3.4. Forms of work on pre-mathematical development of children

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:

1. 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.
2. Development of the content of a preschool educational program in the area of ​​mathematical education and development.
3. Determination of optimal means and methods, technologies and forms of teaching preschoolers the basics of mathematics.
4. Creating conditions for continuity in mathematical education of preschoolers and primary schoolchildren.
5. Preparing teachers for professional activities in the field of mathematical education and development of preschool children.
6. Development of recommendations for the mathematical development of a child by parents.
7. 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 420 ₽ Abstract Methodology of mathematical development 250 ₽ Examination Methodology of mathematical development 240 ₽

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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.

3.4. Forms of work on pre-mathematical development of children

3..4. Forms of work on pre-mathematical development of preschool children.

1. Forms of work on pre-mathematical development of preschool children.
2. Types and types of occupations, their features, structure
3. Forms of work outside of class

1. Forms of work on pre-mathematical development of preschool children.

In didactics, “form” (device, structure, system of organization, internal structure) is considered as a way of constructing educational activities. Organizational forms of education must reliably ensure the implementation of the objectives of the educational process, the ultimate goal of which is to promote the comprehensive and, first of all, intellectual development of children.

Variety of training forms

is determined by the number of students, the place and time of classes, the methods of children’s activities, as well as the methods of managing this activity by the teacher.

Based on the characteristics of the organization of training, determined by the number of students, there are individual, collective and group (differentiated) forms of training.

.

Individual training

– lies in the fact that the child receives new ideas, performs different tasks, and has the opportunity to receive direct help from an adult.

Collective learning

– involves the work of a teacher with a group of children. There is mutual assistance and mutual learning. The disadvantage is that individual differences are not sufficiently taken into account.

Differentiated learning

in pedagogical practice it is called “group”, “individual-group”, or “collective-group” learning.
Differentiated training is carried out according to the following criteria:

• by ability or inability to learn;
• by interest;
• by volume of material and degree of complexity;
• by the degree of independence and pace of progress in learning.

In the 40s of the 20th century, Leushina A.M. first proposed classes as a form of teaching mathematics in kindergarten

. Metlina L.S. in the 80s she developed notes for mathematics lessons for all age groups of preschool children. Until the 90s, it was believed that the main form of teaching mathematics to preschoolers was the classroom. To teach children mathematics, classes were held once a week.

However, it must be taken into account that those mathematical concepts that are formed in preschool age are of an applied nature for children. Children need mathematical concepts for daily orientation in the world around them. Therefore, they should be formed in a variety of activities (communication, play, cognitive-practical, artistic, labor).

1. Types and types of occupations, their features, structure.

At the present stage of development of the preschool education system, state documents (Code on Education of the Republic of Belarus, Standards of Preschool Education, Model Curriculum for Preschool Education) determine the status of the game, classes

as
the main form
of a specially organized educational process.

The number of classes in
the educational field
“
Elementary mathematical concepts
” and the time allotted for their implementation are regulated by the Standard Preschool Education Curriculum.

• first junior group – once every 2 weeks (10 min.)
• second junior group – 1 time per week (15 min.)
• middle group – 1 time per week (20 min.)
• senior group 5-6 years old – once a week (25 min.)
• senior group 6-7 years old – once a week (30 min.)

Classes in the educational area “Elementary Mathematical Concepts” are held mid-week in the morning in combination with classes that do not require a high mental load (physical education, music classes or visual arts classes).

During the holidays, these classes are not conducted; the concepts and skills acquired by children are consolidated in everyday life: in games, play exercises, on walks, etc.

In all age groups, classes are conducted frontally, i.e. simultaneously with all children. Only in the first junior group is it recommended to conduct classes in subgroups (6-8 people), including all children, in order to gradually teach them to study together.

Requirements for conducting classes
in the educational field “Elementary mathematical concepts”

• are built taking into account general didactic principles: scientific character, systematicity and consistency, accessibility, clarity, connection with life, individual approach to children, etc.;
• implement all the contents of the educational field “Elementary mathematical concepts”;
• the implementation of educational, educational and developmental tasks in the classroom occurs in a comprehensive manner;

• the content of each specific lesson, the formulation of its tasks, is carried out on the basis of the content of the educational field “Elementary mathematical concepts”, taking into account the characteristics of children and their level of development;

• each lesson occupies its own, strictly defined place in the system of lessons for the study of a specific program task in the educational field “Elementary mathematical concepts”;
• The program objectives of the lesson determine its structure. In the structure of the lesson, separate parts are distinguished: from one to four or five, depending on the number, volume, nature of the tasks and the age of the children. All parts of the lesson are independent, varied and related to one another;
• in one lesson one new problem is solved, the rest are for repetition and consolidation;
• new material is given in the first part of the lesson, as it is mastered, it moves to other parts; subsequent parts of the lesson are usually conducted in the form of a didactic game, in which children’s ideas and skills are consolidated and applied in new conditions;
• widespread use of didactic games and exercises with handouts;
• organization of physical education (after the first or second part).

Since the leading activity in preschool age is play, play methods and techniques of interaction between teacher and student are predominant in the lesson, i.e. classes can be of a playful nature or presented as play-based didactic complexes.

In accordance with the didactic objectives, the type of lesson is determined:

1. Training type

   (learning new ideas).
   Goal:
   setting cognitive tasks for children, presenting, expanding and clarifying children’s ideas about quantity, size, geometric figures and the shape of objects, space and time;

1. Fastening type

   (consolidation and systematization of children’s accumulated experience).
   Goal:
   understanding the perceived ideas and forming primary generalizations.

1. Combined (mixed) type

   classes.
   Goal:
   learning new content and repetition, consolidation and systematization

Types of activities

in the educational field "Elementary mathematical concepts"

Combined lesson

can be integrated - by selecting objects of knowledge from different educational fields or components of one educational field; can be playful or non-playful - according to the predominance of methods of educational interaction, according to the nature of the interaction between students and the teacher, and between students.

Its structure:

1. Organizing time.
2. Implementation of the learning task. Mastering new material.
3. Consolidating newly acquired ideas in children’s independent activities.
4. Movable pause.
5. Implementation of educational content from other components of the educational field.
6. Bottom line.

Complex lesson

involves a combination of classes in the educational area “Elementary mathematical concepts” with classes in other educational areas. In this case, in the lesson on the formation of elementary mathematical concepts (it is the first part of a complex lesson), learning tasks are implemented, children master new educational content, and in classes in other educational areas - the use, consolidation, expansion, clarification, deepening of the newly mastered educational content takes place. content. The structure of a complex lesson is flexible and variable. It should be remembered that the greatest pedagogical effect can be achieved by combining classes in the educational area “Elementary mathematical concepts” with classes in the educational area “Art”, “Child and Society”, “Child and Nature”.

Game complexes with mathematical content

(as a game version of a combined lesson):

1. didactic in nature.

   A didactic game is selected to solve each program problem, and children play it either in a sequence determined by the plot of the lesson, or in a random sequence determined by the “magic arrow”, spinning top, child’s choice, etc.;

2) educational and developmental in nature.

Complex diagram:

1. a game or gaming exercise to develop attention, perception, sensation, and activate memory;
2. a game or game task for the development of reproductive thinking, the formation of certain mathematical concepts (training);
3. a game or play exercise that helps develop independent reproductive thinking and consolidate acquired ideas in independent practical activities;
4. an outdoor game or exercise aimed at increasing motor activity, consolidating mathematical concepts, and developing cognitive processes;
5. a game or play exercise for the development of divergent thinking (creative, productive), imagination, logical thinking, the formation in children of the ability to use their ideas in new conditions, the development of elements of logical thinking;
6. a game or play exercise for relaxation and imagination development.

Lesson using educational visual aids
(
with individual notebooks).

Structure:

1. Didactic game or game exercise.
2. Work with educational visual aids (formation of new ideas, expansion and deepening of the mastered material).
3. An outdoor game, or a relay game, or a physical education break.
4. Working with educational visual aids (completing graphic tasks, actions with cut material).
5. Didactic game or game exercise.

Classes using computers.

In some preschool institutions there are computer and gaming complexes (one room is a computer class, the second is a room for mental and physical relaxation).

Advantage

this form: the possibility of an individual approach to learning, the computer is an interesting toy for the child - children develop attention and interest in learning, etc.

If you violate the rules for using a computer, your work can have a negative effect.

A child 4-6 years old can be at the computer for no more than 10 minutes, 1-2 times a week (otherwise the child’s posture, vision, and psyche will be impaired). Therefore, with the help of a computer it is necessary to solve only those software problems that are solved less effectively in other forms.

1. Forms of work outside of class

(unregulated activity)

Individual work

with the child allows for pedagogical correction. The forms of this work are exercises, work with individual material (notebooks, didactic material), etc.

Game with mathematical content.

It is planned at least 2-3 times a week individually, in a group (or part of it).
All types of games can be planned. Didactic games.
There are many collections with d/i on mathematics by such authors as Sai, Udaltsova, Mironova, Starzhinskaya, Novikova.

Plot-didactic games

(this term was proposed by A. Smolentsova, “Plot-didactic games with mathematical content,” 1985)

Educational games

. Proposed by Z.A. Mikhailova, B.P. Nikitin (“Steps of creativity or educational games”).

On the day of the lesson in the educational area “Elementary mathematical concepts”, a game with mathematical content is not planned.

Examination.

It is planned at least 2 times a week individually, in a group (or part of it) when developing the ability to group objects; establishing a one-to-one correspondence in a practical way; bills by touch; dividing a whole into parts; comparing quantities and ordering; examination of geometric figures and determination of the shape of an object; orientation from oneself, in the surrounding environment.

Experiences, experiments.

Planned as needed, but no more than once a week individually, in a group (or part of it) while developing an understanding of the independence of number from qualitative and spatial characteristics; understanding the dependence of the result of ordinal counting on the direction of counting and the independence of the result of quantitative counting on the direction of counting; skills of transfiguration and transformation.

Observations.

Planned daily individually, in a group while forming ideas about the parts of the day and their sequence; ideas about the seasons and their sequence.

Story, conversation.

Planned as necessary individually, in a group when forming temporary ideas; ideas about geometric figures and the shape of objects; ideas about size, about ordering by size.

Entertainment with mathematical content.

It is planned no more than 1 time per quarter by group. It can be planned as a competition, theatrical or circus performance, folklore festival, travel, etc. It can replace a complex lesson or game complex. On this day, a lesson in the educational area “Elementary Mathematical Concepts” is not planned.

Viewing works of fine art.

It is planned as needed, but at least once a month by the group (or part of it) when forming quantitative, spatial and temporal ideas; ideas about size and space. Artistic illustrations, photographs, reproductions of paintings, paintings (still lifes, everyday life, animalistic, mythological genres) are used.

Reading literary works with mathematical content.

It is planned as needed, but at least once a month by the group (or part of it). When reading, mathematical characteristics, mathematical actions (their necessity, sequence, correctness, adequacy of the situation, etc.) that are performed by the heroes of the works are highlighted.

Independent cognitive activity

:

• games with didactic material,
• role-playing games,
• situations of work and everyday activities.
• working with a book (coloring, cutting out, comparing by size): books like coloring books, books like math notebooks - “Geometry for Kids”, etc.,
• performing entertaining exercises (puzzles, games with sticks)

Signs of independent cognitive activity are:

children's interest in it; manifestation of creative initiative; independence in choosing a game and how to implement the plan.

In independent cognitive activity, children’s ideas about numbers, sizes, geometric shapes, time, and space are clarified, deepened and expanded.

Each of the listed forms is planned in different types of activities with a certain frequency and has specifics in the way children are organized, depending on the age group and the content of the problem being solved.

LITERATURE

1. Zhitko, I.V. Formation of elementary mathematical concepts in children from 4 to 5 years old: educational method. A manual for preschool teachers. education. Minsk: Ecoperspective, 2016. – 200 p.
2. Formation of elementary mathematical concepts in preschoolers / ed. A.A.Stolyar. – M., Education 1988
3. Shcherbakova, E.I. Methods of teaching mathematics in kindergarten: a textbook for preschool students. department and faculty avg. ped. textbook establishments. M., Ed. , 1998 – 272s

6

Principles of mathematical learning and development of preschoolers

The method of mathematical development of a child is based on the following principles of mathematical teaching and development of preschool children:

• The principle of visualization of learning . Training will be effective when using visual teaching aids that meet the age and individual characteristics of children’s cognitive development and perception of information.
• The principle of clarity in organizing classes . Mathematics classes should have a clear structure. The plot of the game and the sequence of actions must have a clear structure in accordance with which the development of the preschooler will take place.
• The principle of relying on developmental psychology . Mathematical learning tasks should be developed in accordance with the age-related characteristics of the child’s development, his needs and capabilities of mathematical perception.
• The principle of learning variability . It is necessary to use different methods and means of forming the child’s mathematical concepts and ideas. This can be gaming activities, logical tasks, exercises of a creative nature, but with a logical focus, etc.
• The principle of multitasking learning. In the course of studying mathematics, one should focus not only on the formation of elementary mathematical concepts in the child, but also on the development of spatial perception,
• The principle of game learning . It is important to implement the mathematical development of preschoolers in a playful form, since play is the leading activity of preschoolers. The game motivates to learn. It contains an element of surprise, captivates and develops interest in mathematics.
• The principle of orientation towards the development of cognitive activity . The child must develop not just mathematical knowledge, but also a desire to independently study mathematical science and form logical judgments and conclusions.
• The principle of creating a developing space . In preschool educational institutions, a subject-development environment is created in which fundamental cognitive processes are formed.
• The principle of development of perception of quantitative and qualitative characteristics of objects . If a child masters the differences between objects based on quantitative and qualitative characteristics, this will lay the foundation for the formation of mathematical concepts.

Numbers, quantity, counting

Children get acquainted with the numbers 0...20, learn to write printed numbers in notebooks. They learn to count within 20, using ordinal numbers (second, fifth). Learn to compare adjacent numbers. Get acquainted with such concepts as less, more, the same amount. Convert equalities into inequalities and vice versa. Get acquainted with the mathematical signs + - = < >. They learn to compare numbers, figures, and the number of objects up to 20. They learn to count by 2s and 3s within 21. They study the composition of the number of the first ten. They come up with problems based on drawings and solve them based on clarity.

Orientation in space

1) Preschoolers learn to determine the position of objects in space - right, left, below, above.

2) Determine the direction of movement - from right to left, from top to bottom, back, forward, in the opposite direction, in the same direction;

3) Get acquainted with the concepts - close and far, low and high, closer, further, nearby.

4) Determine their position in space - outside or inside. Among the objects: on, in, under, over, in front of, between, to, from, through.

5) Orient themselves on a piece of paper, in a column and line of cells.

Formation of elementary ideas about time

In kindergarten, children can actively develop basic knowledge about time. Children should know all four parts of the day, name what time of day they go to bed, and when it is time to get up and go to kindergarten. In this process, a large role is given to the daily routine in the group.

The teacher calls the time of day and says what the children should do now: should they have breakfast, go for a walk, or will they have a nap?

Conversations should be regularly held with children in which parts of the day are mentioned, it is explained why this or that action should be carried out at a certain time of the day (sleep - at night, wash and have breakfast - in the morning, walk, have lunch - during the day, in the evening - play with the family, engage in various activities).