Preschool age is a time when the cognitive, moral, and physical development of a child occurs especially intensively. In particular, it is before the age of 5-6 that a child acquires more than half of the total thinking skills that will be useful to him in the future. That is why it needs to be given special attention. In particular, it is at this age that the child should develop his first mathematical skills. Let's consider the theoretical foundations of the mathematical development of children of junior and senior preschool age.
Math lesson in kindergarten, senior group
Why is this so important?
- Mathematics is one of the most significant subjects. However, it is precisely this that often causes considerable difficulties for students.
- Studying this subject has a beneficial effect on the child’s cognitive abilities (thinking, memory, speech)
- Mathematical skills improve the emotional-volitional sphere, form perseverance and determination
- Improves the basics of a child's imagination
The role of mathematics in life
What skills should a child develop by the end of the preschool period?
By the end of the preschool period, the child should have the following mathematical skills:
- Ability to compare values based on basic characteristics; the formation of ideas about the concepts of “more-less”, “higher-lower”, etc.
- The ability to group objects according to their basic properties (basics - size, color, purpose, material, shape)
- Ability to compare parts and wholes; ability to assemble a picture from at least 12-24 fragments
- Developed counting skills and the ability to perform mathematical operations with numbers within ten
- Children’s development of quantitative and qualitative representations of the subject
The essence of mathematical development
Necessary conditions for conducting math classes with a child
What is the theory and methodology of mathematical development for preschoolers based on? In order for the lessons to be truly interesting for the child, and for him to assimilate information faster and easier, they must be built taking into account the following recommendations:
- The use of visual didactic material selected taking into account the age and other individual characteristics of the child
- The presence of a clear plot for the lesson according to which its development will take place
- Selection of tasks in strict accordance with the age characteristics of the child and the level of his intellectual development
- Using a variety of methods and forms to create the basis of work (these include solving logical problems, didactic games, working with handouts, etc.)
- Multitasking (focus on the development of spatial, temporal, quantitative concepts)
- Using a game form of conducting classes
- Emphasis on the formation of gaming motivation; elements of surprise and surprise
- Helping the child not only master a certain system of knowledge and skills, but also develop his skills of independent cognitive activity, independence of judgment, etc.
- Formation of an optimal developmental environment for the development of basic cognitive processes in a child
- Teaching children to perceive the quantitative and qualitative features of objects, forming appropriate ideas
Objectives for the development of mathematical abilities
Article:
The concept of “Method”
In the theory and methodology of children’s mathematical development, the term “method” is used in two senses: broad and narrow.
The method is a historically established approach to the mathematical preparation of children in kindergarten (monographic, computational and the method of reciprocal actions).
When choosing methods, the following are taken into account:
- goals, objectives of training;
- the content of the knowledge being formed at this stage;
- age and individual characteristics of children;
- availability of necessary teaching aids;
- the teacher’s personal attitude to certain methods;
- specific conditions in which the learning process takes place, etc.
At the beginning of the 20th century. the classification of methods was mainly carried out according to the source of knowledge - these were verbal, visual, practical methods.
Practical methods
- (exercises, experiments, productive activities) are most consistent with the age characteristics and level of development of thinking of preschoolers. The essence of these methods is that children perform actions that consist of a number of operations.
- Practical methods are characterized primarily by independent performance of actions and the use of didactic material. On the basis of practical actions, the child develops the first ideas about the knowledge being formed. Practical methods ensure the development of skills and abilities and allow the widespread use of acquired skills in other types of activities.
Visual and verbal methods in teaching mathematics are not independent. They accompany practical and playful methods. But this does not detract from their importance in the mathematical development of children.
Visual and verbal methods
Visual teaching methods include: demonstration of objects and illustrations, observation, demonstration, examination of tables and models.
Verbal methods include: storytelling, conversation, explanation, explanations, verbal didactic games. Often in one lesson different methods are used in different combinations.
Techniques
The components of the method are called methodological techniques.
The main ones used in mathematics classes are: overlay, application, didactic games, comparison, instructions, questions for children, examination , etc.
Reception "Show"
- A widely used methodological technique is demonstration .
- This technique is a demonstration; it can be characterized as visually practical and effective.
- There are certain requirements for the display: clarity and dissection; consistency of action and word; accuracy, brevity, expressiveness of speech.
Reception "Instructions"
One of the essential verbal techniques in teaching children mathematics is instruction , which reflects the essence of the activity that the children have to perform.
Reception “Questions for Children”
Questions for children occupy a special place in the methodology of teaching mathematics . They can be reproductive-mnemonic, reproductive-cognitive, productive-cognitive. In this case, the questions must be accurate, specific, and concise. They are characterized by logical consistency and variety of formulations.
Features of the formation of mathematical concepts depending on age
Considering that preschool age is conventionally divided into three main periods, goals, objectives, as well as methods and forms of mathematical education of children will also differ.
Junior preschool period. At this time, the necessary mathematical skills and concepts are just beginning to develop. Therefore, the child needs to be given an idea of basic operations. The best games for developing thinking skills are children's mosaics (from 5 fragments), addition of geometric shapes (from 4 parts). The method of developing quantitative and qualitative concepts in preschoolers requires special attention.
Middle preschool period. There is an active development of the sign-symbolic function of consciousness. The child can already be taught to count and the simplest mathematical operations. The foundations of logical thinking are laid. The most preferred games include: “Nonsense”, “Count the objects”, “Find a pair”, “Mathematical lotto”, “Domino figures”. To develop a child’s analytical and synthetic abilities, you can offer him games like tangram, where he will need to make a geometric figure, a silhouette of an animal, etc. from individual parts.
Individual lesson to determine the level of mathematical development
In older preschool age, the child’s independence and his ability to self-organize begin to play an increasingly noticeable and significant role. Logical thinking is becoming increasingly important.
The child begins to try to compose stories from pictures, compose logical series, observing the correct sequence of elements.
Math tests for kids 3-4 years old
“Methodological recommendations for the mathematical development of children of senior preschool age”
METHODOLOGICAL
RECOMMENDATIONS
ON MATHEMATICAL DEVELOPMENT OF SENIOR PRESCHOOL CHILDREN
Educator:
Biryukova Ekaterina Yurievna
MBDOU "Kindergarten No. 59 "Yagodka"
Tambov
What is activity in cognitive activity or what is cognitive activity?
The cognitive activity of a preschooler can be characterized as a manifestation of independence, initiative, and creativity in the process of activity. This is the desire to learn, comprehend, understand, find, and experience the joy of success from independently finding a way to solve a cognitive problem.
The prerequisite, the physiological basis of cognitive activity, is certainly an oriented reflex: “What is this?” But the precondition can develop into a quality called cognitive activity only under certain favorable conditions. The main task of pedagogy is to create such conditions.
This includes, first of all, the development of motives for learning activities, as well as knowledge, skills and an emotionally positive background for learning.
Activity manifests itself mainly:
- the ability to see and independently set a cognitive task;
- draw up a plan and select ways to solve a problem using the most reliable and effective methods possible;
- achieve a result and understand the need to check it.
These provisions already show: the cognitive activity of children cannot be considered as a volitional, purposeful action, where the goal most often goes beyond the immediate situation.
In this case, cognitive activity is the mobilization of intellectual, moral-volitional and physical forces to achieve specific learning goals. We proceed from the position: activity in the learning process is determined not by motor activity, not by the degree of employment, but by the level of mental activity, which carries elements of creativity.
And it is absolutely necessary to remember that the age characteristics of children (even older preschool age) make it possible to organize an active state in the learning process, but rather connectedness in the learning process, connectedness with individual main tasks of a specific task.
It is known that cognitive activity begins with living contemplation in a broad sense - with sensations and perceptions.
Children observe, listen, examine, apply, measure, examine the shape of objects, etc. Already this stage of learning is characterized by activity. However, in these cases it would be more correct to talk about general mental activity.
At the beginning, the child develops the ability to see, hear, compare specific objects directly, determine their color, size, shape. Somewhat later, the ability to analyze, compare, contrast, draw conclusions, etc. appears. At the same time, mental actions acquire a special connotation - the desire for independence.
By what indicators can a teacher judge the activity of children in the learning process? This is, first of all:
— passion for studying the material (concentration, attention);
- a clearly expressed desire to perform a variety of, especially complex tasks;
- desire to continue classes (often such children themselves are the initiators of games, joint cognitive activities with adults: they offer to play, consider, find a way);
— manifestation of independence in the selection of means, methods of action, achieving results, and exercising control;
— use of knowledge in independent activities (play, work, constructive);
- contacting the teacher with questions aimed at cognitive interests;
— quality of knowledge and skills (awareness, flexibility, efficiency).
In such cases, children achieve the goal not intuitively, but consciously, and are able to explain how they performed the action and why exactly (“Why do you think that this problem is given for addition?” - “Because the problem says that the children took three large and two small balls. Do you need to find out how many balls they took? To do this, you need to add them up").
In the process of mathematical development, much attention is paid to the formation of knowledge and extremely little to mastering methods of activity.
Mathematical knowledge in independent activities: (children build buildings, ignoring the ratios of objects in size, play “shop” without resorting to counting, set the table without proper orientation to quantitative relationships), diagrams, diagrams, tables, where it is possible to compare and analyze , generalize, abstract.
In individual work with each student, the teacher can maximize cognitive activity, identify the characteristics of this activity, build on what has been achieved and help to rise higher, using the desire for independence for this.
Cognitive activity is formed mainly in cognitive activity, which is associated with the purposeful actions of children. Pedagogically correctly organized activities contribute most effectively to its formation. Formed in the process of activity, cognitive activity at the same time affects the quality of this activity. Activity here acts as a means and as a condition for achieving a goal.
In our pedagogical work, we proceeded from the position: cognitive activity is always individual in nature. For some children it is higher, for others it is lower, some need certain means, others need others. And, nevertheless, as experience shows, it is possible to increase the cognitive activity of all children and each individual in the following way. This:
— strict selection of the content of educational (cognitive) material for each lesson, reasoned, logical connection between the parts of this material;
— adequacy (compliance) of methods and teaching techniques with the program content of the lesson;
— creating optimal conditions for independent work;
- a combination of collective and individual forms of educational (cognitive) activity in and outside of class.
By integrating program tasks for each lesson, we strive to ensure that children’s educational activities simultaneously influence the intellectual, emotional, and moral-volitional sphere of each person’s personality. This required, first of all, to improve the means and methods of teaching, to increase the time and variety of tasks for independent work. In order for children to understand the goal setting of the lesson - and this is what we consider the main thing - the teacher, communicating the topic and main cognitive objectives of the lesson, clearly highlighted what new things they will learn today, what they will learn. At the same time, he was in no hurry to give ready-made knowledge or immediately show implementation techniques, but always provided the opportunity for independent search and creative solution to the problem.
The cognitive activity of children must be in strict accordance with the main objectives of the lesson and the stage of formation of knowledge and skills. So, at the first stage - the formation of knowledge and skills - the activity of the teacher should be higher. He is obliged to show the methods of performing the activity, the sequence of actions, etc. At the second stage - consolidation - it is quite natural to introduce greater independence and activity to children.
Of course, he pays special attention to children who are more difficult to learn the material than others. As a rule, the teacher works with them before learning new material. So, the day before the upcoming lesson, the teacher says to the child: “Soon we will get acquainted with a new figure, no one knows what it’s called yet, but I’ll tell you now, just try to remember - it’s a rhombus (cone).” The child repeats the name of the geometric figure and examines it together with the teacher. On the eve of the lesson, you can once again remember what it is called and how it differs from those already known.
After such preparation, it is naturally easier to cope with the task and, as a rule, the child is active during the lesson.
At each lesson, organizing cognitive activities, the teacher strives to ensure that in individual work children develop the ability to analyze, compare, generalize, and prove. It is important to create conditions for the manifestation of independence and creativity, to provide children with the opportunity to take initiative and find their own ways of solving a cognitive problem.
What methods are best used to develop a preschooler's mathematical understanding?
The visual method plays the most important role in teaching children mathematics, especially when it comes to the early preschool period.
Methods for developing mathematical knowledge
There are the following types of visual teaching methods:
- Working with handouts or demonstration materials. Using a plotless or plot method (you can take as a basis the plot of any fairy tale familiar to a child, where counting or numbers would appear)
- Volumetric or planar. Classes using special counting materials (for example, children's abacus, sticks, cubes, etc.)
- Homemade or factory made.
Handouts for mathematical classes
In order to use visual material more effectively, it is necessary to build developmental classes taking into account the following patterns:
- The study of each new topic should begin with more voluminous visual material. This will make it easier for the child to understand
- As the child grows up, it is necessary to ensure that the proportion of volumetric and plot-based visual material decreases, and the proportion of flat and plotless material increases
- It is advisable to use several types of visual material to solve one software problem
- It is very advisable to familiarize the child with new material in advance.
Separately, it is worth considering the requirements for visual aids.
Didactic material for classes
As we have already indicated above, it can be either ready-made at the factory or made by parents. However, it is important that it matches the following:
- Hygiene. Toys must be made from environmentally friendly, safe materials and have all the necessary certificates
- Aesthetics. Attractive material is more likely to attract the child's attention
- A reality that allows a child to perceive the material being studied without distortion
- Durability and reliability
- Variety and sufficient quantity to allow the use of variable techniques
- The principle of logical construction that combines the basics of the material
- Uniformity
Play corner with didactic materials
A significant advantage of the practical teaching method is that it most fully explains to the child why he is studying this or that material. And how exactly will the knowledge gained be useful to him in the future?
- Active application in practice of a variety of didactic material
- Performing a variety of both mental and practical activities
- Development of the skill of predicting the outcome of actions with various types of didactic material
- Not only instilling mathematical skills in the child, but also a detailed explanation of their role in the child’s life (in play activities, in everyday life, etc.)
The verbal method of teaching is based on direct interaction between the child and the parent or teacher.
That is why the main requirements for this method will be aimed at the speech of the participants in the process
The speech of the parent or teacher should be:
- Literate
- Rosary
- Emotional and alive
- Available
- Friendly
- Moderately loud
Speech development in mathematics classes
The pace of speech, its intonation and other features must be adjusted depending on the individual age characteristics of the child. For example, a child of primary preschool age perceives rather slow speech much better; unformed memory processes require repeated repetitions.
Development of logic and spatial thinking in a playful way
When talking with an older child, you can somewhat speed up the pace of speech and also make more active use of problem situations.
Certain requirements are also imposed on children’s speech. She must be:
- Competent
- Contain the necessary mathematical terminology and basic mathematics by age
- Legible and understandable
- The child must speak in complete common sentences with correct grammatical structure
- Have sufficient volume
Structure of a math lesson for a preschooler
The correct structure of the lesson is another important condition on which the methodology for the mathematical development of preschool children is based.
Games used in mathematics classes
- Introductory part. Logical warm-up. Includes the simplest tasks for children, which should “warm up” the child’s mind, interest him and prepare him for the lesson.
- The main part of the lesson, during which new material is studied to form mathematical concepts, or reinforcement of what has already been learned. Exercises can be selected using special methodological literature (a good example is the book compiled by E.I. Shcherbakova “Theory and Methods of Mathematical Development for Preschool Children”).
- 3Finger gymnastics. Redirects the child's attention and serves as a warning against fatigue. For the same purposes, you can use physical exercise (if the lesson was associated primarily with intellectual activity), articulatory gymnastics or eye exercises (if the child had an active lesson using outdoor games).
- Repetition of covered material.
- Drawing, lacing, or games aimed at developing fine motor skills.
Studying shape and size in physical education classes
Developed mathematical skills in preschool children will allow him not only to successfully start school, but also to develop such qualities as perseverance, attention, and determination.
leave a comment
Methods and techniques for teaching preschoolers elements of mathematics
Methods and techniques for teaching preschoolers elements of mathematics
The concept of "Method"
In the theory and methodology of children's mathematical development, the term “method” is used in two senses: broad and narrow.
The method is a historically established approach to the mathematical preparation of children in kindergarten (monographic, computational and the method of reciprocal actions).
When choosing methods, the following are taken into account:
- goals, objectives of training;
- the content of the knowledge being formed at this stage;
- age and individual characteristics of children;
- availability of necessary teaching aids;
- the teacher’s personal attitude to certain methods;
- specific conditions in which the learning process takes place, etc.
At the beginning of the 20th century. classification of methods was mainly carried out according to the source of knowledge - these were verbal, visual, practical
methods.
Practical methods
- (exercises, experiments, productive activities) are most consistent with the age characteristics and level of development of thinking of preschoolers. The essence of these methods is that children perform actions that consist of a number of operations.
- Practical methods are characterized primarily by independent performance of actions and the use of didactic material. On the basis of practical actions, the child develops the first ideas about the knowledge being formed. Practical methods ensure the development of skills and abilities and allow the widespread use of acquired skills in other types of activities.
Visual and verbal
methods in teaching mathematics are not independent. They accompany practical and playful methods. But this does not detract from their importance in the mathematical development of children.
Visual and verbal methods
Towards visual methods
training includes: demonstration of objects and illustrations, observation, display, examination of tables, models.
Towards verbal methods
include: storytelling, conversation, explanation, explanations, verbal didactic games. Often in one lesson different methods are used in different combinations.
Techniques
Components of the method
are called methodological
techniques.
The main ones used in mathematics classes are: overlay, application, didactic games, comparison, instructions, questions for children, examination
etc.
Reception "Show"
- A widely used method is: show
.
- This technique is a demonstration; it can be characterized as visually practical and effective.
- There are certain requirements for the display: clarity and dissection; consistency of action and word; accuracy, brevity, expressiveness of speech.
Reception "Instructions"
One of the essential verbal techniques in teaching children mathematics is instruction.
, reflecting the essence of the activity that children have to perform.
Reception “Questions for Children”
Questions for children occupy a special place in the methodology of teaching mathematics.
. They can be reproductive-mnemonic, reproductive-cognitive, productive-cognitive. In this case, the questions must be accurate, specific, and concise. They are characterized by logical consistency and variety of formulations.
