The concept of mathematical development in preschool education. Formation of the foundations of mathematical culture in preschoolers

Note: This article does not provide a summary of the event, but its possible structural components. The duration of the event, the number of classes, and the content of tasks are determined based on the identified difficulties of teachers in the field of mathematical education of preschoolers.

Leading: Does modern man need mathematics? What is it for? Give examples. The one who answers “palm to palm” passes the baton to answer to any other teacher. We recommend using this technique when working with children in order to activate them. Name professions in which mathematics is not needed. ( There are no such people).

Thus, you yourself have proven the relevance of our workshop. For a substantive conversation, we need to establish at what age does a child’s mathematical education begin? Why do you think so? Justify your statement. All possible guesses are heard. ( Summarizing answers from presenters: the prerequisites for mathematical education are observed from the first days of a child’s life, when the mother talks to the child (“you’ll grow up big,” “we’ll wash the left hand, then the right one,” etc.), sings lullabies to the baby, reads nursery rhymes, etc.)

Warm-up: With the introduction of the Federal State Educational Standard, many are wondering in what form to provide mathematical education for preschoolers: in the form of classes or in the form of direct educational activities? What does Order of the Ministry of Education and Science of the Russian Federation dated October 17, 2013 No. 1155 say about this?

Exercise: One of the principles of the standard (clause 1.4.3.) - « assistance and cooperation of children and adults, recognition of the child as a full participant (subject) of educational relations.” According to this principle, analyze the tasks of cognitive activity (mathematics) for their compliance with the Federal State Educational Standard. Indicate in the table with arrows the correspondence (←) or non-compliance (→) of the listed tasks of forming elementary mathematical concepts with the federal state educational standard for preschool education. Justify your choice.

Leading: At an early age, children need repeated examination of different objects for the same characteristic, repeated pronunciation of speech combinations with the naming of this characteristic. Consequently, the teacher must show the same sign every day, each time on new objects in the surrounding world, in new situations. Let's agree that there are thirty-six 5-day working weeks in the academic year. This means that the teacher must have in his arsenal an average of 210 examples of the attribute (quality) of the subject being mastered by children.

Exercise: At an early age, children comprehend such signs of objects in the surrounding world as “big - small”. Give examples of familiarizing young children with quantities from the children’s immediate object environment. ( The mother has large gloves, and the children have small ones; dad has big shoes, and children have small ones; The teacher has a large chair, and the children have small chairs; Children have large plates, and dolls have small plates; The matryoshka is big, and in it the matryoshka is small, etc.). You can activate participants using a relay baton.

Task (same as previous): Give examples of the formation of the concepts “One - many” in young children from the immediate object environment of children

Exercise: Give examples of integrating cognitive and productive activities using the example of mathematics (“one - many”) and drawing. ( Stars in the sky (Fig. 1), fireworks, rain, snowing, lights on the Christmas tree, leaves falling, dandelions in the grass, grains for the birds, etc.). The teacher prepares the main image in advance. Children complete the drawing with a poke or finger, saying together with an adult: “One star, another star, ... many stars.”

Exercise: Give examples of comparing groups of objects from the everyday environment of the 2nd junior group using the technique of superimposition. ( To find out whether there are more bears or cars, you need to put one bear in each car; put one spoon on each plate (put one cup); put one scoop in each bucket, one child sit on each chair, etc.).

Exercise: Give examples of comparing groups of objects from the everyday environment of the 2nd junior group using the application. ( To find out whether there are more dolls or plates, you need to place one plate in front of each doll; We will give each child an apple, etc.). Technique for activating participants: the one who last gave an example wins.

Leading: There are didactic principles for selecting demonstration and handout material based on the physiological and psychological characteristics of each age.

Exercise: On what form (Fig. 2) will we begin to develop the ability to lay out objects in the 2nd junior group? Why?

(On the strip, because this form helps children lay out objects strictly in one line, does not distract children from the important rules of laying out objects from left to right, leaving “windows” between them)

Exercise: What forms of handouts (Fig. 3) will we begin to develop the ability to lay out objects on a strip in the 2nd junior group? Why?

(From the image of objects that have a rounded silhouette, for example, balls, and then from circles, because no matter how you place a round shape, it will lie correctly)

Leading: In accordance with paragraph 2 of part 3 of Article 28 of the Law “On Education in the Russian Federation”, the competence of an educational organization includes the logistics of educational activities and equipment of premises.

Exercise: Name the games, materials and equipment that contribute to the mathematical education of younger preschoolers.

(Signets, stencils, templates; natural and waste materials; printed board games; sets of cut-out pictures, puzzles; various plastic construction sets; mosaics; insert games; multifunctional panels on topics; games to familiarize yourself with color, shape, size, etc. p.)

Leading: Work on mathematics education for preschoolers contains enormous potential for speech development. It is important to take children away from monotonous speech stereotypes, give them many examples of literate speech, and show them a variety of question-answer speech structures. At first these are short two-word questions. Accordingly, the answers will be two words. Gradually, the construction of questions increases, and accordingly, the speech construction of answers also increases.

Exercise: Use the cards (Fig. 4, 5) to formulate questions for children of the 2nd junior group and answers to them in different ways. In order to activate teachers, they can be divided into two teams. Each team asks questions on a card, and their opponents answer. The team that provides the most questions and answers wins.

Leading: Speech development is closely related to cognitive development. The technique “Say it differently” helps to activate children’s speech

Exercise: Where is the circle? (Fig. 6). Say it differently.

(The circle is (located, lies) in the center of the sheet; in the middle of the sheet; under the red triangle; above the yellow triangle; to the right of the blue triangle; to the left of the green triangle; between the red and yellow triangles; between the blue and green triangles)

Exercise: Read the examples: 5+1=6; 6-1=5. Read these examples differently.

(Five plus one equals six. Five plus one equals six. Five increased by one equals six. Six minus one equals five. Six subtracted equals five. Six subtracted by one equals five.)

Leading: In mathematics, every action has an inverse - checking - action. This principle is taken into account when dividing a whole into parts.

Exercise: From which figure (Fig. 7) do we begin to divide the whole into two equal parts? Why?

(We start with a circle, because the circle is divided into two equal parts in one single way, with the reverse (checking) action - to assemble a whole from the parts - only the circle gives one single initial option).

Leading: Mathematical warm-ups are relevant when working with children of senior preschool age.

Exercise: Name tasks to clarify ideas about adjacent numbers

(Name the missing number; Name the number between the numbers; Name the neighbors of the number; Name the previous number; Name the next number; Name the number 1 more; Name the number 1 less, etc.)

Leading: At the end of any lesson, entertaining logic tasks are appropriate.

Exercise: Guess the fairy tale (Fig. 8). Prove it.

(Fairy tale "The Three Little Pigs") Make up your own diagrams based on the famous fairy tales “Three Bears”, “Turnip”, “Teremok”, “The Wolf and the Seven Little Goats”, etc.

Olga Stulnikova
Concept of mathematical development in preschool education

Concept of mathematical development in preschool education

Stulnikova Olga Gennadievna, senior teacher,

SP GBOU Secondary School No. 10 "OTs LIK" kindergarten No. 16,

Samara region, Otradny

Mathematical development of children in preschool educational the institution is designed based on preschool concept education and training, institution programs, goals and objectives child development, diagnostic data, predicted results. concept the ratio is determined pre-mathematics and prelogical components in the content education. The predicted results: development children's intellectual abilities, their logical, creative or critical thinking; formation of ideas about numbers, computational or combinatorial skills, methods object transformations, etc.. d.

The acquisition of knowledge and skills is influenced by developing

training and thanks to the special organization of the educational process are developing all cognitive mental processes associated with sensation, perception, memory, attention, speech, thinking, as well as volitional and emotional processes in general. Developmental the learning effect should be focused on "the zone of the closest development» . Children are offered, along with tasks that they can now complete independently, and tasks that require their guesswork, ingenuity, and observation. Purchased this way way of knowledge, and most importantly - systematic improvement of their quality, plus development of thinking, provide general child development.

PROCESS MATHEMATICAL DEVELOPMENT

Process child's mathematical development is related, first of all, with development

his cognitive sphere ( diverse ways of knowing, educational

activities, etc., as well as with development of mathematical thinking style.

Thanks to mathematical development in preschoolers develop personal qualities: activity, curiosity, perseverance in overcoming difficulties, independence and responsibility. In progress mathematical development there is general intellectual and speech child development(evidential and reasoned speech, vocabulary enrichment).

Purpose mathematical development of a preschooler is an introduction to the basics

mathematical culture and instilling interest in further knowledge

the surrounding world using elements of this culture (Order of the Government of the Russian Federation “On approval Concepts for the development of mathematics education in the Russian Federation", December 2013).

MAIN TASKS MATHEMATICAL DEVELOPMENT:

Formation of skills and abilities in counting, calculations, measurement,

modeling.

Development of logical-mathematical ideas and ideas about

mathematical properties and relationships of objects, specific quantities, numbers, geometric figures, dependencies and patterns.

Development of sensory(subject-effective) ways of knowing

mathematical properties and relationships, namely surveys, comparisons,

grouping, ordering.

Development children have logical ways of knowing mathematical properties and

relations, namely analysis, comparison, generalization, classification, seriation.

GENERAL DIDACTIC PRINCIPLES OF TEACHING PRESCHOOL CHILDREN ELEMENTS OF MATHEMATICS

The principle of educational training.

Education and training - educational training characterized by

concrete mental and practical work of children, which develops in them

organization, discipline, accuracy, responsibility.

Level preschooler development depends on specially organized

"mental education", which is a pedagogical process aimed at developing preschoolers elementary knowledge and skills, methods of mental activity, as well as development children's abilities and their needs for mental activity. The main component of mental education preschooler are ways of mental action. Every mental action is a corresponding mental operation. These operations are different, interconnected aspects of thinking that transform into each other.

Basic thinking operations: analysis, synthesis, comparison, classification, generalization, abstraction. All of these operations cannot manifest themselves in isolation without connection with each other, that is, it is impossible to form any mental operation separately without connection and reliance on other operations. “An indicator of mastering a technique is its conscious transfer to solving new problems.” U preschooler methods of mental action must be laid down precisely at this age; moreover, without the formation of mental operations, the mental education of a child is impossible.

The principle of humanization of the pedagogical process.

This is the principle of a personality-oriented model of education and training.

The main thing in training should be development opportunities to acquire knowledge and

skills and use them in life, individualization of learning, creating conditions for the development of the child as an individual.

The principle of an individual approach.

The principle of an individual approach provides for the organization of training based on a deep knowledge of the child’s individual abilities, creating conditions for active cognitive activity of all children in the group and each child individually.

The principle of scientific teaching and its accessibility.

This principle means the formation in children preschool age

elementary, but essentially scientific, reliable mathematical knowledge.

Ideas about quantity, size and shape, space and time are given to children in such a volume and at such a level of specificity and generality that it is accessible to them, and that this knowledge does not distort the content, taking into account the age of the children, the characteristics of their perception, memory, attention, thinking.

The implementation of the principle of accessibility is also facilitated by the fact that material, which

studied, presented in accordance with rules: from simple to complex; from the known to the unknown; from general to specific.

So way, children's knowledge gradually expands, deepens, better

they are absorbed, but new knowledge should be offered to children in small doses, ensuring repetition and consolidation of it through various exercises using their application in different types of activities.

The principle of accessibility also provides for the selection not too much material

difficult, but not too easy either. When organizing children's education, the teacher must

based on the accessible level of difficulty for children of a certain age.

The principle of awareness and activity.

Conscious assimilation of educational material provides for the activation

mental (cognitive) processes in a child.

Cognitive activity is independence, awareness,

meaningfulness, initiative, creativity in the process of mental activity, the child’s ability to see and independently set cognitive tasks, draw up a plan and choose ways to solve a problem using the most reliable and effective techniques, and achieve results.

The principle of systematicity and consistency.

Logical order of study material, in which knowledge is based on

previously received. This principle is especially important when studying mathematicians, where each new knowledge seems to follow from the old, known. The teacher distributes the program material this way, to ensure its consistent complication, the connection of subsequent material with previous. It is this kind of study that provides lasting and deep knowledge.

The principle of visibility.

This principle is important in teaching children preschool age, since the child’s thinking is predominantly visual figurative character. In the methodology of teaching children mathematics the principle of clarity is closely connected with the child’s activity. Conscious mastery of elements mathematical knowledge is possible only if children have some sensory cognitive experience, through direct perception of the surrounding reality or knowledge of this reality through fine art and technical means.

SUBJECT-SPATIAL ENVIRONMENT

For successful work, a specially organized subject-matter is required.

spatial development environment: a room with both space for children to work at tables and enough space for games, including outdoor games. Availability of a game library, materials for making games and material. Availability of balls, cubes and other physical education equipment.

PRINCIPLES OF ORGANIZATION EDUCATIONAL PROCESS

For organization educational a three-block model was selected for the process,

which collects all the known basic models on which they work

preschool institutions: educational, complex-thematic, subject-specific

spatial - environmental. In this case, the strengths of each individual model are used, and, if possible, their shortcomings are eliminated.

I block. Specially organized training in the form of classes - content

organized by "subjects".

II block. Joint adults and children (affiliate) activity - content

is organized comprehensively – thematically.

III Block. Free independent activity of children - in accordance with

traditional types of children's activities.

Within the first block, training is organized in the form of special

classes based on the program. Learning process preschoolers is built taking into account the age characteristics of children preschool age. Game techniques and means that are attractive to children are predominantly used (the principle is implemented "learning with passion", a combination of voluntary and involuntary, static and dynamic forms in the classroom is ensured that is comfortable for the child’s psychophysiological state.

Within the framework of the second block, educational and research work is organized

children's activities based on standards. The goal is to help students learn to independently acquire knowledge, develop research skills, to form a holistic picture of the world and an understanding of one’s place in it. During research pupils: conduct experiments and practical work; collect information and process data; make projects and give presentations;

Within the third block, children’s independent activities are carried out in classes at activity centers and in free play activities.

Activities are aimed at development cognitive abilities and

children's search actions. In activity centers the room is divided into

several zones, each of which contains materials for classes, games,

conducting experiments and research.

The role is undeniable preschool preparation for school is not only in the formation, development and replenishment of mathematical knowledge, skills and abilities preschooler, but also in the intellectual development of the child as a whole. Mathematics education in the early stages of development- a powerful tool for developing a personality with developed logical thinking, skills of analysis and synthesis, classification and systematization. These skills will become the key to success not only in school mathematics, but also in other subjects of the school cycle, and in the further professional activity of the growing citizen. Preparing the base mathematical knowledge should take an important place in programs preschool education and training.

LITERATURE.

1. N. N. Poddyakov. Contents and methods of mental education preschoolers.

2. N. Yu. Boryakova, A. V. Soboleva, V. V. Tkacheva. Workshop on development mental activity in preschoolers.

3. E. A. Yuzbekova. Steps of creativity.

4. A. V. Beloshistaya. Education mathematics at preschool educational institution.

5. Z. A. Mikhailova. Mathematics from three to seven.

6. T. I. Erofeeva. Preschooler studying mathematics.

7. A. A. Smolentseva. Plot-didactic games with mathematical content.

8. Dagmar Alythauz, Erna Doom. Color, shape, quantity.

9. A. I. Ivanova. Naturally - scientific observations and experiments in kindergarten.

10. A. I. Savenkov. Methodology for conducting educational research in kindergarten.

One of the most important tasks raising a child preschool age - this is the development of his mind, the formation of such thinking skills and abilities that make it easy to learn new things.

For a modern educational system (and the development of cognitive activity is one of the tasks of mental education) . 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.

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Modern approaches to organizing the formation of mathematical concepts of preschoolers in accordance with the requirements of the Federal State Educational Standard for 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 tasksraising a preschool child- this is the development of his mind, the formation of such thinking skills and abilities that make it easy to learn new things.

For a modern educational systemproblem of mental education(and the development of cognitive activity is one of the tasks of mental education)extremely important and relevant. It is so important to learn to think creatively, outside the box, and to independently find the right solution.

It's mathematicssharpens the child’s mind, develops flexibility of thinking, teaches logic, forms memory, attention, imagination, speech.

The Federal State Educational Standard for Education requires the process of mastering elementary mathematical concepts to be completedattractive, unobtrusive, joyful.

In accordance with the Federal State Educational Standard for Preschool Education, the main goals of the mathematical development of preschool children are:

1. Development of logical and mathematical ideas about the mathematical properties and relationships of objects (specific quantities, numbers, geometric figures, dependencies, patterns);
2. Development of sensory, subject-effective ways of knowing mathematical properties and relationships: examination, comparison, grouping, ordering, partitioning);
3. Children's mastery of experimental and research methods of learning mathematical content (experimentation, modeling, transformation);
4. Development in children of logical ways of knowing mathematical properties and relationships (analysis, abstraction, negation, comparison, classification);
5. Children's mastery of mathematical ways of understanding reality: counting, measurement, simple calculations;
6. Development of intellectual and creative manifestations of children: resourcefulness, ingenuity, guesswork, ingenuity, desire to find non-standard solutions;
7. Development of accurate, reasoned and demonstrative speech, enrichment of the child’s vocabulary;
8. Development of children's initiative and activity.

Target guidelines for the formation of elementary mathematical concepts:

Mathematical development of preschoolers– positive changes in the cognitive sphere of the individual that occur as a result of mastering mathematical concepts and related logical operations.

Formation of elementary mathematical conceptsis a purposeful process of transferring and assimilating knowledge, techniques and methods of mental activity provided for by program requirements. Its main goal is not only preparation for successful mastery of mathematics at school, but also the comprehensive development of children.

Mathematics education for preschoolersis a purposeful process of teaching elementary mathematical concepts and ways of understanding mathematical reality in preschool institutions and the family, the purpose of which is to cultivate a culture of thinking and the mathematical development of the child.

How to “awaken” a child’s cognitive interest?

Answers: novelty, unusualness, surprise, inconsistency with previous ideas.

That is, it needs to be donelearning in an entertaining way. With entertaining learning, emotional and mental processes are intensified, forcing you to observe, compare,reason, argue, 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 alla properly organized subject-spatial environment allows every childfind something you like, believe in your strengths and abilities, learn to interact with teachers and peers, understand and evaluate feelings and actions, and justify your conclusions.

Teachers are helped to use an integrated approach in all types of activities by the presence of entertaining material in each kindergarten group, 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.(photo) 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.

Thus, puzzles are useful for consolidating ideas about geometric shapes and their transformation. Riddles, tasks - jokes are appropriate during learning to solve arithmetic problems, operations with numbers, and when forming ideas about time.Children are very active in the perception of tasks - jokes, puzzles, logical exercises. The child is interested in the final goal: folding, finding the right shape, transforming - which captivates him.

Experience of preschool education

In the 2015-2016 academic year, our preschool educational institution continues to work on the formation of the cognitive interests of preschoolers through educational mathematical games and the creation of a developing subject-spatial environment for the formation of mathematical concepts in accordance with the Federal State Educational Standard for Preschool Education.

Particular attention is paidmedium saturation –The educational space must be equipped with teaching and educational means (including technical ones). So, in kindergarten we werevariousmodern educational games: constructors – Polikarpov constructor, plot constructor “Transport”, “City”, “Castle”, TIKO constructor “Balls”, “Geometry”, mathematical tablet, arithmetic counting, logical pyramids “Colored Columns”,"Learning to count" with numbers, logical dominoes, labyrinths,wooden building constructors "Tomik",counting material “Geometric figures”,educational games by Voskobovich.

Construction

A tool for developing children’s creative and logical abilities are practical exercises with the “TIKO” constructor for planar and volumetric modeling.In our preschool institution, teachers, enthusiastically working with the TIKO construction set, discovered its great possibilities for the mathematical development of children, starting from a young age. When playing with a construction set, a child remembers the names and appearance of planar figures (triangles - equilateral, acute-angled, rectangular), squares, rectangles, rhombuses, trapezoids, etc. Children learn to model objects in the surrounding world and gain social experience. Children develop spatial thinking; they can easily change the color, shape, size of the structure if necessary. Skills and abilities acquired inpreschool period will serve as the foundation for acquiring knowledge and developing abilities at school age. And the most important among these skills is the skill of logical thinking, the ability to “act in the mind.”

Wooden construction sets are a convenient teaching material. Multi-colored details help the child not only learn the names of colors and geometric flat and three-dimensional figures, but also the concepts of “more-smaller”, “higher-lower”, “wider-narrower”.

For young children, working with a logic pyramid gives them the opportunity to manipulate components and compare them by size using the comparison method. When folding a pyramid, the child not only sees the details, but also feels them with his hands.

Lego

At the end of 2015, we purchased a LEGO Wedo 9580 first robot construction set to work with children of senior preschool age. It is designed for assembling and programming simple LEGO models that connect to a computer. The WeDo designer is based on a proprietary base LegoSystem - bricks with spikes, which modern children, as a rule, become familiar with very early. Sensors and a USB switch have been added to them for connecting to a computer and bringing the created structures to life. Therefore, laptops were purchased for the groups and the appropriate programs were installed. From the construction set you can create different models, either according to Lego’s instructions or by inventing them yourself. In the form of a game, you can get acquainted with various mechanisms and even learn how to design.

We plan to introduce you to this designer in more detail at a seminar in the fall.

Educational games by Voskobovich

Voskobovich's educational games are of particular interest to teachers and children. The use of Voskobovich's games in the pedagogical process allows us to rebuild educational activities into cognitive gaming activities.

There are many educational games by Voskobovich. Among the most common ones in our kindergarten are: “Two-color and four-color squares”, Igrovisor, “Transparent square”, “Geocont”, “Miracle - crosses”, “Miracle flower”, “Cord-entertainer”, “Logo molds", "Carpet "Larchik",Ship "Splash - splash" and others. During the game, the child masters numbers; recognizes and remembers color, shape; trains fine motor skills of the hands; improves thinking, attention, memory, imagination. Games are based on three basic principles - interest, knowledge, creativity. These are not just games - these are fairy tales, intrigues, adventures, funny characters that encourage the child to think and be creative.

To develop children’s mathematical understanding, teachers use another modern form of working with children - iris folding.

Iris folding develops the ability to compare and find differences between two or more objects, restores from memory what was previously seen (diagram, drawing, model), and also allows children to create unusual visual images to remember the desired operation.

Iris folding allows children to develop the ability to think logically: find similarities and differences, highlight the essential, establish cause and effect relationships. All mental activity is activated.

Interaction with parents

An equally important condition for the formation of elementary mathematical concepts in children is the active participation of parents in the educational process.

In kindergarten we use the following forms of work with families: consultations, design of moving folders, holding mathematical entertainment, fairs, master classes on the topics: “Logical - mathematical game - as a means of teaching and educating preschool children”; “Fairy-tale labyrinths of games by V.V. Voskobovich."

In groups, parents made mini-books together with their children.fairy tales on mathematical subjects: "Numbers", "Circle and Square" and others.

Teachers Brochures with tasks on Dienesh logic blocks and Cuisenaire rods have been developed; booklets “Mathematical games with a child at home”, “Mathematics for the development of your child” and others for reinforcing mathematical concepts with children at home.

Project activities

Of course, one of the modern and effective forms of supporting children's initiative is project activity, in which the participation of parents is always relevant. Using project activities to develop children’s mathematical understanding, teachers thereby activate the child’s cognitive and creative development, and also pay attention to the formation of the child’s personal qualities. The knowledge acquired by children during the implementation of the project becomes the property of their personal experience. Such projects in mathematics as “Fun Mathematics” in secondary group No. 9, “Entertaining Mathematics” in secondary group No. 14, “ABC of Numbers” in secondary group No. 1 and others made it possible to put the personal developmental nature of interaction between adults and children into practice, taking into account their needs, opportunities, desires in the educational process.

Personnel

The quality of teaching activities in the use of modern tools for the formation of mathematical concepts mainly depends on qualified teachers. In this regard, 2 teachers of our kindergarten were trained at KOIRO on gaming technology for the intellectual and creative development of children 3-7 years old “Fairytale labyrinths of the game V.V. Voskobovich." Training at KOIRO under the advanced training program “Updating the content of educational and educational activities in the integration of technical orientation”; 2 teachers studied under the program “Development of technical creativity in an educational organization under the conditions of the Federal State Educational Standard”, and 1 teacher studied under the program “Tutor activity in additional vocational education”.

Teachers actively participate in seminars and workshops held in preschool educational institutions on the topics: “Organization and implementation of work on the formation of cognitive interests of preschool children through educational mathematical games”, “Features of organizing mathematical games in preschool age”; in municipal seminars on the topics: “Development of technical creativity of students within the framework of network interaction of institutions of general and additional education”, “Dissemination of innovative models for the development of the technosphere of activities of institutions of additional education within the framework of the development of a network model of interaction with preschool educational institutions”; regional seminars “Game is the most important sphere of self-expression”, international seminars “Preschool education: the experience of Italy”, where teachers exchanged experience on TIKO design, as well as in webinars organized by the Federal State Autonomous Institution “FIRO” and the magazine “Obruch”, such as “How to prepare a preschooler to solving arithmetic problems”, “Geometric propaedeutics in a modern preschool educational institution” and others.

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The basis for the formation of mathematical concepts in preschoolers is the theory of L.S. Vygotsky on the leading role of learning in the development of a child, as well as provisions on the leading role of activity in human development and the theory of the gradual formation of mental actions, which were developed and studied by such psychologists and teachers as P.Ya. Galperin, A.N. Leontyev, N.F. Talyzina.
Modern concepts of mathematical development of children of early and preschool age include the following: early mathematical development, early introduction of children into the world of the logic of mathematics, mastery of ways of knowing, creation of prerequisites in preschool age for the formation of theoretical thinking in the primary grades of school, developmental focus of the proposed game activities, combination practical and play activities.

Preschool education is the first and most important link in the general education system. At preschool age, the foundation of ideas and concepts is laid, which ensures the successful mental development of the child. A number of psychological studies have established that the rate of mental development of preschool children is very high compared to later age periods (L.A. Wenger, A.V. Zaporozhets, V.S. Mukhina). Any defects in upbringing made during preschool childhood are actually difficult to overcome at an older age and have a negative impact on the entire subsequent development of the child.

When developing issues of mental education of preschool children, Russian scientists proceed from the basic principles of Russian psychology, which considers the process of human mental development as a result of the appropriation of social experience embodied in the products of physical and spiritual labor. At the same time, the child’s mental development appears as the assimilation of the simplest forms of this experience: mastery of objective actions, elementary knowledge and skills as the most universal means of consolidating and transmitting universal human experience.

Thus, the mental, including mental development of a child acts as a concrete historical and social process, all the main stages of which are determined by the peculiarities of the transfer of social experience. This position of Russian psychology sets the direction for the study of the problem of interaction of biological and social factors in the process of individual development.

As is known from the works of L.S. Vygotsky, in the spontaneous experience of preschoolers, pre-conceptual formations first arise - complexes, pseudo-concepts, and only then are full-fledged concepts formed in the process of schooling. In the works of P.Ya. Galperina, N.F. Talyzina provides data indicating that in conditions of organized learning the very process of concept formation has significantly different patterns than in spontaneous learning. Used in the work of P.Ya. Galperin’s method of gradual formation of mental actions allows the formation of full-fledged concepts in older preschool age, and their scope is limited only by the presence of the necessary preliminary knowledge and skills.

The most significant changes in a child’s mental development are the result of the assimilation not of any individual knowledge and skills, but, firstly, of a certain system of knowledge, reflecting the essential connections and dependencies of a particular area of ​​reality, and, secondly, of general forms of mental activity underlying this knowledge system. In this regard, the problem of developing basic principles for the selection and systematization of preschool knowledge is acute.

The system of preschool knowledge, of course, should be fundamentally different from the system of school knowledge and be more elementary. So, P.G. Samorukova notes that the systematization of knowledge is possible at varying degrees of depth and generality: both at the empirical level, when the main content of knowledge is presented in the form of ideas (images of previously perceived objects and phenomena), and at a higher theoretical level, when knowledge has the form of concepts, and connections are characterized as deep patterns. She further points out the great possibilities for expanding and deepening the system in the process of teaching children.

The mathematical development of preschool children is carried out both as a result of the child’s acquisition of knowledge in everyday life (primarily as a result of communication with an adult), and through targeted training in classes to develop basic mathematical knowledge. It is the elementary mathematical knowledge and skills of children that should be considered as the main means of mathematical development.

G.S. Kostyuk proved that in the process of learning, children develop the ability to more accurately and completely perceive the world around them, identify the signs of objects and phenomena, reveal their connections, notice properties, interpret what is observed; mental actions, methods of mental activity are formed, internal conditions for transition are created to new forms of memory, thinking and imagination.

Psychological experimental research and pedagogical experience indicate that thanks to the systematic teaching of mathematics to preschoolers, they develop sensory, perceptual, mental, verbal, mnemonic and other components of general and special abilities. In the studies of V.V. Davydov, L.V. Zankov and others It has been proven that the inclinations of an individual are transformed into specific abilities through learning. The difference in the levels of development of children, as experience shows, is expressed mainly in the pace and success of their acquisition of knowledge.

However, despite the importance of learning in the mental development of the individual, the latter cannot be reduced to teaching. Development is not limited to those personality changes that are a direct consequence of learning (G.S. Kostyuk). It is characterized by those “mental turns” that occur in a child’s head when he learns the art of speaking, reading, counting, and assimilates the social experience transmitted to him by adults ( I.I.Sechenov).

As studies show (A.V. Zaporozhets, D.B. El-konin, V.V. Davydov, etc.), development goes beyond what is learned at one time or another during training. During the learning process and under the influence of learning, a holistic, progressive change in personality, its views, feelings, abilities. Thanks to training, opportunities expand

Further learning of new, more complex material creates new learning reserves.

There is a reciprocal relationship between learning and development. Learning actively contributes to the development of the child, but it also depends significantly on his level of development. In this process, much depends on how much the training is aimed at development.

Learning can develop a child in different ways depending on its content and methods. It is the content and its structure that guarantee the child’s mathematical development.

In methodology, the question “what to teach?” has always been and remains one of the main questions. Whether to give children the basics of scientific knowledge, whether to equip them only with a set of specific skills with which they would have some practical orientation, is an important problem in kindergarten didactics.

Selecting educational material for study, taking into account its significance and in accordance with the capabilities of children, is a very difficult task. The content of training, i.e., the program for the formation of elements of mathematics, has been worked out over many years. In the last 50 years, this process has been carried out on the basis of experimental research ( A. M. Leushina, V. V. Danshgova, T. V. Taruntaeva, R. L. Berezina, G. A. Korneeva, N. I. Nepomnyashchaya, etc.).

An analysis of various (variable) mathematics programs in kindergarten allows us to conclude that the main content of their content is a fairly diverse range of ideas and concepts: quantity, number, set, subset, magnitude, measure, shape of an object and geometric figures; ideas and concepts about space (direction, distance, relative position of objects in space) and time (units of time, some of its features).

At the same time, it is important to emphasize that each mathematical concept is formed gradually, step by step, linearly.

but to the concentric principle. Different mathematical concepts are closely related to each other. Thus, when working with children of the fourth year of life, the main attention is paid to the formation of knowledge about sets. Children learn to compare “contrasting” and “adjacent” sets (many And one; more (less) for one). Later, in groups of the fifth, sixth, and seventh years of life, knowledge about the set deepens: children compare the set of elements by the number of components, divide the set into subsets, establishing dependencies between the whole and its parts, etc.

Based on ideas about set, children form ideas and concepts about numbers and quantities, etc. By mastering the concepts of numbers, the child learns to abstract quantitative relationships from all other features of the elements of the set (size, color, shape). This requires the child to be able to identify individual properties of objects, compare, generalize, and draw conclusions.

The formation of concepts about size is closely related to the development of numerical concepts in children. The formation of estimates of size and knowledge about number has a positive effect on the formation of knowledge about the shape of objects (a square has 4 sides, all sides are equal, and a rectangle has only opposite sides, etc.).

At preschool age, basic mathematical concepts are introduced descriptively. Thus, when becoming familiar with numbers, children practice counting specific objects, real and drawn (counting girls and boys, bunnies and foxes, circles and squares), and at the same time become familiar with the simplest geometric figures, without any definitions and even descriptions of these concepts. In the same way, children learn the concepts: more, less; one two Three; first, second, last etc.

Each concept is introduced visually, through contemplation of specific objects or practical operation of them.

During the period of preschool childhood, as noted by N.N. Poddyakov, A.A. Stolyar and others, there is a fairly extensive area of ​​“pre-conceptual”, “everyday” concepts. The content of “everyday” concepts is very vague, diffuse, it covers a variety of forms that precede real concepts. Nevertheless, “everyday concepts” are important for the child’s mathematical development.

The specific feature of “everyday concepts” is that they are built on the basis of a generalization of the characteristics of objects that are significant from the point of view of any human needs.

catcher, performing various types of practical activities.

Interesting data in this regard were obtained by Z.M. Boguslavskaya (1955), who studied the peculiarities of the formation of generalizations in children of various preschool ages in the process of didactic play. In younger preschoolers, cognitive activity was subordinated to the solution of one or another specific game task and served it. Children learned only the information given to them that was necessary to achieve a certain practical effect in the game. The assimilation of knowledge was of a utilitarian nature. The acquired knowledge was immediately used to complete a given grouping of pictures.

In older preschoolers, cognitive activity in the process of didactic games went beyond the scope of just the direct service of practical tasks, losing its purely empirical character, and appeared in the form of extensive meaningful activity with characteristic specific methods of implementation. As a result, the ideas and concepts formed in children quite fully and adequately reflected a certain circle of phenomena.

Another direction in teaching preschoolers mathematics is to familiarize them with a number of mathematical dependencies and relationships. For example, children understand some relationships between objective sets (equal numbers - unequal numbers), the order relation in the natural series, time relations; dependencies between the properties of geometric figures, between magnitude ,measure and measurement result, etc.

Particular attention should be paid to the requirements for the formation of certain mathematical actions in children: applying, applying, recalculating, counting, measuring, etc. It is the mastery of actions that has the greatest impact on development.

The methodology distinguishes two groups of mathematical actions:

basic: counting, measurement, calculations;

additional: propaedeutic, designed for didactic purposes; practical comparison, imposition, application (A.M. Leushina); equalization and acquisition; comparison (V.V. Davydov, N.I. Nepomnyashchaya).

As we see, the content of “pre-mathematics” preparation in kindergarten has its own characteristics. They are explained by: the specifics of mathematical concepts;

traditions in teaching preschoolers; the requirements of a modern school for the mathematical development of children (A.A. Stolyar).

The educational material is programmed so that, on the basis of already acquired simpler knowledge and methods of activity, children develop new ones, which in turn will be a prerequisite for the development of complex knowledge and skills, etc.

In the process of learning, along with the formation of practical actions in children, cognitive (mental) actions are also formed, which the child cannot master without the help of adults. It is mental actions that play the leading role, since the object of knowledge in mathematics is hidden quantitative relationships, algorithms, and relationships.

The entire process of forming the elements of mathematics is directly related to the assimilation of special terminology. The word makes the concept meaningful, leads to generalizations, to abstraction.

A special place in the implementation of educational content (program objectives) is occupied by the planning of educational work in the classroom and outside of it in the form of a long-term and calendar plan. Significant assistance in the work of the teacher can be provided by indicative long-term plans; plans-notes of lessons in mathematics. The teacher should use these plans and notes as indicative ones, and their content should be constantly compared with the level of mathematical development of children in this group.

The lesson plan for mathematics includes the following structural components: topic of the lesson; program objectives (goals); activation of children's vocabulary; didactic material; course of the lesson (methodological techniques, their use in different parts of the lesson), summary.

The teacher conducts classes in accordance with the plan. Each lesson, regardless of its duration and form, is an organizationally, logically and psychologically complete whole. The organizational integrity and completeness of the lesson lies in the fact that it begins and ends at a clearly designated time.

Logical integrity lies in the content of the lesson, in logical transitions from one part of the lesson to another.

Psychological integrity is characterized by achieving a goal, a feeling of satisfaction, and a desire to continue working further.

Self-test exercises

mathematics intellectual

In the process of teaching children... their..., in particular mathematical, development takes place.

mathematical cognitive

mathematical tool

base

mathematics

state development

In the preschool period, children master a fairly large volume of... concepts, acquire practical and... skills.

The content of education is considered in the methodology... of children's development primarily as... leading to the accumulation of knowledge, skills and to those internal changes that constitute... the basis of development. In choosing the specific content of education... the educator should focus on A program... and education of children, reflecting... the standard of knowledge of preschoolers and their actual level in this group.