Topic 6. Learning to solve arithmetic problems
TOPIC 6.
TRAINING IN SOLVING ARITHMETIC PROBLEMS
Plan
1. The role of the arithmetic problem in understanding the essence of the arithmetic operation
2. Features of older preschoolers’ understanding of an arithmetic problem
3. Types of arithmetic problems used in working with preschoolers
4. Consecutive stages and methodological techniques in teaching solving arithmetic problems
The role of an arithmetic problem in understanding
the essence of an arithmetic operation
In the process of mathematical and general mental development of children of senior preschool age, an essential place is occupied by learning to solve them and compose simple arithmetic problems.
In kindergarten, preparatory work is carried out to develop children's confident calculation skills in adding and subtracting single-digit numbers and rapid mental calculations with two-digit numbers in order to prepare them for learning in primary school.
If in school calculations are taught by solving examples and arithmetic problems, then in the practice of preschool institutions it is customary to introduce children to arithmetic operations and the simplest calculation techniques based on simple problems, the conditions of which reflect real, mainly play and everyday situations.
Every arithmetic problem includes
numbers given and sought. The numbers in the problem (we mean only problems used in teaching preschoolers) characterize the number of specific groups of objects or the values of quantities.
The task structure includes
condition and question. The condition of the problem indicates the connections between the given numbers, as well as between the data and the required ones. These connections determine the choice of arithmetic operation.
Having established these connections, the child quite easily comes to understand the meaning of arithmetic operations and the meaning of the concepts “add”, “subtract”, “get”, “remain”. By solving problems, children master the ability to find relationships between quantities.
At the same time, tasks are one of the means of developing logical thinking, ingenuity, and ingenuity in children. In working with tasks, the skills of analyzing and synthesizing, generalizing and concretizing, revealing the main thing, highlighting the main thing in the text of the problem and discarding the unimportant and secondary are improved.
Word problems can fully correspond to their role only with the correct organization of methods for teaching children to solve problems. The basic requirements of the methodology for teaching children to solve problems will be more clear if we consider the features of older preschoolers’ understanding of an arithmetic problem.
Peculiarities of understanding of an arithmetic problem by older preschoolers
In the works of famous teachers (1955, 1976, etc.), it was shown that most children perceive the content of the task as an ordinary story or riddle, are not aware of the structure of the task (condition and question), and therefore do not attach importance to those numerical data mentioned in the problem statement, without understanding the meaning of the question.
Children's ignorance of the simplest structure of a problem causes serious difficulties in composing its text. If the first part of the problem, i.e., numerical data, is understood faster, then posing the question, as a rule, causes serious difficulties for the child.
The question is very often replaced by an answer, for example: “There were three flowers in the vase. One flower has withered and two flowers remain.” Even by the end of their stay in the preparatory group, children find it difficult to compose the text of the problem from the pictures.
Typical mistakes of children:
1. Instead of a problem, a story is written: “Two caterpillars are sitting on a leaf, and another one is sitting on the grass. They eat everything."
2. The problem correctly perceives the question, but there is no recording of numerical data: “A girl was walking and dropped a flag. How many flags are there?
3. The question is replaced with an answer-solution: “The girl was holding flags in her hands. This one has two and this one has two. If you add it up, you get four.”
Quite often, children refuse to create a problem based on a picture, because “we haven’t solved such problems.”
Their mistakes when composing problems
Based on the pictures, we can draw the following conclusion:
1. Independently composing a problem, even in the presence of visual material, is a more difficult activity than finding the answer when solving ready-made problems;
2. Children learn the structure of a task fragmentarily, not completely, therefore not all of its components are present in the tasks they create; Educators make little use of a variety of visual materials when teaching how to write problems.
How do preschoolers cope with problem solving?
found out
· Do children understand the specific meaning of an arithmetic operation (addition or subtraction)
Do children understand the connections between the components and the result of these actions?
· are they able to identify the known and the unknown in a problem, and in connection with this choose one or another arithmetic operation
· Do children understand the connections between the operations of addition and subtraction?
She found that the majority of preschoolers
· do not have the necessary amount of knowledge about the arithmetic operations of addition and subtraction, since they understand the connection between practical actions with aggregates and the corresponding arithmetic operations mainly on the basis of the association of an arithmetic action with a life action (added - came running, subtracted - flew away, etc.)
· they are not yet aware of the mathematical connections between the components and the result of this or that action, since they have not learned to analyze the problem, identifying the known and the unknown in it
· even in those cases when children formulated an arithmetic action, it was clear that they mechanically learned the scheme for formulating the action without delving into its essence, that is, they did not realize the relationships between the components of the arithmetic action as a unity of relationships between the whole and its parts, and therefore solved the problem in the usual way of counting, without resorting to reasoning about the connections and relationships between the components.
Those children who have previously practiced performing various operations on sets (union, selecting the correct part of a set, addition, intersection) have a different approach to solving problems. They understand the relationship between part and whole, and therefore intelligently approach the choice of arithmetic operations when solving problems.
Types of arithmetic problems used in working with preschoolers
Simple problems, i.e. problems solved by one action (addition or subtraction), are usually divided into the following groups.
The first group includes simple problems in which children learn the specific meaning of each arithmetic operation, i.e., which arithmetic operation corresponds to a particular operation on sets (addition or subtraction). These are problems on finding the sum of two numbers and finding the remainder.
The second group includes simple problems, in solving which it is necessary to understand the connection between the components and results of arithmetic operations. These are tasks to find unknown components:
a) finding the first term from a known sum and the second term (“Nina sculpted several mushrooms and a bear from plasticine, and in total she sculpted 8 figures. How many fungi did Nina sculpt?”);
b) finding the second term from the known sum and the first term (“Vitya sculpted 1 bear and several bunnies. In total, he sculpted 7 figures. How many bunnies did Vitya sculpt?”);
c) finding the minuend from the known subtrahend and difference (“The children made several garlands for the Christmas tree. One of them has already been hung on the tree, they have 3 garlands left. How many garlands have the children made in total?”);
d) finding the subtrahend from the known minuend and difference (“Children, made 8 garlands on the Christmas tree. When they hung several garlands on the tree, they had one garland left. How many garlands did they hang on the Christmas tree?”).
The third group includes simple problems related to the concept of difference relations:
a) increasing the number by several units (“Lesha made 6 carrots, and Kostya made one more. How many carrots did Kostya make?”);
b) decreasing the number by several units (“Masha washed 4 cups, and Tanya washed one cup less. How many cups did Tanya wash?”).
There are other types of simple problems in which a new meaning of arithmetic operations is revealed, but, as a rule, preschoolers are not introduced to them, since in kindergarten it is enough to bring children to a basic understanding of the relationships between the components and results of arithmetic operations - addition and subtraction.
Depending on the visual material used to compose problems, they are divided into
· dramatization tasks
· illustration tasks
Each type of these tasks has its own characteristics and reveals to children certain aspects (the role of the theme, plot, the nature of the relationship between numerical data, etc.), and also contributes to the development of the ability to select the necessary life, everyday, game material for the plot of the task, teaches logically think.
Features of dramatization tasks
is that their content directly reflects the life of the children themselves, that is, what they have just done or usually do.
In dramatization tasks their meaning is most clearly revealed. Children begin to understand that the problem always reflects the specific lives of people. The ability to think about how the content of a problem corresponds to real life contributes to a deeper understanding of life and teaches children to consider phenomena in diverse connections, including quantitative relationships.
Problems of this type are especially valuable at the first stage of learning: children learn to compose problems about themselves, talk about each other’s actions, pose a question for solution, therefore the structure of the problem using the example of dramatization problems is most accessible to children.
Illustrative tasks occupy a special place in the system of visual aids
. If in dramatization tasks everything is predetermined, then in illustration tasks, with the help of toys, space is created for the variety of the plot, for the play of imagination (they are limited only by themes and numerical data). For example, there are five planes on the table on the left, and one on the right. The content of the task and its conditions can vary, reflecting children’s knowledge of the life around them and their experience. These tasks develop imagination, stimulate memory and the ability to independently come up with problems, and, therefore, lead to solving and composing oral problems.
Various pictures are widely used to illustrate problems. The main requirements for them: simplicity of plot, dynamism of content and clearly expressed quantitative relationships between objects. Such pictures are prepared in advance, some of them are published. On some of them, everything is predetermined: the topic, the content, and the numerical data. For example, the picture shows three cars and one truck. With this data, you can create 1-2 variants of tasks.
But picture problems
may also be more dynamic. For example, a panel painting is given with a background of a lake and shore; a forest is drawn on the shore. In the image of the lake, shore and forest, cuts are made into which small outline images of various objects can be inserted. The picture is accompanied by sets of such objects, 10 pieces of each type: ducks, mushrooms, hares, birds, etc. Thus, the theme here is predetermined, but the numerical data and content of the task can be varied to a certain extent (ducks swim, go out to shore, etc.) as well as creating different versions of problems about mushrooms, hares, birds.
The teacher himself can create a picture task. For example, based on a drawing of a vase with five apples and one apple on the table near the vase, children can create addition and subtraction problems.
These visual aids help to understand the meaning of an arithmetic problem and its structure.
Consecutive stages and methodological techniques in teaching solving arithmetic problems
Teaching preschoolers to solve problems goes through a number of interconnected stages.
The first stage is preparatory.
The main goal of this stage
— organize a system of exercises for performing operations on sets.
Preparation for solving addition problems includes exercises on combining sets. Exercises on isolating parts of a set are carried out to prepare children for solving subtraction problems. With the help of operations on sets, the relationship “part - whole” is revealed, the meaning of the expressions “more by...”, “less by...” is brought to understanding.
Taking into account the visual-effective and visual-figurative nature of children’s thinking, one should operate with such sets, the elements of which are specific objects. The teacher invites the children to count and put six mushrooms on the card, and then add two more mushrooms. “How many mushrooms are there in total? (Children count). Why did there become eight of them? We added two to six mushrooms (shows on objects) and got eight. How many more mushrooms have there become?
Children are taught to establish connections between data and what they are looking for and, on this basis, select the necessary arithmetic operation to solve. The best way to understand the structure of a task is through dramatization tasks. The teacher introduces the children to the word task
and when analyzing the compiled problem, emphasizes the need for numerical data and questions: “What is known?”, “What needs to be known?”.
At this stage of learning, problems are composed in which the second addend or subtrahend is the number 1. This is important to take into account so as not to make it difficult for children to find ways to solve the problem. They can add or subtract the number 1 based on their knowledge of the formation of the next or previous number.
For example, a teacher asks a child to bring and place seven flags in a glass, and one flag in another. These actions will be the content of the task that the teacher creates. The text of the problem is pronounced so that the condition, question and numerical data are clearly separated. The completed task is repeated by two or three children. At the same time, the teacher must ensure that the children do not forget the numerical data and formulate the question correctly.
When teaching preschoolers how to write problems, it is important to show how a problem differs from a story or riddle.
, emphasize the significance and nature of the issue.
To understand the meaning and nature of the issue
in the problem, you can apply the following technique: to the conditions of the problem compiled by the children, a question of a non-arithmetic nature is posed (“They put two girls on one side of the table, and one boy on the other side.” “What are the names of these children?”).
The children notice that the task did not work out. Next, you can invite them to pose such a question themselves so that it is clear that this is a task. You should listen to different versions of the questions and note that they all begin with the word how much.
To show the difference between a task and a story
and emphasize the importance of numbers and questions in the problem, the teacher should offer children a story similar to the problem. In reasoning about the content of the story, it is noted how the story differs from the task.
To teach children to distinguish a problem from a riddle
, the teacher selects a riddle that contains numerical data. For example: “Two rings, two ends, and a stud in the middle.” "What is this?" - asks the teacher. “This is not a task, but a riddle,” the children say. “But the numbers are indicated,” the teacher objects. However, it is clear that this riddle describes scissors and does not need to be solved.
In the next lesson, while continuing to teach children how to write problems, we need to emphasize the need for numerical data
. For example, the teacher offers the following text of the task: “I gave Lena geese and ducks. How many birds did I give Lena? In the discussion of this text, it turns out that such a problem cannot be solved, since it is not indicated how many geese and how many ducks were given. Lena herself composes the problem, asking the children to solve it: “Maria Petrovna gave me eight ducks and one goose. How many birds did Maria Petrovna give me?” “There are only nine birds,” the children say.
To convince children of the need for at least two numbers in a problem
, the teacher deliberately omits one of the numerical data: “Seryozha held four balloons in his hands, some of them flew away. How many balls does Seryozha have left?” Children come to the conclusion that such a problem is impossible to solve, since it does not indicate how many balls flew away.
The teacher agrees with them that the second number is not named in the problem; There should always be two numbers in a problem. The task is repeated in a modified form. “Seryozha was holding four balls in his hands, one of them flew away. How many balls does Seryozha have left?”
Using specific examples from life, children become more clearly aware of the need to have two numbers in the problem statement, better understand the relationships between quantities, and begin to distinguish between the known data in the problem and the unknown unknown.
After such exercises, you can lead children to a generalized understanding of the components of the problem.
The main elements of a task are
a condition and a question .
The condition explicitly contains the relationship between the numerical data and implicitly - between the data and the desired one. Analysis of the condition leads to an understanding of the known and to the search for the unknown. This search occurs in the process of solving a problem. Children need to be explained that solving a problem means understanding and telling what actions need to be performed on the numbers given in it in order to get the answer.
Thus, the task structure includes four components:
· condition
· question
· solution
· answer.
Having figured out the structure of the problem, children easily move on to identifying individual parts in it. Preschoolers should be trained in repeating a simple task as a whole and its individual parts. You can invite some children to repeat the conditions of the problem, and others to pose a question in this problem.
Formulating a question
, children, as a rule, use the words
became, remained.
You should show them that the wording of the question in addition problems can be different.
For example: “There were five planes at the airfield. Then another one came back." The child asks the question: “How many planes are there?” The teacher explains that instead of the word it has become
better to say
it,
because the planes are at the airfield.
Thus, in the question you should use verbs that reflect actions related to the content of the task (They arrived, bought, grew up, walked, played,
etc.).
When children learn to formulate the question correctly, you can move on to the next task of this stage
— teach how to analyze problems, establish relationships between data and what is being sought. On this basis, you can already learn to formulate and write an arithmetic operation using numbers and signs +, -, =.
Since the task represents the unity of the whole and the part, children should be led to its analysis from this position.
Let's give an example. The task is based on the actions performed by the children: “Nina put five flags in one vase, and one flag in another.” The children tell what Nina did and in fact already know that the description of Nina’s actions is called the condition of the task. “What is known from the problem? - asks the teacher. (Five flags in one vase and one in another.) - What is unknown, what still needs to be found out? How many flags did Nina put in both vases? What is unknown in a problem is the question of the problem. (Children repeat the question in the problem.) What numbers are known in
task? (There are five about the number of flags in one vase and one about the number of flags in another vase.) It is proposed to represent this data in numbers on paper and on the board: “What do you need to know? How many flags are there in both vases?
Children analyze a subtraction problem in a similar way. Based on the practical actions of the children, the content of the task is compiled. For example, duty officer Kolya placed six chairs around the table, and duty officer Sasha removed one chair. Children formulate the conditions of the problem and pose a question. The condition and the question are repeated separately.
Next, the problem is analyzed, it is found out what is known from the problem (six chairs were placed, and then one was removed) and what is unknown (how many chairs are left at the table). Children are asked to solve a problem and answer its question.
The educational value of the above addition and subtraction problems is not so much to get the answer, but to teach how to analyze the problem and, as a result, choose the right arithmetic operation.
So, at the second stage of working on tasks, children should:
a) learn to write problems;
b) understand their difference from a story and a riddle;
c) understand the structure of the task;
d) be able to analyze problems, establishing relationships between the data and the required ones.
The task of the third stage is to teach children to formulate the arithmetic operations of addition and subtraction.
At the previous stage, preschoolers easily found the answer to the question of the problem, relying on their knowledge of the sequence of numbers, connections and relationships between them. Now we need to introduce them to the arithmetic operations of addition and subtraction, reveal their meaning, teach them how to formulate them and “write them down” using numbers and signs in the form of a numerical example. (“Recording” is done using cards with numbers and symbols depicted on them.)
First of all, children must be taught to formulate the action of finding the sum of two terms when composing a problem using specific data
(five fish on the left and one on the right). “The boy caught five crucian carp and one perch,” says Sasha. “How many fish did the boy catch?” - Kolya formulates the question. The teacher invites the children to answer the question. After listening to the answers of several children, he asks them a new question: “How did you know that the boy caught six fish?” Children, as a rule, answer in different ways: “We saw”, “Counted”, “We know that five and one will be six”, etc. Now we can move on to reasoning: “There were more fish or fewer when the boy caught one more?" “Of course, more!” - the children answer. "Why?" - “Because they added one more fish to the five fish.” The teacher encourages this answer and formulates an arithmetic operation: “Dima said correctly, we need to add the two numbers named in the problem. Add one fish to five fish. This is called the action of addition. Now we will not only answer the question of the task, but also explain what action we are performing.”
Based on the proposed visual material, one or two more problems are compiled, with the help of which children continue to learn to formulate the operation of addition and give an answer to the question.
In the first lessons, the verbal formulation of an arithmetic operation is reinforced with practical actions: “To three red circles we add one blue circle and we get four circles.” But gradually the arithmetic operation should be distracted from the specific material: “Which number was added to which?” Now, when formulating an arithmetic operation, numbers are not named. There is no need to rush to the transition to operating with abstract numbers. Such abstract concepts as “number” and “arithmetic operation” become accessible only through long-term exercises by children with specific material.
When children have basically mastered the formulation of the operation of addition, they move on to learning the formulation of subtraction
. The work is carried out in the same way as described above.
When formulating an arithmetic operation, it can be considered correct when children say subtract, add, subtract, add.
The words
add, subtract, turn out, equal
are special mathematical terms.
These terms correspond to the everyday words add, subtract, became, will be.
Of course, everyday words are closer to the child’s experience and you can start learning with them. But it is desirable that the teacher use mathematical terminology in his speech, gradually accustoming children to the use of these words. For example, a child says: “You need to subtract one apple from five,” and the teacher should clarify: “You need to subtract one apple from five apples.”
When teaching children how to formulate an arithmetic operation, it is useful to offer problems with the same numerical data for different operations. For example: “Sasha had three balloons. One ball flew away. How many balls are left? or: “Kolya was given three books and one car. How many gifts did Kolya receive? It is established that these are tasks for the same action. It is important to pay attention to the correct and complete formulation of the answer to the problem question.
You can show tasks that are similar in appearance, but require different arithmetic operations. For example: “Four birds were sitting on a tree, one bird flew away. How many birds are left on the tree? or: “Four birds were sitting on a tree. Another one has arrived. How many birds are sitting on the tree? It’s good when such problems are compiled by children at the same time.
Based on the analysis of these tasks, children come to the conclusion that although both tasks involve the same number of birds, they perform different actions. In one problem, one bird flies away, and in another, it flies in, so in one problem the numbers need to be added, and in the other, they need to subtract one from the other. The questions in the problems are different, therefore the arithmetic operations are different, and the answers are different.
Such a comparison of problems and their analysis are useful for children, since they better assimilate both the content of the problems and the meaning of the arithmetic operation determined by the content.
Dynamics of teacher questions to children to formulate arithmetic operations
1. In the first lessons, a detailed question is asked, the content of which is close to the content of the question for the problem: “What needs to be done to find out how many birds are sitting on the tree?”
2. Then the question is formulated in a more general form: “What needs to be done to solve this problem?” or: “What needs to be done to answer the problem question?”
The teacher should not put up with children’s monosyllabic answers ( “subtract”,
“add”
). The arithmetic operation performed must be formulated completely and correctly. It is important to involve all children in thinking about the most accurate answer.
Since by the time they learn to solve problems, children are already familiar with numbers and signs +, -, =, they should be trained in writing an arithmetic operation and taught to read the notation (3+ 1=4). (Add one bird to three birds. You get four birds.) The ability to read a record provides the ability to compose problems based on a numerical example. For example, on the board there is a note: 10 - 1=? The teacher suggests reading the entry and saying what this sign (?) means. Then he asks to compose a problem in which the same numbers are given as on the board. The teacher makes sure that the content of the tasks is varied and interesting, and that the question is posed correctly. The most interesting problem is selected for solution. One of the children repeats it. Children, highlighting the data and what they are looking for in the problem, name the arithmetic operation, solve the problem and write down the solution on their paper. One of the children formulates the answer to the problem. The conversation accustoms the children to think logically, teaches them to correctly construct answers to questions posed - about the topic, the plot of the problem, about numerical data and their relationships, and to justify the choice of an arithmetic operation.
To exercise children in recognizing addition and subtraction entries, the teacher is recommended to use several numerical examples and invite the children to read them. Based on these examples, problems are compiled for various arithmetic operations, and children are asked to independently write down the solved problems and then read it. It is imperative to correct the answers of children who made mistakes in the recording. By reading the entry, children are more likely to discover their own mistake.
Recording actions convinces children that in every problem there are always two numbers from which they need to find the third - the sum or difference.
and recommend another way of writing an arithmetic operation. The authors proposed introducing children to a model that helps them master the generalized concept of an arithmetic operation (addition and subtraction) as a relationship between a part and the whole.
This model of recording arithmetic operations promotes the transition from the perception of specific connections and relationships between parts and the whole set to a model of depicting connections and relationships of arithmetic operations using conventional and mathematical signs. The recording model is an intermediate link in the transition from a graphical representation of relationships between sets to numerical equality.
Children are already familiar with the signs plus (+), minus (-), equals (=), now they are introduced to the model of writing an arithmetic operation with the symbols whole - circle, part of the whole - semicircle and are taught to form an equality.
During the learning process, you should compose and solve problems involving addition and subtraction of quantities.
. As visual material, cords, ribbon, ribbons, soft wire and other objects to be measured are used, as well as conventional measurements of different sizes, etc.
Children are already familiar with the methods and techniques of measuring quantities (length, mass) and know how to use such correct expressions as a piece of rope, a piece of braid
(but not a piece of rope or braid).
Let's give an example of such a task. A picture is hung of a doll holding a basket of washed laundry. There are two pegs in front of the doll, between which you need to stretch a rope to hang clothes on it. The flannelgraph shows two pegs between which a rope should be pulled.
The child must take a rope out of the basket to pull it between the pegs, but it turns out to be small, and then he must take another piece of rope and connect it to the first so that the length of the rope is sufficient to stretch between the pegs.
Children are asked to look at the picture and create a problem based on it. To do this, you must first measure the length of both pieces of rope. Sections of rope are measured: one section is equal to six measurements, and the other is equal to one. A problem is set up: one piece of rope taken to pull it between the pegs turned out to be insufficient; it contained six measures. They took another segment equal to one measurement and connected it to the first segment. How many measures are in the length of the entire rope? The teacher suggests making a record so that the known and unknown numbers are visible. Children formulate the action and result, give an answer to the question of the task.
The teacher should then be asked to think about whether it is possible to create another task based on this picture. Children suggest first measuring the length of the entire rope and the length of one of the sections of the rope, so that they can subtract the length of the section of rope from the length of the entire rope and get the length of the second section. A new problem is created for the action of subtraction, in which the unknown number becomes the length of the second segment
It should be noted that the experience acquired by children in the process of measuring quantities is also used when composing problems. Let's list some of them.
“Mom bought 1 m of blue ribbon and 2 m of red. How many meters of tape did mom buy in total?”
“We went to the store and bought 2 kg of apples and 1 kg of plums. How much fruit did we buy in total?
“The boy got into the boat and swam 6 m, but the river is only 8 m wide. How much more does he need to swim?”
“The driver poured 6 liters of gasoline into the car’s tank, and then added another 3 liters. How much gasoline did the driver put into the tank?”
So, at the third stage, children must learn to formulate arithmetic operations (addition, subtraction), distinguish between them, and compose problems for a given arithmetic operation.
At the fourth stage of working on problems, children are taught calculation techniques - counting and counting units.
If until now the second addend or subtraction in the problems being solved was the number 1, now you need to show how to add or subtract the numbers 2 and 3. This will diversify the numerical data of the problem and deepen the understanding of the relationships between them, and will prevent automaticity in the children’s answers. However, here you need to be careful and gradual. First, children learn to add by counting by one and subtract by counting by one the number 2, and then the number 3.
Counting
- this is a technique when a second known term is added to an already known number, which is divided into units and counted sequentially by 1: 6 + 3=6+ 1 +1 +1 + 1=7+1 + 1=8+1=9.
Countdown
- this is a technique when a number (divided into units) is subtracted from a known amount sequentially by 1: 8-3 = 8 - 1 - 1-1 = 7 - 1 - 1 = 6 - 1 = 5.
Children's attention should be drawn to the fact that when adding there is no need to recalculate the first number by one, it is already known, and the second number (second addend) should be counted by one (the terms “sum”, “addend”, “subtracted”, “minued”) ", "difference" are not communicated to children in the preparatory school group); we only need to remember the quantitative composition of this number of units. This process reminds children of what they did when they counted further from any number to the number given to them. When subtracting the numbers 2 or 3, remembering the quantitative composition of the number from units, you need to subtract this number from the one being reduced by one. This reminds children of practicing counting backwards within a range of numbers given to them.
So,
When studying the actions of addition and subtraction when solving arithmetic problems, we can limit ourselves to these simplest cases of adding (subtracting) numbers 2 and 3. There is no need to increase the second addend or subtracted number, since this would require other calculation techniques. The goal of kindergarten is to lead children to understand an arithmetic problem and to understand the relationships between the components of the arithmetic operations of addition and subtraction.
At the final fifth stage of working on problems, you can invite preschoolers to compose problems without visual material (oral problems).
In them, children independently choose the topic, the plot of the problem and the action with which it should be solved. The teacher regulates only the second addend or subtraction, reminding the children that they have not yet learned to add and subtract numbers above three. (There may be exceptions here.)
When introducing oral tasks, it is important to ensure that they are not formulaic. The condition should reflect life connections, everyday and gaming situations. It is necessary to teach children to reason, justify their answer, and in some cases use visual material for this.
After children have mastered solving oral problems of the first and second types, they can move on to solving problems involving increasing and decreasing a number by several units.
Research and practice show that preschoolers can solve some types of indirect problems.
They can be offered to children, being confident that they have mastered the required program material well. And only if it is necessary to complicate the work, such tasks can be introduced. Since in indirect problems the logic of an arithmetic operation contradicts the action in the content of the problem, they provide great scope for reasoning, evidence, and teach children to think logically.
Here are examples of such tasks:
“Five glasses of water were poured out of the decanter, but one glass of water remained in it. How much water was in the decanter?
“Lesha made Christmas tree decorations. He hung three of them on the tree and left two. How many toys did Lesha make?”
“Lena had seven sweets. She treated the kids and had four candies left. How many candies did she give to the guys?
“Birds were sitting on a tree. When four more arrived, there were eight of them. How many birds were sitting on the tree at first?
It is best to offer such problems for solution in the form of a surprise: “Who will figure out how to solve the problem that I am going to ask you now?” It should be noted that these tasks are of great interest to children.
So, working on problems not only enriches children with new knowledge, but also provides rich material for mental development.
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First steps into mathematics. notes notes in the preparatory group - a child in kindergarten
The summary of the educational activities in the preparatory group was compiled by teachers Olga Anatolyevna Sorokina, MADOU Child Development Center - kindergarten No. 41 “Rosinka”, Nizhnevartovsk.
The GCD summary in the preparatory group is included in the section “First steps in mathematics.”
GCD tasks:
- Continue to learn how to compose arithmetic problems and write down their solutions using numbers.
- Strengthen children's knowledge about geometric shapes.
- Continue to form children's ideas about days of the week, months and numbers.
- Strengthen the ability to navigate on a sheet of paper in a square.
- Strengthen the ability to distinguish between spatial representations: left, right, middle, top, bottom, behind, in front.
Developmental tasks:
- Create conditions for the development of logical thinking, intelligence, and attention.
- Develop ingenuity, visual memory, imagination.
- Contribute to the formation of mental operations, speech development, and the ability to give reasons for one’s statements.
