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
Mathematical development of preschool children in the context of the Federal State Educational Standard (FSES) Consultation on mathematics on the topic
Mathematical development of preschool children in the context of Federal State Educational Standards for Preschool Education
“The further path of mathematical development and the success of a child’s advancement in this area of knowledge largely depend on how elementary mathematical concepts are laid down.”
L.A. Wenger
One of the most important tasks in raising a preschool child is the development of his mind, the formation of such thinking skills and abilities that make it easy to learn new things.
For the modern educational system, the problem of mental education (and the development of cognitive activity is one of the tasks of mental education) is extremely important and relevant. It is so important to learn to think creatively, outside the box, and to independently find the right solution.
It is mathematics that sharpens a child’s mind, develops flexibility of thinking, teaches logic, forms memory, attention, imagination, and speech.
The Federal State Educational Standard for Education requires making the process of mastering elementary mathematical concepts attractive, unobtrusive, and joyful.
In accordance with the Federal State Educational Standard for Preschool Education, the main goals of the mathematical development of preschool children are:
- Development of logical and mathematical ideas about the mathematical properties and relationships of objects (specific quantities, numbers, geometric figures, dependencies, patterns);
- Development of sensory, subject-effective ways of knowing mathematical properties and relationships: examination, comparison, grouping, ordering, partitioning);
- Children's mastery of experimental and research methods of learning mathematical content (experimentation, modeling, transformation);
- Development in children of logical ways of knowing mathematical properties and relationships (analysis, abstraction, negation, comparison, classification);
- Children's mastery of mathematical ways of understanding reality: counting, measurement, simple calculations;
- Development of intellectual and creative manifestations of children: resourcefulness, ingenuity, guesswork, ingenuity, desire to find non-standard solutions;
- Development of accurate, reasoned and demonstrative speech, enrichment of the child’s vocabulary;
- Development of children's initiative and activity.
Target guidelines for the formation of elementary mathematical concepts:
Oriented in quantitative, spatial and temporal relationships of the surrounding reality
Counts, calculates, measures, models
Knows mathematical terminology
Developed cognitive interests and abilities, logical thinking
Possesses basic graphic skills and abilities
Knows general techniques of mental activity (classification, comparison, generalization, etc.)
How to “awaken” a child’s cognitive interest?
Answers: novelty, unusualness, surprise, inconsistency with previous ideas.
That is, it is necessary to make learning entertaining. With entertaining learning, emotional and mental processes are intensified, forcing you to observe, compare, reason, argue, and prove the correctness of the actions performed.
The adult’s task is to maintain the child’s interest!
Today, the teacher needs to structure educational activities in kindergarten in such a way that every child is actively and enthusiastically engaged. When offering children tasks with mathematical content, it is necessary to take into account that their individual abilities and preferences will be different and therefore children’s mastery of mathematical content is of a purely individual nature.
Mastering mathematical concepts will only be effective and efficient when children do not see that they are being taught something. They think they are just playing. Unbeknownst to oneself, during game actions with game material, one counts, adds, subtracts, and solves logical problems.
The possibilities for organizing such activities are expanded provided that a developing subject-spatial environment is created in the kindergarten group. After all, a properly organized subject-spatial environment allows every child to find something to their liking, believe in their strengths and abilities, learn to interact with teachers and peers, understand and evaluate feelings and actions, and give reasons for their conclusions.
Each group should be provided with entertaining material, namely card files with a selection of mathematical riddles, funny poems, mathematical proverbs and sayings, counting rhymes, logical problems, joke problems, and mathematical fairy tales. Entertaining in content, aimed at developing attention, memory, and imagination, these materials stimulate children's display of cognitive interest. Naturally, success can be ensured under the condition of personality-oriented interaction between the child and adults and other children.
Particular attention is paid to the richness of the environment - the educational space must be equipped with teaching and educational means (including technical ones).
For 1st junior group
It is recommended that the sensory development center have a variety of didactic and visual materials:
Didactic games on color, shape, size, development of tactile sensations;
Educational games - Dienesh blocks, Cuisenaire sticks, Montessori frames, etc., with teaching aids for them (albums, instructions, etc.);
Attributes and materials for playing with sand and water;
Visual material on sensory education;
Board and printed games;
"Wonderful bag";
A card index of artistic words for introducing children to sensory standards.
Helper devices: magnifying glass, hourglass, magnets, measuring spoons, rubber bulbs of different sizes
For children 3-4 years old
The center of entertaining mathematics can include didactic toys and board games that develop children’s skills:
compare objects according to various criteria - size, shape, color, purpose, etc.;
group objects based on common characteristics (this is dishes, these are shoes; ribbons are the same length and the same color); compose a whole image from 6-8 parts (“Toys”, “Animals”, “Flowers”): lotto (dishes, clothes, furniture, animals, plants);
make rows of identical objects in descending or ascending order of one or another characteristic: volume, height, color intensity, etc.;
real objects: games “Freeze”, “Magic Pictures”, “Invent It Yourself”, etc.;
Didactic games: “Loto”, paired pictures, large and medium plastic mosaics, for example: “Geometric Shapes”, puzzles from 6 to 18 parts, sets of cut pictures on cubes, pictures - stencils: “Fold the flower”, “Fold the Christmas tree”, “Build a house with a window (for a cockerel)”, “Wonderful bag”, etc.
Educational games: “Fold the pattern”, “Dots”, “Corners”, “Unicube”, “Dyenesh Blocks”, “Cuisenaire Sticks”, Montessori frames, etc. in accordance with age goals.
For children 4-5 years old
An entertaining mathematics center for the middle group may contain:
Didactic toys and board games that develop children's skills:
- compare objects according to various criteria - size, shape, color, purpose, etc.;
- group objects based on common characteristics (this is dishes, this is shoes, this is furniture; ribbons are the same length and the same color); compose a whole image from 6-8 parts (“Toys”, “Animals”, “Flowers”, etc.): lotto (dishes, clothes, furniture, animals, plants); geometric mosaic;
- make rows of identical objects in descending or ascending order of one or another characteristic: volume, height, color intensity, etc.;
- draw up a simple plan diagram using various substitutions of real objects: games “Freeze”, “Magic Pictures”, “Invent It Yourself”, “Where is Mom?” and etc.;
Didactic games:
-games for understanding symbolism, schematics and conventions (“What does it look like?”, “Complete”);
-models: numerical ladder, a series of quantities, spiral models for the knowledge of time relations;
-games for mastering magnitude, numerical, space-time relationships (“Make the same pattern”);
-games with algorithms, including 3-5 elements (“Growing a Tree”), etc.
Educational games: “Fold the pattern”, “Dots”, “Corners”, “Unicube”, “Dyenesh Blocks”, “Cuisenaire Sticks”, Montessori frames, etc. in accordance with age goals
For children 5-7 years old
In senior preschool age groups, an entertaining mathematics center may contain:
Stencils, rulers and other measuring standards
Didactic games:
- games for dividing a whole object into parts and composing a whole from parts (“Fractions”, “Make a circle”);
- games with numbers, coins;
— games for the development of numerical concepts and the ability to quantify different quantities. (“Compare and match”);
- Games with algorithms).
— Models of numerical and temporal relations (“Number ladder”, “Days of the week”).
— Calendar, calendar model.
Educational games
- games that develop mental processes: chess, checkers, backgammon, lotto-barrels, etc.
— game-aid “Hundred Counting” by N.A. Zaitseva, designer watch, scales;
- Nikitin’s games, Dienesh’s blocks, Cuisenaire’s sticks, Voskobovich’s games, etc. in accordance with age-related tasks, natural and “waste” material.
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
Methods of mathematical development as a science
Definition 1
Methodology of mathematical development is a branch of scientific knowledge that studies the processes of development of the cognitive sphere of children and the formation in them of the foundations of logical thinking and skills in performing elementary mathematical operations.
The methodology of mathematical development is focused on the formation of elementary mathematical concepts in preschoolers. She develops a methodology for their formation and determines the patterns of functioning of different areas of thinking and logic, which affect the overall development of the individual and the mastery of mathematical science.
Mathematical development is important for a child's overall development. Therefore, teaching mathematics occupies the core of the preschool educational program. Mathematical concepts activate the cognitive activity of a preschooler and develop his thinking abilities.
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The methodology of mathematical development, as a science, is aimed at developing elementary mathematical concepts in children. This determines the following tasks of the methodology of mathematical development:
- Scientific confirmation of the level of mathematical development of preschool children at each stage of their development and the requirements for children to master the educational program.
- Development of the content of a preschool educational program in the area of mathematical education and development.
- Determination of optimal means and methods, technologies and forms of teaching preschoolers the basics of mathematics.
- Creating conditions for continuity in mathematical education of preschoolers and primary schoolchildren.
- Preparing teachers for professional activities in the field of mathematical education and development of preschool children.
- Development of recommendations for the mathematical development of a child by parents.
- Development of the main directions of cognitive activity, focused on the child’s mathematical development when engaged in different types of activities (work, sports, etc.).
Finished works on a similar topic
Course work Methodology of mathematical development 430 ₽ Abstract Methodology of mathematical development 270 ₽ Examination Methodology of mathematical development 200 ₽
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Since the methodology of mathematical development is a scientific branch, it has connections with other sciences. It is closely related to developmental psychology, which determines the functioning of a child’s mental processes, sensitive periods of development of specific areas, and helps in developing optimal methods for the formation of elementary mathematical concepts in preschoolers of different age groups. In addition, the methodology of mathematical development is closely related to pedagogy. This connection can be traced in the reliance of this science on didactic methods and principles of teaching children mathematics.
In addition, there is a connection between this scientific field and sociology, anthropology, mathematics, special pedagogy and cultural studies.
The subject of the methodology of mathematical development is teaching mathematics, implemented in certain forms and focused on achieving specific goals and objectives.
The object of research into the methodology of mathematical development is the methods and means of mathematical teaching used in the preschool education system.
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
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.
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.
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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.
