts?» (The child should know this by heart. You need to check it like this: “What question do we answer with an ordinal score?” Ask often and make sure that the child gives a complete answer, as written).
For example, first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth. In the park which by account from U.S red shop? - Sixth. - Right! And in this case, we are not interested in the total number of items, but which on the account is the item we need. It is only important to indicate in what order the account should go, starting from what subject. At first, I recommend that when counting, the child names each item.
For example, the car is the first, the bunny is the second, the carrot is the third, etc. Soon this need will disappear. Lay out five sticks different colors. Which counting the red stick? - Red - the third. Of all the toys which chicken count? - The fourth chicken.
The lesson ends. In the next lesson, we will learn how to teach children how to count within 10.
I warn parents that they should not teach their child to write numbers or letters. Leave this matter to professionals so that children do not have to be retrained, and this negatively affects their psyche and attitude to learning and to the teacher. Because for the child the authority of the parents is very great, and the teacher has to relearn what the parent has done.
Homework for parents: continue to work on the previous lessons and in this lesson make sure that the child answers the question you posed about the quantitative and ordinal account.
In 2 weeks we will move on to the study of the second topic and talk about the development fine motor skills brushes.
Love your children and take care of them!!!
Good luck in everything!
P.S. Pay attention to the short neurological test for parents. Try to pass it and smile. Perhaps this is true. Let your parents pass it! :)
Hello Nina!
Thanks for the question! Yes, of course, with an ordinal count, there should be an interrogative pronoun "which"? In Russian, there are differences in the use of two interrogative pronouns "what" and "which".
1. "What" is used in the case of determining the quality or property of an object.
For example.
- What is this cube?
- Big.
- What rain?
- Strong.
- What notebook?
- In the box.
2. "Which" is used in the case of determining the ordinal place of the subject from the beginning of the count.
For example.
- Which backpack is yours - this one or that one (first or second)?
- This (first).
- What's the number of carrots?
- Third.
- Which boy in line is your friend?
- Fourth.
- What time is it now?
- Tenth.
- Which cube is green?
- First.
Unfortunately, these interrogative pronouns are often not distinguished in use. Including at school.
Good health to all your family!
Good luck to your child!
Write, ask - do not be shy!
Sincerely, Anatoly Ivanovich.
I'm sorry, I didn't quite understand. With an ordinal account, we ask the child “which one?” or "what's the score?". You write "which?", and below all the questions on the ordinal account "which?" or "what?".
How to ask the question correctly: which machine is in a row? Or what kind of machine? I would love to sort it out. Thanks a lot!
Thank you! I'm very glad if I could help you! Good health and success in learning to you and your child (children) !!! Get busy, write! :)
Very informative!
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IN preschool age laying the foundations of knowledge the child needs At school. Mathematics is complex science, which can cause certain difficulties during schooling. In addition, not all children have inclinations and have a mathematical mindset, so when preparing for school, it is important to introduce the child to the basics of counting.
In modern schools, the programs are quite saturated, there are experimental classes. In addition, new technologies are entering our homes more and more rapidly: in many families, computers are purchased to educate and entertain children. The requirement of knowledge of the basics of computer science presents us with life itself. All this makes it necessary to introduce the child to the basics of computer science already in the preschool period.
When teaching children the basics of mathematics and computer science, it is important that by the beginning of schooling they have the following knowledge:
Counting up to ten in ascending and descending order, the ability to recognize numbers in a row and randomly, quantitative (one, two, three ...) and ordinal (first, second, third ...) numbers from one to ten;
Previous and subsequent numbers within one ten, the ability to make up the numbers of the first ten;
Recognize and depict basic geometric shapes (triangle, quadrilateral, circle);
Shares, the ability to divide an object into 2-4 equal parts;
Basics of measurement: the child should be able to measure length, width, height with a string or sticks;
Comparing objects: more - less, wider - narrower, higher - lower;
Fundamentals of computer science, which are still optional and include an understanding of the following concepts: algorithms, information encoding, computer, computer control program, the formation of basic logical operations - "not", "and", "or", etc.
The basis of the foundations of mathematics is the concept of number. However, the number, as, indeed, almost any mathematical concept, is an abstract category. Therefore, it is often difficult to explain to a child what a number is.
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 the baby. However, you can teach your child to count on specific subjects. The child understands that toys, fruits, objects can be counted. At the same time, objects can be counted "between times". For example, on the way to kindergarten, you can ask your child to count the objects you meet on the way.
It is known that the execution of a small homework the baby likes it very much. 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 you need for the job. 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.
When a child sees, feels, feels an object, it is much easier to teach him. Therefore, one of the main principles of teaching children the basics of mathematics is visibility. Make math aids, because it is better to count some specific objects, such as colored circles, cubes, strips of paper, etc.
It’s good if you make geometric shapes for classes, if you have the Lotto and Domino games, which also contribute to the formation of elementary counting skills.
The school course of mathematics is not at all easy. Often, children experience various kinds of difficulties in mastering the school curriculum in mathematics. Perhaps one of the main reasons for such difficulties is the loss of interest in mathematics as a subject.
Therefore, one of the most important tasks of preparing a preschooler for schooling will develop his interest in mathematics. Introducing preschoolers to this subject in a family environment in a playful and entertaining way will help them in the future to quickly and easily learn the complex issues of the school course.
Formation in a child mathematical representations promotes the use of a variety of didactic games. Such games teach a child to understand some complex mathematical concepts, form an idea of the relationship between numbers and numbers, quantities and numbers, develop the ability to navigate in the directions of space, draw conclusions.
When using didactic games are widely used various items and visual material that helps keep the lessons fun, entertaining and accessible.
If a child has difficulty counting, show him, counting aloud, two blue circles, four red ones, three green ones. Ask him to count the objects out loud. Constantly count different objects (books, balls, toys, etc.), from time to time ask your child: "How many cups are on the table?", "How many magazines are there?", "How many children are walking on the playground?" and so on.
The acquisition of oral counting skills is facilitated by teaching kids to understand the purpose of some household items on which numbers are written. These items are watches and a thermometer.
However, a preschooler should not be given a thermometer in their hands, as this can be dangerous. Yes, and this is not necessary, since you can make visual material, simulating the action of a thermometer.
The thermometer is made of thin board or cardboard. At the same time, it is advisable to paint some parts of the thermometer in different colors: the part that shows the temperature below zero is painted in Blue colour- this is a symbol of the fact that it is cold, and water turns into ice at this temperature.
The upper part of the training thermometer contains a temperature of over one hundred degrees. What is below a hundred degrees is red - at this temperature it is warm or hot outside, and the ice begins to melt. At temperatures above one hundred degrees, water turns into steam, respectively, this part of the training thermometer is white.
Such visual material opens up scope for imagination when conducting various games. Once your child has been taught how to take their temperature, ask them to check their temperature on an outdoor thermometer every day. You can keep track of air temperature in a special "journal", noting daily temperature fluctuations in it. Analyze the changes, ask the child to determine the decrease and increase in temperature outside the window, ask how many degrees the temperature has changed. Make a schedule with your baby for changes in air temperature for a week or a month.
Thus, not only the improvement of counting skills takes place, the child also gets acquainted with the concepts of positive and negative numbers, learns some laws of physical phenomena, learns to draw coordinate axes, build graphs.
It is very important to teach the child to distinguish the location of objects in space (in front, behind, between, in the middle, on the right, on the left, below, above). To do this, you can use different toys. Arrange them in different order and ask what is in front, behind, near, far, etc. Consider with the 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 such concepts as many, few, one, several, more, less, equally. During a walk or at home, ask the child to name objects that are many, few, one object. For example, there are many chairs, one table; many books, few notebooks.
Put the cubes of different colors in front of the child. Let there be seven green cubes and five red cubes. Ask which cubes are larger, which are smaller. Add two more red cubes. What can be said about the red cubes now?
When reading a book to a child or telling fairy tales, when numerals are encountered, ask him to put aside as many counting sticks as, for example, there were animals in history. After you counted how many animals there were in the fairy tale, ask who was more, who was less, who was the same number. Compare toys by size: who is bigger - a bunny or a bear, who is smaller, who is the same height.
Let your child come up with fairy tales with numerals. Let him say how many heroes are in them, what they are (who is more - less, higher - lower), ask him to put down counting sticks during the story. And then he can draw the heroes of his story and talk about them, make their verbal portraits and compare them.
It is very useful to compare pictures that have both common and different. It is especially good if the pictures will have a different number of objects. Ask your child how the drawings are different. Ask him to draw a different number of objects, things, animals, etc.
Preparatory work for teaching children elementary mathematical operations of addition and subtraction includes the development of such skills as breaking a number into its component parts and determining the previous and next number within the first ten.
IN game form Children are happy to guess the previous and next numbers. Ask, for example, what the number is greater five, but less than seven, less than three, but more than one, etc. Children are very fond of guessing numbers and guessing what they have planned. Think of, for example, a number within ten and ask the child to name different numbers. You say whether the named number is greater than what you intended or less. Then switch roles with your child.
Counting sticks can be used to parse numbers. Have your child place two sticks on the table. Ask how many sticks are on the table. Then spread the sticks on two sides. Ask how many sticks on the left, how many on the right. Then take three sticks and also lay them out on two sides. Take four sticks and let the child separate them. Ask him how else to arrange the four sticks. Let him change the arrangement of the counting sticks so that one stick lies on one side and three sticks on the other. In the same way, sequentially parse all the numbers within ten. The higher the number, the more parsing options, respectively.
It is necessary to introduce the child to the basic geometric shapes. Show him a rectangle, a circle, a triangle. Explain what a rectangle (square, rhombus) can be. Explain what is a side, what is an angle. Why is a triangle called a triangle (three angles). Explain that there are other geometric shapes that differ in the number of angles.
Let the child make geometric shapes from sticks. You can ask him required dimensions based on the number of sticks. Invite him, for example, to fold a rectangle with sides into three sticks and four sticks; triangle with sides two and three sticks.
Make shapes too different size and figures with different amount sticks. Ask your child to compare the shapes. Another option would be combined figures, in which some sides will be common.
For example, from five sticks you need to simultaneously make a square and two identical triangles; or make two squares out of ten sticks: a large one and a small one (a small square is made up of two sticks inside a large one).
By combining counting sticks, the child begins to better understand mathematical concepts ("number", "greater", "less", "same", "figure", "triangle", etc.).
Chopsticks are also useful for making letters and numbers. In this case, a comparison of the concept and the symbol takes place. Let the kid pick up the number of sticks that this number makes up for the number made up of sticks.
It is very important to instill in the child the skills necessary for writing numbers. To do this, it is recommended to spend with him a large preparatory work aimed at clarifying the line of the notebook. Take a notebook in a cage. Show the cage, its sides and corners. Ask the child to put a dot, for example, in the lower left corner of the cage, in the upper right corner, etc. Show the middle of the cage and the middle of the sides of the cage.
Show your child how to draw simple patterns using cells. To do this, write separate elements, connecting, for example, the upper right and lower left corners of the cell; right and left upper corners; two dots located in the middle of neighboring cells. Draw simple "borders" in a checkered notebook.
It is important here that the child wants to do it himself. Therefore, do not force him, let him draw no more than two patterns in one lesson. Such exercises not only introduce the child to the basics of writing numbers, but also instill fine motor skills, which in the future will greatly help the child in learning to write letters.
To develop certain mathematical skills and abilities, it is necessary to develop the logical thinking of preschoolers. At school, they will need the ability to compare, analyze, specify, generalize. Therefore, it is necessary to teach the child to solve problem situations, draw certain conclusions, and come to a logical conclusion. Solution logical tasks develops the ability to highlight the essential, independently approach generalizations.
Logic games of mathematical content educate children in cognitive interest, the ability for creative search, the desire and ability to learn. Unusual game situation with elements of problematic character for each entertaining task is always of interest to children.
Entertaining tasks contribute to the development of the child's ability to quickly perceive cognitive tasks and find the right solutions for them. Children begin to understand that in order to correctly solve a logical problem, it is necessary to concentrate, they begin to realize that such an entertaining problem contains a certain “trick” and in order to solve it, it is necessary to understand what the trick is.
Logic puzzles can be as follows:
Worth maple. There are two branches on a maple, on each branch there are two cherries. How many cherries grow on a maple? (Answer: none - cherries do not grow on maple.)
If a goose stands on two legs, then it weighs 4 kg. How much will a goose weigh if it stands on one leg? (Answer: 4 kg.)
Two sisters have one brother. How many children are in the family? (Answer: 3.)
If the child does not cope with the task, then perhaps he has not yet learned to concentrate and remember the condition. It is likely that, while reading or listening to the second condition, he forgets the previous one. In this case, you can help him draw certain conclusions already from the condition of the problem. After reading the first sentence, ask the child what he learned that he understood from it. Then read the second sentence and ask the same question. And so on. It is quite possible that by the end of the condition the child will already guess what the answer should be here.
Solve a problem out loud. Make certain conclusions after each sentence. Let the baby follow the course of your thoughts. Let him understand how problems of this type are solved. Having understood the principle of solving logical problems, the child will be convinced that solving such problems is simple and even interesting.
Common riddles created folk wisdom also contribute to the development logical thinking child:
Two ends, two rings, and carnations (scissors) in the middle.
- A pear is hanging, you can’t eat (light bulb).
- In winter and summer in one color (Christmas tree).
- Grandfather is sitting, dressed in a hundred fur coats; whoever undresses him sheds tears (bow).
Knowledge of the basics of computer science is currently for training in primary school is not mandatory, compared to, for example, numeracy, reading or even writing skills. However, teaching preschoolers the basics of computer science will certainly bring some benefits.
First, the practical benefits of learning the basics of computer science will include the development of abstract thinking skills. Secondly, in order to master the basics of actions performed with a computer, the child will need to apply the ability to classify, highlight the main thing, rank, compare facts with actions, etc. Therefore, teaching the child the basics of computer science, you not only give him new knowledge that will be useful to him when mastering a computer, but also along the way you consolidate some general skills.
One of the foundations of computer science is coding. practical action numbers. In order to instill this skill in a baby, it is not at all necessary to use special reference books, manuals or visual material. Everything you need is already in your home. Yes, and children may already be familiar with the basics of encoding.
You probably know games that are not only sold in stores, but also published in various children's magazines. This Board games with playing field, colored chips and dice or spinning top. The playing field usually contains various pictures or even a whole story and there are step-by-step indicators. According to the rules of the game, participants are invited to roll a die or a spinning top and, depending on the result, perform certain actions on the playing field. For example, when a certain number is rolled out, the participant can start his journey in the game space. And having made the number of steps that fell on the die, and having got into a certain area of the game, he is invited to perform some specific actions, for example, jump three steps forward or return to the beginning of the game, etc.
Do not neglect such games, often play them with your baby. Firstly, they teach him to be precise and attentive, and secondly, this is a great opportunity to spend time together and communicate with children.
To participate in the game, you can invite other children or even join teams, you can arrange competitions. This, of course, will develop certain qualities in your baby that will be useful to him when studying at school.
Games that teach kids to classify objects according to some specific criteria are also very useful. There are many options.
For example, several geometric figures are given in a certain sequence and in accordance with a certain pattern. The child needs to identify this pattern and add (draw) the missing figure or, conversely, remove the extra one.
There are many examples similar games. You can use the existing ones that are offered in the relevant literature, or develop them yourself.
For example, you can design the following game with your child. Make a square, divide it into nine areas (three rows of three squares) and make various colored geometric shapes (circle, square, triangle, etc.). From the available figures, you can build various patterns and come up with tasks in which the child will have to identify this pattern and perform certain actions with the figures.
To teach your child the basics school knowledge you can also use special teaching aids containing practical advice and descriptions of various games.
Thus, in a playful way, you will instill in your child knowledge from the field of mathematics, computer science, the Russian language, teach him to perform various actions, develop memory, thinking, and creativity. During the game, children learn complex mathematical concepts, learn to count, read and write, and in the development of these skills, the child is helped by the closest people - his parents.
But it's not only training, it's also a great time with your own child. However, in the pursuit of knowledge, it is important not to overdo it. The most important thing is to instill in the child an interest in learning. To do this, classes should be held in a fun way.
Counting is an activity with finite sets. The account includes structural components:
Purpose (to express the number of items as a number),
Means of achievement (counting process, consisting of a series of actions reflecting the degree of development of the activity),
Result (final number): the difficulty is presented for children in achieving the result of the count, that is, the result, generalization. Developing the ability to answer the question "how much?" in words a lot, a little, one two, the same, equally, more than ... speeds up the process of children's understanding of the knowledge of the final number when counting.
At the age of three to six years, children master the account. During this period they the main mathematical activity is counting. At the beginning of the formation of counting activity (the fourth year of life), children learn to compare sets element by element, by overlapping and applying, that is, they master the so-called "pre-numerical stage" of counting (A. M. Leushina). Later (fifth-seventh year of life) learning to count also occurs only on the basis of practical and logical operations with sets
A. M. Leushina determined six stages of development of counting activity in children. In this case, the first two stages are preparatory. During this period, children operate with sets without using numbers. Quantity is estimated using the words "many", "one", "none", "more - less - equally". These stages are characterized as sub-numerical.
The first stage can be correlated with the second and third years of life. The main goal of this stage is to get acquainted with the structure of the set. The main methods are the selection of individual elements in the set and the compilation of the set from individual elements. Children compare contrasting sets: many and one.
The second stage is also pre-numeric, however, during this period, children master the account in special classes in mathematics.
The goal is to teach how to compare adjacent sets element by element, i.e. compare sets that differ in the number of elements by one.
The main methods are superposition, application, comparison. As a result of this activity, children must learn to establish equality from inequality by adding one element, that is, increasing, or removing, that is, reducing, the set.
The third stage is conditionally correlated with the education of children of the fifth year of life.
The main goal is to familiarize children with the formation of numbers.
Typical methods of activity are comparing adjacent sets, establishing equality from inequality (they added one more object, and they became equal - two, four, etc.).
The result is the total of the score, indicated by a number. Thus, the child first masters the account, and then realizes the result - the number.
The fourth stage of mastering counting activity is carried out in the sixth year of life. At this stage, children are introduced to the relationship between adjacent numbers of the natural series.
The result is an understanding of the basic principle of the natural series: each number has its place, each subsequent number is one more than the previous one, and vice versa, each previous one is one less than the next.
The fifth stage of learning to count corresponds to the seventh year of life. At this stage, children understand the account in groups of 2, 3, 5.
The result is bringing children to an understanding of the decimal number system. This is where the education of preschool children usually ends.
The sixth stage in the development of counting activity is associated with the mastery of the decimal number system by children. In the seventh year of life, children get acquainted with the formation of the numbers of the second ten, begin to realize the analogy formed by any number based on the addition of one (increase: i numbers per unit). Understand that ten units make one ten. If you add ten more units to it, you get two tens, etc. A conscious understanding of the decimal system by children occurs during the period of schooling.
All work on the development of counting activities preschoolers pass strictly in accordance with the requirements of the program content. In each age group kindergarten tasks for the development of elementary mathematical representations in children, in particular, for the development of counting activities, in accordance with the "Program of Education and Training in Kindergarten" are outlined.
IN THE SECOND JUNIOR GROUP begin to carry out special work on the formation of elementary mathematical representations. On how successfully the first perception of quantitative relations and spatial forms of real objects will be organized, the further depends. mathematical development children. Toddlers don't learn to count, but organizing a variety of actions with objects, lead to the assimilation of the account, create opportunities for the formation of the concept of a natural number.
program material second junior group limited pre-numeric learning period.
In children ideas about singularity and plurality are formed objects and items. In the process of exercises, combining objects in the aggregate and breaking up the whole into separate parts, children master the ability to perceive in unity each individual object and the group as a whole. In the future, when getting acquainted with numbers and their properties, this helps them to master the quantitative composition of numbers.
Children are learning group items one at a time, A then on two or three signs- color, shape, size, purpose, etc., pick up pairs of objects. At the same time, children perceive a set of objects formed in a certain way as a single whole, presented visually and consisting of single objects. They make sure that each of the objects has common quality features (color and shape, size and color).
Grouping items on the grounds develops in children the ability to compare, to carry out logical operations of classification. From understanding the identified features as properties of objects in the older preschool age, children move on to mastering the community in terms of quantity. They develop a more complete understanding of the numbers.
In children an idea is formed about subject diverse sets: one, many, few (meaning several). They gradually master the ability to distinguish between them, to compare, to single out independently in the environment.
METHODS AND TECHNIQUES OF TRAINING
Children's education junior group wears visual-effective character. The child acquires new knowledge on the basis of direct perception when he follows the action of the teacher, listens to his explanations and instructions, and acts with the didactic material himself.
Classes often start with elements of the game, surprise moments- the unexpected appearance of toys, things, the arrival of guests, etc. This interests and activates the kids. However, when highlighting a property for the first time and important focus on it children, game moments may or may not be present.
Elucidation of mathematical properties carry out based on item comparison, characterized by either similar or opposite properties(long - short, round - non-round, etc.). Are used items, whose knowable property is pronounced. that are familiar to children, without unnecessary details, differ no more than 1-2 signs.
Perceptual Accuracy contribute movements (hand gestures), circling a model of a geometric figure (along the contour) with a hand helps children to more accurately perceive its shape, and holding a hand along, say, a scarf, ribbon (when compared in length) - to establish the ratio of objects precisely on this basis.
children teach to consistently identify and compare homogeneous properties of things. (What is it? What color? What size?) Comparison is based on practical ways mappings: overlays or applications.
Great importance attached work of children with didactic material. Toddlers are already able to perform rather complex actions in a certain sequence (impose objects on pictures, sample cards, etc.). However, if the child fails to complete the task, works unproductively, it loses interest quickly tired and distracted from work. Considering this, the teacher gives the children a sample of each new way of doing things.
Seeking to warn possible mistakes, He shows all the methods of work and explains in detail the sequence of actions. At the same time, explanations should be extremely clear, clear, specific, given at a pace accessible to perception. small child. If the teacher speaks in a hurry, then the children stop understanding him and get distracted. The teacher demonstrates the most complex methods of action 2-3 times, each time drawing the attention of the kids to new details. Only the repeated display and naming of the same methods of action in different situations when changing visual material, they allow children to learn them.
In the course of work, the teacher not only points out mistakes to children, but also finds out their causes. All errors are corrected directly in action with didactic material. Explanations should not be intrusive, wordy. In some cases, children's mistakes are corrected without explanation at all. (“Take it in your right hand, in this one! Put this strip on top, you see, it is longer than this one!” Etc.) When the children learn the method of action, then showing it becomes unnecessary.
Small children are much better assimilate emotionally perceived material. Their memorization is characterized by unintentionality. Therefore, in the classroom are widely used playing tricks And didactic games . They are organized in such a way that, if possible, all children participate in the action at the same time and they do not have to wait for their turn. There are games related to active movements: walking and running. However, using playing tricks, teacher does not allow them to distract children from the main(albeit elementary, but mathematical work).
Spatial and quantitative relations can be reflected at this stage only with words. Every new way actions, assimilated by children, each the newly highlighted property is fixed in the exact word. The teacher pronounces the new word slowly, highlighting it with intonation. All the children together (in chorus) repeat it.
The most difficult for toddlers is reflection in speech of mathematical connections and relationships, since it requires the ability to build not only simple, but also complex sentences, using the adversative union A and the connecting union I. First, you have to ask the children auxiliary questions, and then ask them to tell you everything at once. For example: How many pebbles are on the red stripe? How many pebbles are on the blue stripe? Now tell me right away about the pebbles on the blue and red stripes. So baby lead to the reflection of connections: There is one pebble on the red stripe, and many pebbles on the blue one. The teacher gives an example of such an answer. If the child finds it difficult, the teacher can start the answer phrase, and the child will finish it.
For children to understand the way of action they are offered to say in the course of work what and how they are doing, and when the action has already been mastered, before starting work, make an assumption about what and how to do. (What needs to be done to find out which board is wider? How to find out if the children have enough pencils?) Connections are established between the properties of things and the actions by which they are revealed. At the same time, the teacher does not allow the use of words whose meaning is not clear to children.
In the process of various practical actions with aggregates, children learn and use in their speech simple words and expressions, denoting the level of quantitative representations: many, one, one at a time, not one, not at all (nothing), few, the same, the same (in color, shape), the same, equally; as much as; more than; less than; each of all.
So , at preschool age, in the pre-numerical period of learning, children master practices comparisons (overlay, application, pairing), as a result of which mathematical relations are comprehended: “more”, “less”, “equally”. On this basis, the ability to identify the qualitative and quantitative characteristics of sets of objects, to see the commonality and differences in objects according to the selected characteristics is formed.
MIDDLE GROUP PROGRAM directed for further development mathematical concepts in children.
One of the main program tasks education of children of the fifth year of life consists in the formation of their ability to count, the development of appropriate skills and on this basis development of the concept of number.
Formed at a younger preschool age (2-4 years) the ability to analyze sets of objects in terms of their number, to see the sequence and differences in terms of qualitative and quantitative characteristics, the idea of equality and inequality subject groups, the ability to properly answer the question "how much?" (the same, more here than there) is the basis for mastering the account.
Middle preschool age(fifth year of life) in the process of comparing two groups of objects, highlighting their properties, as well as counting in children representations are formed:
1. about the number, allowing them to give an accurate quantitative assessment of the totality, they master the techniques and rules for counting objects, sounds, movements (within 5);
2. about the natural series of numbers (sequence, place of a number) they are introduced to the formation of a number (within 5) in the process of comparing two sets of objects and increasing or decreasing one of them by one;
3. attention is paid to comparing sets of objects by the number of their constituent elements (both without counting and in combination with counting), equalizing sets that differ in one element, establishing the relationship of “more - less” relationships (if there are fewer bears, then there are more hares);
4.children, having mastered the ability to count objects, sounds, movements, answer the question “how much?”, Learn to determine the order of objects (first, last, fifth), answer the question “which?”, i.e. practically use a quantitative and ordinal account;
5.children develop the ability to reproduce sets, counting objects according to a model, according to a given number from more, memorize numbers, the idea of a number as common ground variety of sets (objects, sounds), they make sure that the number is independent of insignificant features (for example, color, occupied area, size of objects, etc.), use various ways getting equal and unequal in number of groups and learn to see identity (identity), generalize the number of objects of sets (the same number, four, five, the same number, i.e. number).
6. ideas are formed about the first five numbers of the natural series (their order, the relationship between adjacent numbers: more, less), skills are developed to use them in various everyday and game situations.
Learning to count within 5. Teaching counting should help children understand the purpose of this activity (only by counting the objects, you can accurately answer the question how much?) And master its means: naming numerals in order and correlating them to each element of the group. It is difficult for four-year-olds to learn both sides of this activity at the same time. Therefore, in middle group Learning to count is recommended to be carried out in two stages.
AT THE FIRST STAGE based comparison of the sizes of two groups items for children reveal the purpose this activity ( find the final number). They are taught to distinguish between groups of objects in 1 and 2, 2 and 3 elements and name the final number based on the teacher's score. Such "collaboration" is carried out in the first two lessons.
Comparing 2 groups of subjects, located in 2 parallel rows, one under the other, the children see which group has more (less) objects or they are equally divided in both. They designate these differences with numeral words and make sure: in groups there are equal numbers of objects, their number is indicated by the same word (2 red circles and 2 blue circles), they added (removed) 1 object, they became more (less), and the group became denoted by a new word.
Children begin to understand that each number represents a certain amount items, gradually make connections between numbers (2 > 1, 1 < 2 и т. д.).
Organizing comparison of 2 populations subjects, in one of which there is 1 more subject than in the other, the teacher counts objects And draws attention children on the total. He first finds out which items are larger (less), and then which number is larger, which is smaller. The basis for comparing numbers serves distinction children set sizes(groups of) objects and their names are numerals.
Important for the children to see not only how you can get the next number (n+1), but also how to get previous number: 1 out of 2, 2 out of 3, etc. (n - 1). The teacher either increases the group by adding 1 item, then reduces it by removing 1 item from it. Every time finding out which items are more, which are less, goes to comparing numbers. He teaches children to indicate not only which number is greater, but also which is smaller (2> 1, 1<2, 3>2, 2<3 и т. д.). Отношения "more", "less" always considered in connection with each other. In the course of work, the teacher constantly emphasizes: in order to find out how many objects in total, you need to count them.
Focusing the attention of children on the total, the teacher accompanies naming it generalizing gesture(circling a group of objects with a hand) and names(i.e. pronounces the name of the item itself). In the process of counting, the numbers are not named (1, 2, 3 - only 3 mushrooms).
Children are encouraged name and show,where 1, where 2, where 3 items, which serves to establish associative links between groups, containing 1, 2, 3 items, and corresponding numeral words.
great attention give reflection in the speech of children of the results of comparison of aggregates objects and numbers. ("There are more matryoshkas than roosters. There are fewer roosters than nesting dolls. 2 is more, and 1 is less, 2 is more than 1, 1 is less than 2.")
AT THE SECOND STAGE children master counting operations. After the children learn to distinguish between sets (groups) containing 1 and 2, 2 and 3 objects, and understand what exactly to answer the question how much? it is possible, only by counting the objects, they are taught keep count of objects within 3, then 4 and 5.
From the first lesson numeracy should be structured in such a way that for the children to understand, how each subsequent (previous) number is formed, i.e. general principle of constructing natural series. Therefore, the display of the formation of each next number is preceded by a repetition of how the previous number was obtained.
Sequential comparison of 2-3 numbers to show children that any natural number greater than one and less than another, "neighbor" (3 < 4 < 5), разумеется, except for one, less than which there is no no natural number. In the future, on this basis, children will understand the relativity of the concepts "more", "less".
They must learn independently transform sets items. For example, decide how to make the items equal, what needs to be done to make (remain) 3 items instead of 2 (instead of 4), etc.
In the middle group develop numeracy skills. The teacher repeatedly shows and explains counting techniques, teaches children to count objects right hand from left to right; in the process of counting, point to objects in order, touching them with your hand; having named the last numeral, make a generalizing gesture, circle a group of objects with your hand.
Children usually find it difficult to agree numerals with nouns(the numeral one is replaced by the word times). The teacher selects masculine, feminine and neuter items for counting (for example, color images of apples, plums, pears) and shows how words one, two change depending on which items are counted. The child counts: "One, two, three." The teacher stops him, picks up one bear and asks: "How many bears do I have?" - "One bear", - the child answers. "That's right, one bear. You can't say "once a bear." And you need to count like this: one, two ..."
To consolidate counting skills used a large number of exercises. Exercises in the account should be in almost every lesson until the end of the school year. In order to create the prerequisites for independent counting, they change the counting material, the classroom environment, alternate team work with independent work children with benefits, diversify techniques. A variety of game exercises are used, including those that allow not only to consolidate the ability to count objects, but also to form ideas about the shape, size, and contribute to the development of orientation in space. Counting is associated with comparing the sizes of objects, with distinguishing geometric shapes and highlighting their features; with the definition of spatial directions (left, right, front, rear).
Children are offered to find a certain number of objects in the environment. First, the child is given a sample (card). He is looking for as many toys or things as there are circles on the card. Later, children learn to act only on the word. ("Find 4 toys.") When working with handouts, it must be taken into account that children still do not know how to count objects. Tasks are initially given such that require them to be able to count, but not to count.
Application of the account in different types children's activities.
Teaching counting should not be limited to conducting formal exercises in the classroom. The teacher should strive to ensure that the account is used by children everywhere, and the number, along with the quantitative and spatial characteristics of objects, would help children better navigate the surrounding reality.
The teacher constantly uses and creates various life and game situations that require children to use counting skills. In games with dolls, for example, children find out if there are enough dishes for receiving guests, clothes to collect dolls for a walk, etc. In the game of "shop" they use receipt cards on which a certain number of objects or circles are drawn. The teacher promptly introduces the appropriate attributes and prompts game actions, including counting and counting objects.
In everyday life, situations often arise that require counting: on the instructions of the teacher, children find out whether there will be enough of certain benefits or things for children sitting at the same table (boxes with pencils, coasters, plates, etc.). Children count the toys they took for a walk. Going home, check if all the toys are collected. The guys love to simply count the items that they meet along the way.
Learning to count accompanied by conversations with children about the appointment, application of the account in various activities. In an effort to deepen the children's ideas about the meaning of counting, the teacher explains to them why people think they want to know when they count objects. He advises children to see what their mothers, fathers, grandmothers think.
So, in the middle group under the influence of training, counting activity is formed, the ability to count various sets of objects in different conditions and relationships.
IN THE SENIOR GROUP program is aimed at expanding, deepening and generalizing elementary mathematical concepts in children, further developing the activity of counting.
- continues Job on the formation of ideas about the number(quantitative characteristics) of sets, ways of forming numbers, quantification of quantities by measurement;
Children master the techniques of counting objects, sounds, movements by touch within 10, determine the number of conditional measures when measuring extended objects, volumes of liquids, masses of bulk substances;
Children learn to form numbers by increasing or decreasing a given number by one, equalize sets according to the number of items subject to quantitative differences between them in 1, 2 and 3 elements, as in the middle group, children count the number of objects according to the named number or pattern(numerical figure, card) or more (less) per unit, exercise in generalizing the number of objects of a number of specific sets that differ in spatial and qualitative features (shape, location, direction of counting, etc.) based on perception by various analyzers;
In order to prepare children for counting groups of their teaches the ability to split aggregates in 4, 6, 8, 9, 10 items in groups of 2, 3, 4, 5 items, determine the number of groups and the number of individual items;
Children get acquainted with the quantitative composition of numbers from units within 5 on specific objects and in the process of measurement, which clarifies and concretizes the idea of a number, unit, place of a number in the natural series of numbers;
- continues children's education distinction between quantitative and ordinal value of a number, skills are developed to apply quantitative and ordinal counting in practical activities;
During the comparison of sets and numbers, children learn numbers from 0 to 9, They learn to relate them to numbers, to distinguish, to use in games.
METHODS AND TECHNIQUES OF TEACHING ACCOUNT
Repetition of the past. In the middle group, children were taught to count objects within 5. Consolidation of the relevant ideas and methods of action serves as the basis for the further development of counting activities.
Comparison of two sets containing an equal and unequal (more or less by 1) number of objects within 5 allows you to remind children how the numbers of the first heel are formed. In order to bring to the consciousness of children the meaning of counting and methods of piece-by-piece comparison of objects of two groups one to one to clarify the relationship "equal", "not equal", "more", "less", tasks are given to equalize the aggregates. ("Bring so many cups so that all the dolls have enough and there are no extra ones", etc.)
Much attention is paid to strengthening counting skills; children are taught to count objects from left to right, pointing to objects in order, agree on numerals with nouns in gender and number, name the result of the count. If one of the children does not understand the final value of the last number called when counting, then he is invited to circle the counted objects with his hand. A circular generalizing gesture helps the child to correlate the last numeral with the entire set of objects. But in working with children of 5 years old, as a rule, it is no longer needed. Children can now be offered to count objects at a distance, silently, that is, to themselves.
Children are reminded of the methods of counting sounds and objects by touch. They reproduce a certain number of movements in a pattern and a specified number.
Count within 10. To obtain the numbers of the second heel and learn to count up to 10, methods are used similar to those used in the middle group to obtain the numbers of the first heel.
The formation of numbers is demonstrated on the basis of a comparison of two sets of objects. Children must understand the principle of obtaining each subsequent number from the previous one and the previous one from the next (n + 1). In this regard, in one lesson it is advisable to consistently receive 2 new numbers, for example, 6 and 7. As in the middle group, the display of the formation of each next number is preceded by a repetition of how the previous number was obtained. Thus, at least 3 consecutive numbers are always compared. Children sometimes confuse the numbers 7 and 8. Therefore, it is advisable to conduct more exercises in comparing sets consisting of 7 and 8 elements.
Healthy compare not only collections of objects of different types(for example, Christmas trees, mushrooms, etc.), but also groups of objects of the same type are divided into parts and compared with each other(apples are large and small), finally, a collection of objects can be compared with its part. ("Who is more: gray bunnies or gray and white bunnies together?") Such exercises enrich the experience of children with multiple objects.
When assessing the numbers of sets of objects, five-year-old children are still disoriented by the pronounced spatial properties of objects. However, now it is not necessary to devote special classes to showing the independence of the number of objects from their size, shape, location, and the area they occupy. It is possible to simultaneously teach children to see the independence of the number of objects from their spatial properties and to receive new numbers.
The ability to compare collections of objects of different sizes or occupying different areas creates prerequisites for understanding the meaning of the account And piece matching techniques elements of two compared sets (one to one) in revealing the relations "equal", "greater", "less". For example, to find out which apples are more - small or large, which flowers are more - marigolds or daisies, if the latter are located at greater intervals than the former, you must either count the objects and compare their number, or compare the objects of 2 groups (subgroups) one to alone. Different methods of comparison are used: overlay, application, use of equivalents. Children see: in one of the groups there was an extra object, which means there are more of them, and in the other - one object was not enough, which means there are fewer of them. Based on a visual basis, they compare numbers (so 8 > 7, and 7< 8).
Equalizing groups by adding one item to a smaller number or removing one item from a larger number, children learn how to get each of the compared numbers. Considering the relationship of the relationship "greater", "less" will help them further understand the reciprocal nature of the relationship between numbers (7\u003e 6, 6< 7).
Children should tell how each number was received, that is, to what number of objects and how much was added or from what number of objects and how much was taken away (removed). For example, 1 apple was added to 8 apples, it became 9 apples. They took 1 out of 9 apples, 8 apples remained, etc. If the guys find it difficult to give a clear answer, you can ask leading questions: "How much was it? How much was added (removed)? How much was it?"
Change of didactic material, varying tasks help children better understand how to get each number. Receiving a new number, they first act as directed by the teacher (“Add 1 apple to 7 apples”), and then independently transform the aggregates. Achieving conscious actions and answers, the teacher varies the questions. He asks, for example: "What needs to be done to make 8 cylinders? If 1 is added to 7 cylinders, how many will there be?"
To strengthen knowledge, it is necessary to alternate team work with independent work. children with handouts. The child matches 2 sets by laying out items on a card with 2 free strips. Demonstration of methods for obtaining a new number (comparison of 3 neighboring members of the natural series) usually takes at least 8-12 minutes, so that the performance of monotonous tasks does not tire the children, similar work with handouts is carried out more often in the next lesson.
To consolidate counting skills within 10 use a variety of exercises, such as "Show the same." Children find a card on which as many objects are drawn as the teacher showed. ("Find as many toys as there are circles on the card", "Who will quickly find which toys we have 6 (7, 8, 9, 10)?".) To complete the last 2 tasks, the teacher makes groups of toys in advance.
When children are introduced to all numbers up to 10, they are shown that to answer the question how many? no matter which direction the score is taken. They themselves are convinced of this by counting the same objects in different directions: left to right and right to left; top down and bottom up. Later, children are given an idea of what You can count objects located not only in a row, but also in a variety of ways. They count toys (things) arranged in the form of different figures (in a circle, in pairs, in an indefinite group), images of objects on a lotto card, and finally, circles of numerical figures.
Children are shown different ways of counting the same objects And learn to find more convenient (rational), allowing calculate quickly and correctly items. Recalculation of the same items different ways(3-4 ways) convinces children that you can start counting from any object and lead it in any direction, but at the same time you must not skip a single object and not count one twice. Specially complicate the shape of the arrangement of objects.
If the child is mistaken, then they find out what mistake was made (missed an object, one object counted twice). The teacher, counting the items, may intentionally make a mistake. Children follow the actions of the teacher and indicate what his mistake was. They conclude that it is necessary to remember well the object from which the account was started, so as not to miss any of them and not to count the same object twice.
So quantitative representations in children 5-6 years old, formed under the influence of training, are more generalized than in the middle group. Preschoolers count objects regardless of their external signs, summarize by number. They accumulate experience in counting individual objects, groups, using conditional measures.
The skills learned by children to compare numbers on a visual basis, to equalize groups of objects by number indicate the formation of their ideas about the relationship between the numbers of the natural series.
Count, compare, measure, elementary actions over numbers (decrease, increase by one) become available to children in various types of their educational and independent activities.
In the program PREPARATORY FOR SCHOOL GROUP the following areas can be distinguished:
1. Development of counting, measuring activities: accuracy and speed of counting, reproduction of the number of objects in more and less by one of their given number; preparation for the assimilation of numbers based on measurement, the use of numbers in various types of gaming and household activities.
2. Improving the ability to compare numbers, understanding the relativity of the number: when comparing the numbers 4 and 5, it turns out that the number 5 is greater than 4, and when comparing the numbers 5 and 6 - 5 is less than 6. Refine
math score is an action that allows you to determine the amount of something. The score can be quantitative or ordinal.
Quantitative
quantitative account is the determination of the number of objects. A quantitative account allows you to answer the question how much? .
For example, to find out the number of desks in a class or how many trees grow in a garden, you need to count them. The quantitative account lies in the fact that, each time separating one object after another (actually or only mentally), we name the number of separated objects. For example, counting desks in a class, we mentally separate one desk after another and say: one, two, three, four, five, etc. If, when separating the last desk, we said, for example, eight, then there are only eight desks in the class . The number eight in this case is the result of counting.
Score result is the number of items resulting from their count.
The result of the count does not depend on the order in which the items are counted.
So, counting the desks in the class, we get the same number, regardless of whether we count from the front desks to the back or vice versa - from the back to the front. It is only important that when counting the desks, not a single desk is skipped and not a single one is counted twice.
The number at which there is a name of those units from the account of which it was obtained is called named. In our case, since we counted the desks, the number eight is named (eight desks). A number that does not have a unit name is called abstract.
Ordinal
ordinal count- this is the definition of the number of objects and the place of each object relative to others. The ordinal account allows you to answer the question what? (for example, which one in a row? or which one in order?).
For example, to determine the number of pencils, you can use a quantitative account and count the pencils in any order:
But if you need to find out what the green pencil is in the account, then you should use the ordinal account. In this case, each pencil receives a number indicating which account it goes to:
Since the pencils are arranged next to each other, the green pencil will be the third if counted from left to right, and the fourth if counted from right to left.
With ordinal counting, if all items are counted, then the result of the count will be a number indicating the order of the last item counted. In our case, since the last pencil counted is the sixth, the total number of items is six.
Number is the ordinal number of an object in a series of other objects.
Methodology for teaching counting (4 - 6 years)
There is no consensus on teaching children to count. Leushina A.M. thought: there is no need to rush, you need to start learning to count after learning operations on sets.
Before teaching children to count, it is necessary to create situations in which children are faced with the need to be able to count.
Learning to count occurs on the basis of a comparison of two groups of objects by quantity.
Stage 1. The teacher himself leads the counting process, and the children repeat the final number after him. The independence of the number of objects from other attributes of objects is shown.
Stage 2. The teacher teaches children the process of counting and introduces the formation of each number, teaches them to compare adjacent numbers. First, children are taught to count within 3, and then within 5, then - 10 (according to Praleska Ave.), according to the Rainbow program - up to 20 (in the seventh year of life). M. Montessori has developed a methodology and material for teaching counting within 1000.
Consider example learning to count up to three.
At stage 1, the teacher offers the children two groups of objects arranged in two parallel rows, one under one (bunnies and squirrels). Questions:
How many bunnies (squirrels)?
Are there equal numbers of bunnies and squirrels?
sets (a bunny jumped up).
Are there equal numbers of squirrels and bunnies now?
How many were, how many became bunnies?
The teacher himself leads the counting process (“One, two, three.” He circles the whole set with his hand. “Only three bunnies”). Children follow the counting process and repeat the final number - "three".
Adding another squirrel.
Are there equal numbers of bunnies and squirrels now?
How many were whites?
The teacher counts the squirrels (one, two, three; only three squirrels). Agrees nouns and numerals in gender and number. Children see that the number "three" is a common indicator of the number for bunnies and squirrels.
At stage 2, teaching children the counting process, the teacher encourages them to adhere to the following rules:
1. Coordinate each numeral with one object and one movement.
2. Coordinate the numeral and noun in gender, number, case.
3. We do not repeat the noun after each numeral (so that the counting process goes abstractly).
4. After naming the last numeral, it is necessary to circle the entire group of objects with a circular gesture and name the final number.
5. Calling the final number, we pronounce the corresponding noun.
6. The account must be kept with the right hand from left to right (so that the children have a stereotype).
7. Instead of the numeral “one”, you cannot say the word “times” to answer the question “how much?”.
Consider how to show the formation of a number (for example, the number 3).
It is necessary to rely on the comparison of two sets in terms of quantity. Questions:
How many whites? (two)
How many bunnies? (two)
Add one bunny.
How many bunnies were there?
How to get the number 3? (It is necessary to add one to two, we get 3).
In the future (after the children learn to count up to four), it is necessary to show the formation of the number 3 by reducing the set by one. Thus, the formation of each number is shown in two ways, by increasing and decreasing the set by 1.
6. Methodology for teaching the counting of objects (4 - 6 years)
Using the problem situation, it is necessary to show the difference between the counting process and the counting process.
The rules for counting and counting are the same, however, when learning to count Special attention should be given to the following rule: the numeral should be called only for 1 moment of movement.
Types of counting exercises:
Counting according to the sample (as many as); first, the sample is given in close proximity, and then at a distance;
· Counting by named number (or shown figure);
Older children are invited to remember 2 adjacent numbers and count 2 groups of objects (count 2 apples and 3 pears from the basket); Attention is drawn to the fact that the children remember how many items to count (we ask the children to repeat the named numbers).
7. Methodology for teaching ordinal counting (4 - 6 years)
Stage 1. First, children are offered preparatory exercises(with several types of visual material), which show that in order to answer the question "how much?" it is necessary to use the numerals “one, two, three”, i.e. quantitative. It does not matter in which direction the count is kept and how the objects are located in space.
Then, acquaintance with the ordinal account is carried out in the process of dramatization of the fairy tale (“Teremok”, “Turnip”, “Gingerbread Man”).
The teacher shows the children that in order to answer the question “What is the score?” ordinal numbers are used: first, second, third, etc. It is important that the objects are arranged linearly and the direction of the count is indicated.
Example: the fairy tale "Teremok".
The teacher lays out the heroes of the fairy tale. Finds out how many things, invites children to count. Then he himself tells who came in a row: the first is a mouse, the second is a frog .... After that, 2 types of questions are asked:
Who came first, second, third...?
What is the score of a mouse, a hedgehog ...? (indicates that it should be counted from left to right).
Then it is proposed to answer the same questions, but keep the score from right to left.
After that, the teacher leads the children to the fact that it is possible to determine the place of an object among others only if the characters are in a row.
To consolidate, exercises are carried out in which it is determined: which object is located in what order. For example: in the process of getting acquainted with geometric shapes: “What is the name of the figure that is in third place?”.
Stage 2. It is shown to children in which cases quantitative and in which ordinal numbers are used. Exercises are proposed in which we ask 2 questions: “How much?” and "What's the score?" Watch what numbers children use. We explain in which case which numerals should be pronounced. Children are led to the conclusion that in order to determine how many objects, a quantitative account is used, and to determine the place of an object among others, an ordinal account is used.
In addition to such exercises, it is important to create situations in Everyday life and games in which children would see differences in the use of quantitative and ordinal counting. For example, in the game "Theater" we specify what the number on the ticket means: how many seats in total or what is the specified seat in a row.
Types of exercises:
Determine the number of the specified item;
Name the object by the given number.
Game "What has changed?" (It turns out where the toy is located. The command “The eyes are sleeping” is given. Then the teacher changes the location of the toy. After the words “eyes opened”, it is suggested that those who noticed the changes raise their hand and answer: what order did this toy stand before, and what it costs now).
8. Methodology for familiarization with numbers (3 - 5 years)
Familiarization with the name and appearance of the number takes place at the age of four, and after learning to count, children are introduced to the essence of numbers.
Stage 1.
The teacher in various situations introduces children to the name and appearance of the figure (during the walk, pays attention to the numbers of houses, cars; to page numbers).
The teacher reads poems that describe appearance digits. (S. Marshak "Merry Account", G. Vieru "Counting").
Stage 2:(avg.)
Once children have learned to count within the appropriate limits, they must be introduced to the essence of each number in sequence. It is proposed to indicate the number of objects in the group in different ways: the corresponding number of counting sticks, the corresponding numerical card, and, finally, using numbers.
You can invite children to consider a table where the same number of different objects is drawn and they are all indicated by one number.
We bring the children to the fact that the same number of objects is always indicated by the same number. The difference between the concept of "number" and "number" (lik - number, lichba - number): figure - an icon or drawing with which you can write a number or indicate the number of objects. It must be understood that the number is represented not only with the help of numbers. You can introduce children to Roman numeration - the image of a number using drawings. Or offer colored numbers - Cuizener's sticks.
Exercises to consolidate the essence of numbers:
Choose a number for the corresponding set.
Create (find) a group of objects corresponding in quantity to the number shown.
"Find a Pair" (lotto).
"Find your home."
Introduction to the number 0.
Children are offered 3 saucers: on one - 3 items, on the other - 5, on the third - none. Please use numbers to indicate the number of items in each saucer. Children can figure out that you need to put "0" on an empty saucer. If the children find it difficult, then the teacher reads a poem about "0": A number like the letter "O" is "zero" or "nothing".
And then we explain that the absence of objects is also denoted by a number, this is the number "0".
Acquaintance with the image of the number 10.
We need to show the children that the number 10 is depicted using two numbers "1" and "0". The teacher reads the appropriate verse.
A round zero is so pretty, but it doesn't mean anything.
Well, if next to him we fit one -
He will weigh more, because it is ten. (S.Ya.Marshak)
The same games are suitable for fixing as for other numbers. We include 0 and 10 in games and exercises.
9. Formation of ideas about the composition of the number from individual units within 5 (5 - 6 years)
This task is a preparatory task for learning operations on numbers.
Visual material should differ at least in one feature (species) and be homogeneous.
Methodology: children are offered 3 (4, 5) items (for example, flags of different colors) and the following questions are asked:
How many items in total?
How many items of the same kind? (How many red flags? How many blue flags? How many green flags?)
Conclusion: we have only 3 flags: 1 red, 1 green, 1 blue.
Similar work is carried out with two more types of visual material, and then a generalizing conclusion is made: 3 is 1, 1 and 1. To consolidate, it is proposed to name different objects (for example, vegetables), so that there are 3 of them in total.
The composition of the numbers 4 and 5 is considered in a similar way.
For consolidation, games are offered: “I know 5 names of girls”, “Name 5 different pieces of furniture (vegetables)”, “Who will name faster”.
At first, children are allowed to bend their fingers or name numeral words, but by the age of 6, children should learn to keep the composition of the number in their minds.
10. Formation of ideas about the composition of a whole set of parts (5 - 6 years)
This problem is solved in order to prepare children to understand the composition of a number from smaller numbers. The teacher takes two equal sets of homogeneous objects, in one of them the objects differ in one feature (color, shape, etc.). For example, circles are red on one side and blue on the other. The teacher finds out how many elements are in each set (for example, 5 each), and then lays out parts of the second set that are different in number and differ in color from the elements of the second set. There are 4 options in total: 1 blue and 4 red, 2 blue and 3 red, 3 blue and 2 red, 4 blue and 1 red. Then the children are offered the following types of exercises:
Lay out (or draw) as many circles as there are not enough to a whole set.
Put five squares in a row. Under them put 2 (3, 4) circles and as many triangles to make 5 figures together.
Take 5 squares of two colors and tell how many squares and how many of each color.
Arrange 5 buttons on 2 plates in different ways, each time saying how many buttons are on each plate.
11. Formation of ideas about the relationship between numbers (comparison of numbers) (4 - 6 years)
Stage 1(average age). Children are taught to compare adjacent numbers based on comparing 2 sets by number.
It turns out which items are more, how many of each type.
The teacher leads the children to the conclusion: "Since there are more bears and 4 bears, then the number 4 is more than 3."
Stage 2(average age). The constancy of the relations "greater" and "less" between two numbers is shown, i.e. that 4 is always greater than 3. To do this, the qualitative characteristics of objects and their spatial arrangement change in the exercises.
Stage 3(old age). It is shown that the relations "greater than" and "less than" are relative, i.e. that number 3<4, но 3>2. To do this, it is proposed to compare 3 consecutive numbers at once and encourage children to specify when answering: this number is “more” (or “less”) what date.
Stage 4 (old age). Children are taught to compare nonadjacent numbers. The reasoning is based on the property of transitivity. If 3<4<5<6, значит 3<6. При рассуждении следует опираться на наглядно-практический прием «числовая лесенка» (раскладывание предметов в убывающем или возрастающем порядке в параллельные ряды строго один под одним).
Extra items must be of a different color (shape).
Children are shown that each number is greater than all previous ones, but less than all subsequent ones.
Games and exercises:
“Living numbers” (building in the correct order), “What has changed” (what number is missing or swapped and why), “Go on” (with the ball), “Count the other way around”, “Lotto”, “Name the neighbors”.
In all these games - children must give a verbal countdown.
12. Formation of an understanding of the conservation of quantity (4 - 6 years)
Quantity does not depend on the qualitative characteristics of objects, nor on their spatial arrangement, nor on the direction of counting. To bring children to this conclusion, exercises are carried out to compare two groups of objects in quantity.
At the first stage, signs that are easy for children are selected, with age they become more complicated: color - shape - size - distance between objects - different location in space - counting direction - combination of two or more signs. Each exercise should be carried out in different variations. In the exercises, the tasks should be formulated as follows: what items are more (less or equally items), how to find out?
To complete the task and answer questions, children themselves choose 1 of the methods for comparing groups of objects by quantity (overlay, connection with arrows, counting, etc.)
Games: "Find a couple", "Find your house", "Dots".
13. Learning to count objects using various analyzers (4 - 6 years)
Types of exercises: counting sounds; movement count; counting objects by touch.
Exercise options:
Execution according to the pattern (as many - as many): clap as many times as I do.
Counting the number of sounds (movements, objects to the touch). The result of the count can be called or shown using numbers.
Performing a task on the named number or the shown figure.
Mixed exercises (for example, sit down as many times as you hear sounds).
Complications:
· Perform movements 1 more or less.
On 1st stage(in younger age) it is proposed to reproduce 1 or many movements (sounds) according to the model. In the game “We walk around one after another”, the children must repeat those movements and as many times as the leader showed.
On 2nd stage ( in average age) teach children to count sounds and movements within 5, to count objects by touch (cards with buttons sewn in one row, covered with a napkin or in a bag).
Requirements for extracting sounds and performing movements: sounds should be extracted loudly, rhythmically, at a moderate pace, behind a screen, we pay attention to the fact that children listen silently until the very end, count to themselves, if the children said incorrectly - the teacher repeats, if it is wrong again - reduces the amount.
Movements should be rhythmic and at a moderate pace (movements are considered as a whole).
Games "Guess how many", "Who is correct".
14. Learning to divide objects into equal parts (4 - 6 years)
Stage 1. In the art activity classes, children are taught to divide flat symmetrical objects into 2 equal parts (starting from a square), by bending without cutting.
It is necessary to bend so that the corners and sides coincide, the fold line is ironed, the object is unbent. Questions:
How many parts?
Are the parts equal? (check with overlay)
Which is bigger: the part or the whole?
On 2nd stage learn to divide into 4 equal parts, bending 2 times in half (the same questions).
On 3rd stage(end of middle age and beginning of senior age) are taught to divide into 2 (4) equal parts by bending followed by cutting. The questions are the same as in step 1.
The teacher explains that if we have two equal grow, then each of them is called a “half” or “one second (1/2)”, and if it turned out four equal grow, then each of them is called a “quarter” or “one fourth ( ¼)".
Stage 4. Children are taught to divide objects into 8 and 16 equal parts in a similar way. We bend in half three times - we get 8 parts, 4 times in half - 16 parts. Questions and explanations are the same as for division into 2 and 4 equal parts. It is important to draw the attention of children that if we divide the subject into 2 (4) unequal parts, then call them halves (quarters) it is forbidden. It will be simple two (four) parts.
Stage 5 Teach children to divide volumetric objects into equal parts.
There are two methods of dividing a volumetric object into equal parts: by eye or with the help of an intermediary measure. Finding out which part is larger, you can take a strip of paper, attach it to a three-dimensional object, cut it off at the place where the object ended, bend it in half, iron the fold line, attach it to the three-dimensional object, and cut this object along the fold line of the strip.
