Pomoraeva in a pozina famp preparatory group. Irina Alexandrovna Pomoraeva, Vera Arnoldovna Pozina Formation of elementary mathematical representations. The system of work in the kindergarten preparatory group for school. Approximate distribution

Library of the program "FROM BIRTH TO SCHOOL"
under the general editorship of N. E. Veraksa, T. S. Komarova, M. A. Vasilyeva

Pomoraeva Irina Aleksandrovna - Methodist of the Educational and Methodological Center for professional education Moscow, teacher of methods of mathematical development College of Education No. 15, Honored Teacher of Russia

Pozina Vera Arnoldovna - Methodist, teacher of methods of mathematical development of Pedagogical College No. 4, excellent student of public education

Foreword

This manual is addressed to educators working on an exemplary basic general education program preschool education"FROM BIRTH TO SCHOOL", edited by N. E. Veraksa, T. S. Komarova, M. A. Vasilyeva, to organize work in mathematics in a group preparatory to school.
The manual deals with the organization of work on the development of elementary mathematical concepts in children aged 6–7, taking into account the patterns of formation and development of their cognitive activity and age-related capabilities.
The book presents an approximate planning of work in mathematics for the year. The structure of the classes allows you to combine and successfully solve problems from different sections of the program. The proposed system of work, which includes a set of tasks and exercises, various methods and techniques of working with children (visual-practical, playful, verbal), helps preschoolers to master the methods and techniques of cognition, to apply the acquired knowledge in independent activities. This creates the prerequisites for the formation of a correct worldview, allows you to provide a general developmental orientation of learning, connection with the mental, speech development And various types activities.
Game situations with elements of competition, reading excerpts fiction motivate children and direct their mental activity to find ways to solve problems. The method of work does not imply direct teaching, which can negatively affect the comprehension and independent performance of mathematical tasks by the child, but implies the creation of situations of community, cooperation, provides all children with an equal start, which will allow them to successfully study at school.
The proposed system of work allows teachers to take into account the specifics of the activity educational institution and his priorities. The volume of material gives educators the opportunity to realize their creative potential and take into account the characteristics of a particular group of children.
Knowledge gained in the course of organized educational activities on the formation of elementary mathematical concepts must be consolidated in Everyday life. To this end Special attention should be given to the enrichment of role-playing games with mathematical content and the creation of a subject-developing environment, which stimulates the development of independent cognitive activity of each child.
In working with children, preschool and can be used at home workbook"Mathematics for preschoolers: Preparatory group for school" (M.: Mozaika-Sintez, 2012).
The manual includes: a list of didactic games, additional material, recommendations on the organization of the developing environment. They reflect the modern positions of psychologists, teachers and methodologists, allowing to expand the content of work with children of the seventh year of life.
Further in the manual, for convenience of presentation, instead of the term "directly educational activities"we will often use the term "occupation" familiar to educators. However, the term “lesson” should not mislead teachers: it does not imply lesson-type lessons. The task of the teacher is not to turn mathematics into a lesson, but to use the forms of work with children that correspond to their age, indicated in the exemplary basic general educational program of preschool education “FROM BIRTH TO SCHOOL”, edited by N. E. Veraksa, T. S. Komarova, M A. Vasilyeva.

Program content

Quantity

The development of general ideas about the set: the ability to form sets on given grounds, to see the constituent parts of sets in which objects differ in certain characteristics.
Exercises in combining, adding to sets, removing a part from a set or its individual parts.
Consolidation of the ability to establish relationships between the individual parts of the set, as well as the whole set and each of its parts on the basis of counting, pairing objects or connecting objects with arrows.
Improving the skills of quantitative and ordinal counting within 10. Acquaintance with counting within 20.
Introduction to second ten numbers.
Strengthening the understanding of the relationship between the numbers of the natural series (7 is more than 6 by 1, and 6 is less than 7 by 1), the ability to increase and decrease each number by 1 (within 10).
Consolidation of the ability to name numbers in forward and reverse order (oral counting), the subsequent and previous number to the one named or indicated by a number, to determine the missing number.
Introduction to numbers from 0 to 10.
Formation of the ability to decompose a number into two smaller ones and make up a larger one from two smaller ones (within 10, on a visual basis).
Acquaintance with coins of denominations of 1, 5, 10 kopecks, 1, 2, 5, 10 rubles (distinguishing, setting and exchanging coins).
Formation of the ability on a visual basis to compose and solve simple arithmetic problems for addition (less is added to more) and subtraction (subtracted less than the remainder); when solving problems, use the action signs: plus (+), minus (-) and the ratio sign equals (=).

Value

Consolidation of the ability to count according to a given measure, when not one, but several objects or part of an object is taken as a unit of account.
Consolidation of the ability to divide an object into 2–8 or more equal parts by bending an object (paper, fabric, etc.), as well as using a conditional measure; correctly designate parts of the whole (half, one part of two (one second), two parts of four (two fourths), etc.); establish the ratio of the whole and the part, the size of the parts; find parts of the whole and the whole from known parts.
Formation of initial measuring skills. Strengthening the ability to measure the length, width, height of objects (segments of straight lines) using a conditional measure (paper in a cage).
Strengthening the ability of children to measure the volume of liquid and bulk substances using a conditional measure.
Formation of ideas about the weight of objects and how to measure it. Strengthening the ability to compare the weight of objects (heavier - lighter) by weighing them on the palms. Introduction to scales.
The development of ideas that the result of measurement (length, weight, volume of objects) depends on the value of the conditional measure.

Form

Clarification of knowledge about geometric shapes, their elements (vertices, angles, sides) and some of their properties.
Formation of ideas about a polygon (for example, a triangle and a quadrangle), about a straight line, a straight line segment.
Consolidation of the ability to recognize figures regardless of their spatial position, depict, arrange on a plane, arrange by size, classify, group by color, shape, size.
Strengthening the ability to model geometric shapes; make one polygon from several triangles, one large rectangle from several small squares; from parts of a circle - a circle, from four segments - a quadrangle, from two short segments - one long one, etc .; design figures according to verbal description and enumeration of their characteristic properties; make thematic compositions from figures according to your own design.
Consolidation of the ability to analyze the shape of objects as a whole and their individual parts; recreate objects of complex shape from separate parts according to contour samples, according to description, presentation.

Orientation in space

Formation of the ability to navigate on a limited surface (a sheet of paper, a blackboard, a page of a notebook, books, etc.); arrange objects and their images in the indicated direction, reflect in speech their spatial arrangement (above, below, above, below, left, right, left, right, in the upper left (lower right) corner, in front of, behind, between, next to, etc.) .).
Acquaintance with the plan, scheme, route, map. Development of the ability to model spatial relationships between objects in the form of a drawing, plan, diagram.
Formation of the ability to "read" the simplest graphic information, indicating the spatial relationships of objects and the direction of their movement in space: from left to right, from right to left, from bottom to top, from top to bottom; independently move in space, focusing on the conventions (signs and symbols).

Orientation in time

Formation elementary representations about time: its fluidity, periodicity, irreversibility, the sequence of days of the week, months, seasons.
Strengthening the ability to use words-concepts in speech: first, then, before, after, earlier, later, at the same time.
Development of a "sense of time", the ability to save time, regulate one's activities in accordance with time; distinguish between the duration of individual time intervals (1 minute, 10 minutes, 1 hour).
Formation of the ability to determine the time by the clock with an accuracy of 1 hour.

Approximate distribution of program material for the year

I quarter

September

Lesson 1
Exercise in dividing the set into parts and combining its parts; to improve the ability to establish the relationship between the set and its part.
ordinal counting skills within 10, the ability to answer the questions “How much?”, “Which one?”, “In which place?”.
ideas about the relative position of objects in space (in a row): left, right, before, after, between, in front of, behind, next to.
the ability to consistently identify and name the days of the week.

Lesson 2
Exercise in dividing the set into parts and combining the parts into a whole group; to improve the ability to establish the relationship between the set and its part.
Learn to count forward and backward within 5.
the ability to divide a circle and a square into 2 and 4 equal parts, compare and name them.
the ability to distinguish and name familiar geometric shapes.

Lesson 3
Introduce the numbers 1 and 2 and learn to denote numbers by numbers.
Exercise in the skills of quantitative counting forward and backward within 10.
To consolidate the ability to navigate on a sheet of paper, determine the sides and corners of the sheet.
Improve your understanding of triangles and quadrilaterals.

Lesson 4
Get to know number 3.
Learn to name the previous and subsequent number for each number of the natural series within 10.
To improve the ability to compare 10 objects (by length, width, height), arrange them in ascending and descending order, indicate the results of the comparison with the appropriate words.
Exercise in the ability to move in a given direction.

Lesson 5
Get to know number 4.
To consolidate ideas about the quantitative composition of the number 5 from units.
To consolidate the ability to compare two objects in size (length, width) using a conditional measure equal to one of the compared objects.
Develop the ability to indicate in speech your location relative to another person.

Lesson 6
Introduce the quantitative composition of the number 6 from units.
Get to know number 5.
Strengthen the ability to sequentially name the days of the week.
Continue to form the ability to see in the surrounding objects the shape of familiar geometric shapes.

October

Lesson 1
Continue to learn how to make the number 6 from units.
Get to know the number 6.
Clarify the methods of dividing a circle into 2–4 and 8 equal parts, learn to understand the ratio of the whole and the parts, name and show them (half, one second, one fourth, one eighth, etc.).
Develop the ability to move in space in accordance with the conventions.

Lesson 2
Introduce the composition of the numbers 7 and 8 from units.
Get to know the number 7.
Clarify the methods of dividing a square into 2, 4 and 8 equal parts; learn to understand the relationship between the whole and parts, name and show them (half, one second, one fourth, one eighth, etc.).
Reinforce the concept of triangles and quadrilaterals.

Lesson 3
Continue to learn to make the numbers 7 and 8 from units.
Get to know the number 8.
Fix the consecutive naming of the days of the week.
Develop the ability to compose a thematic composition according to the model.

Lesson 4
with the composition of the number 9 from units.
with number 9.
Improve the ability to call numbers in direct and reverse order from any number.
Develop an eye.
To consolidate the ability to navigate on a sheet of paper, identify and name its sides and angles.

Lesson 5
Improve the ability to make the number 9 from units.
Develop an understanding of the independence of the result of the count from its direction.
Give an idea of the weight of objects and compare them by weighing on the palms; learn to label comparison results with words heavy, light, heavier, lighter.
Develop the ability to group geometric shapes by color and shape.

Lesson 6
with the composition of the number 10 from units.
with number 0.
Keep learning to find the previous number to the named, the subsequent number to the named.
Clarify ideas about the weight of objects and the relativity of weight when comparing them.
To form ideas about temporary relationships and learn to designate them with words: first, then, before, after, earlier, later e.

Lesson 7
Continue to learn how to make the number 10 from units.
Learn about the number 10.
Strengthen counting skills in forward and reverse order within 10.
Give an idea of a polygon using the example of a triangle and a quadrilateral.
To consolidate the ability to navigate in space with the help of symbols on the plan, to determine the direction of movement of objects, to reflect their spatial position in speech.

Lesson 8
Learn to make the number 3 from two smaller numbers and decompose it into two smaller numbers.
Continue reading numbers from 1 to 9.
Clarify ideas about a polygon, develop the ability to find its sides, angles and vertices.
To consolidate ideas about the seasons and months of autumn.

November

Lesson 1
Learn to make the number 4 from two smaller numbers and decompose it into two smaller numbers.
Strengthen ordinal counting skills within 10.
Develop the ability to analyze the shape of objects and their individual parts.
Improve ideas about the weight of objects and the ability to determine regardless of their appearance objects weigh the same or not.
To consolidate the ability to consistently identify and name the days of the week.

Lesson 2
Learn to make the number 5 from two smaller numbers and decompose it into two smaller numbers.
Introduce the formation of numbers of the second ten within 15.
To improve the ability to build a serial series by the weight of objects.
To consolidate the ability to navigate on a sheet of paper and reflect in speech the spatial arrangement of objects with the words: top, bottom, left, right.

Lesson 3
Learn to compose the number 6 from two smaller numbers and decompose it into two smaller numbers.
Continue to introduce the formation of the second ten numbers within 15.
To introduce the measurement of quantities using a conditional measure.
Develop the ability to navigate in space with the help of symbols and diagrams.

Lesson 4
Learn to compose the number 7 from two smaller numbers and decompose it into two smaller numbers.
Continue to introduce the formation of the second ten numbers within 20.
Improve the ability to measure the length of objects using a conditional measure.

Lesson 5
Learn to compose the number 8 from two smaller numbers and decompose it into two smaller numbers.
Strengthen counting skills in forward and reverse order within 15.
Exercise in measuring the length of objects using a conditional measure.
Develop the ability to navigate on a sheet of paper in a cage.

Lesson 6
Learn to compose the number 9 from two smaller numbers and decompose it into two smaller numbers.
Improve counting skills within 20.
Exercise in measuring the height of objects using a conditional measure.
Continue to develop the ability to navigate on a sheet of paper in a cage.

Lesson 7
Learn to make the number 10 from two smaller numbers and decompose it into two smaller numbers.
To consolidate the ability to determine the previous, subsequent and missing number to the one named or indicated by a number within 10.
Exercise in the ability to measure the length and width of objects using a conditional measure.

Lesson 8
To consolidate ideas about the quantitative and ordinal value of a number within 10.
To consolidate the ability to make the number 10 from units.
skills of measuring the size of objects; to acquaint with the dependence of the measurement results on the value of the conditional measure.
Develop the ability to move in space in a given direction.
the ability to model objects using familiar geometric shapes.

II quarter

December

Lesson 1
Introduce coins in denominations of 1, 2, 5, 10 rubles and 1, 5, 10 kopecks.
Continue to develop orientation skills on a sheet of paper in a cage.
Clarify ideas about polygons and how to classify them by type and size.

Lesson 2
Continue to acquaint with coins in denominations of 1, 5, 10 rubles.
Learn to count according to a given measure, when not one, but several items are taken as a unit of account.
To form ideas about time, to introduce the hourglass.

Lesson 3
Continue to acquaint with coins in denominations of 1, 5, 10 rubles, their set and exchange.
Develop a sense of time, learn to regulate their activities in accordance with the time interval.
Continue to learn to count according to a given measure within 20.
To develop the ability to recreate complex-shaped objects from separate parts according to contour samples.

Lesson 4
Continue to clarify ideas about coins in denominations of 1, 2, 5, 10 rubles, their set and exchange.
Learn to measure the volume of bulk solids using a conditional measure.
Introduce the clock, learn to set the time on the clock layout.
Continue to learn to determine the shape of objects and their parts.

Lesson 5
Continue to learn how to measure the volume of bulk solids using a conditional measure.
Continue to introduce the clock, learn to set the time on the clock layout.
Develop the ability to navigate on a sheet of paper in a cage.
To consolidate ideas about the polygon; to acquaint with its special cases: a pentagon and a hexagon.

Lesson 6
To introduce the rules for measuring liquid substances using a conditional measure.
To consolidate the understanding of the relationship between the numbers of the natural series, the ability to increase (decrease) the number by 1 within 10.
Develop a sense of time; learn to distinguish the duration of time intervals within 5 minutes.
Develop the ability to model geometric shapes.

Lesson 7
To improve the ability to decompose a number into two smaller ones and make a larger number from two smaller ones within 10.
To consolidate ideas about the sequence of times and months of the year.
To develop the ability to design geometric shapes according to a verbal description and listing of characteristic properties.
Exercise in the ability to combine parts into a whole set, to compare the whole and part of the set.

Lesson 8
To consolidate the ability to decompose a number into two smaller numbers and make a larger number from two smaller ones within 10.
Develop the ability to name the previous, subsequent and missing number to the named one.
Reinforce ideas about the order of the days of the week.
Develop the ability to modify geometric shapes.

January

Lesson 1
Learn to write arithmetic addition problems.
To consolidate the ability to see geometric shapes in surrounding objects.

Lesson 2
Improve the ability to navigate on a sheet of paper in a cage.
Develop attention, memory, logical thinking.

Lesson 3
the ability to measure the volume of liquid substances using a conditional measure.
the ability to navigate on a sheet of paper in a cage.
attention, memory, logical thinking.

Lesson 4
learn to compose and solve arithmetic problems for addition and subtraction.
to acquaint with coins of denomination of 1, 2, 5, 10 rubles, their set and exchange.
Improve the ability to navigate on a sheet of paper in a cage.
Develop attention, logical thinking.

Lesson 5
Continue to learn how to compose and solve arithmetic problems for addition and subtraction.
Continue to introduce the clock and set the time on the clock layout.
Improve the ability to navigate on a sheet of paper in a cage.

Lesson 6
Continue to learn how to compose and solve arithmetic problems for addition and subtraction.
Improve understanding of the sequence of numbers within 20.
Develop the ability to divide the whole into 8 equal parts and compare the whole and its parts.
Develop the ability to determine the location of objects relative to each other.

Lesson 7
Develop ideas about geometric shapes and the ability to draw them on a sheet of paper.
To consolidate the ability to name the previous, subsequent and missing number, indicated by a number.

Lesson 8
Learn how to write and solve addition and subtraction problems on your own.
Improve ideas about the parts of the day and their sequence.
Exercise in the correct use of words in speech: first, then, before, after.
To consolidate the ability to see in the surrounding objects the forms of familiar geometric shapes.
Develop attention, imagination.

February

Lesson 1
Continue to learn how to compose and solve arithmetic problems for addition.
Exercise in counting objects according to the model.
Learn to measure the length of straight line segments in cells.
Develop attention, memory, logical thinking.

Lesson 2
Continue to learn how to compose and solve arithmetic problems for addition and subtraction.
To consolidate the ability to name the winter months.
Improve the ability to make a number from units.
Exercise in drawing up thematic compositions from geometric shapes.

Lesson 3
Continue to learn how to compose and solve arithmetic problems for addition and subtraction.
To consolidate the ability to consistently name the days of the week and use the words correctly in speech: earlier, later, first, then.
Continue to form the ability to determine a segment of a straight line and measure its length by cells.
Develop ideas about the size of objects.

Lesson 4
Continue to learn how to compose and solve arithmetic problems for addition and subtraction.
Expand your understanding of the weight of objects.
To consolidate the ability to modify geometric shapes.
Improve the ability to navigate in a notebook in a cage, perform tasks according to verbal instructions.

Lesson 5
Continue to learn how to compose and solve arithmetic problems for addition and subtraction.
Improve the skills of measuring the height of objects using a conditional measure.

IN senior group kindergarten children of 5-6 years old are engaged, in which at this time logical thinking, fantasy, and curiosity are actively developing. For successful education at school, the pre-school educational institution provides for the so-called pre-mathematical classes - the development of simple mathematics. Classes are aimed at developing the cognitive activity of children and the systematic preparation of preschoolers for school, which are implemented through.

Mathematics in kindergarten is designed to improve intellectual abilities and form:

develop creative thinking, ingenuity and ingenuity;
to teach the logic of actions, reasoning and thoughts;
encourage flexible thinking.

IMPORTANT MATERIALS FOR MANAGERS OF DOE ON THIS TOPIC:

(read in the magazine "Handbook of the senior preschool teacher")

FEMP in the senior group according to the Federal State Educational Standard

The number of lessons on the study of a particular topic in FEMP depends on the success of the children in mastering the material. In the summer, classes in simple mathematics are not held, but knowledge is consolidated in everyday activities: on walks, during outdoor or board games, in creative activities.

Program tasks that are solved during the implementation of the FEMP

In addition to the educational tasks of mastering elementary mathematics, work is carried out in the classroom to educate personal qualities, develop thinking and speech.

Educators often make serious mistakes in the implementation of FEMP, including the inaccuracy of asking questions, the violation of the sequence of presentation of the material, its monotony or the unattractiveness of the visual information chosen to demonstrate the topic. To avoid mistakes, teachers should carefully plan the sequence and essence of the selected material, monitor the diversity and correspondence of information to the level of development of children.

The teacher in the FEMP classes should help create an entertaining atmosphere that stimulates the creative and playful activity of children, their imagination and ingenuity. The use of integrated classes is encouraged - a combination of educational activities with creative, motor, game, artistic and communicative. The study of numbers and figures is combined with drawing, the development of counting with outdoor games or reading poetry. If an integrated lesson is built on the principle of an exciting game with a developing plot, preschoolers will have a happy denouement and a situation of success.

To determine the effectiveness of the work on FEMP, teachers, the head of the preschool educational institution, a psychologist or a methodologist analyze classes to obtain elementary mathematical knowledge. The tasks set and the methods of work chosen for their implementation, the types of activities in the classroom, the differentiation of tasks, the use of an individual approach and methods of integration with other areas of activity are evaluated.

Methods for mastering elementary mathematics in preschool education

Method	Characteristic
Practical	The main working method that uses didactic games and exercises, game tasks of all levels, so that the pupils not only listen to the information and perceive it, but also take an active part in their resolution. The effectiveness of mastering the material on FEMP depends on the implementation of practical tasks.
Game	It is included in the category of the main ones, since play activities for preschoolers are a key way of understanding the world and the main activity. In a playful way, children learn elementary mathematics faster and better. Didactic games in the context of FEMP are divided into: travel games - reveal the ordinary through the unusual; puzzle games - require deciphering concepts; suggestion games - develop imagination and logical thinking; games-conversations - are built on the dialogue of children with the teacher. Game complexes allow you to develop attention, stimulate cognition, and after situations of success, children are more friendly towards their comrades, they feel a desire to learn. They help the children of the senior group of the kindergarten to gradually enter the world of science, introduce them to numbers, and broaden their horizons.
Verbal	Relies on dialogue with children and is not the key. The teacher asks the children direct (How? How much?) or search questions (Why? Why did you decide that? What can be done?).

Various means are used to form elementary mathematical representations:

equipment for independent work and children's games;
educational and cognitive literature on pre-mathematical preparation;
sets of visual demonstration and didactic material;
collections of exercises and didactic games for the development of space-time representations;
teaching aids for teachers with exemplary notes of classes.

The above tools perform a number of functions:

present mathematical concepts in an accessible form for preschoolers, helping them to master the methods of action necessary to obtain elementary mathematical knowledge;
implement the principle of visibility, intensify the educational process, rationalize it;
expand the capabilities of teachers, allowing them to more effectively organize educational and cognitive activities and solve developmental and educational problems;
help children gain experience in perceiving relationships and properties, expand and enrich knowledge.

The structure of the lesson on FEMP in the senior group

Form of traditional school lesson lost its effectiveness in mastering the simplest mathematical knowledge and skills, giving way to observation, didactic games, practical activities in all its forms. The structure of the lesson is dictated by its program content and depends on the age of the children and the tasks set. FEMP classes according to the methodology Pomoraeva in the senior group involves the use of several activities and three to five stages in the course of the implementation of the main program objective. The parts of the lesson are equivalent and closely interconnected with each other.

Following a strict structure of classes allows you to:

combine and implement various program tasks;
to activate not only individual children, but also frontally the whole group;
use a set of didactic tools and methods;
to master and consolidate new knowledge, to repeat the past.

Approximate structure of FEMP in the senior group

First and second stages	New material is studied at the beginning of the lesson, when the children are as concentrated as possible and ready to receive new knowledge, and as it is mastered, it moves to other stages to consolidate in further lessons. At this stage, the teacher motivates children to set the task of the lesson, seeks to interest them in the topic of the lesson, and then demonstrates an example of the application of a mathematical skill.
motor pause	Physical education sessions are held after learning new material and help to restore the working capacity of preschoolers, level out fatigue. The signal for an active pause is distraction, weakening of the attention of children, motor restlessness. Short-term physical exercises in elementary mathematics classes are not only exercises for the fingers or eye gymnastics, but also exercises for the limbs and torso (jumps, bends, squats). You can increase the effectiveness of motor pauses if you accompany them with music, songs or a poem. To consolidate, during the warm-up, you can combine the simplest physical and mathematical exercises: raise your right or left hand at the command of the teacher; squat as many times as the teacher shows; jump one time less or more than indicated in the picture. Didactic games can be used as physical education.
Third stage	Independent performance of tasks to consolidate the acquired knowledge and establish a connection between new material and what has already been studied.
Fourth stage	The end of the lesson is the time of didactic games that help to apply the acquired knowledge in practice and consolidate what has been learned.

In the older group, FEMP practical exercises are actively used in the form of didactic exercises, which, through the use of handouts and demonstration materials, allow children to obtain mathematical representations. The teacher at such lessons explains, shows, indicates, demonstrates a sample, evaluates the work. Since at the senior preschool age educational activity is motivated by educational or practical tasks, the structure of classes includes exciting exercises to determine the length or width, compare shapes and colors, clarify spatio-temporal relationships. To stimulate practical, object-sensory, cognitive and educational activities, various game elements can be included in the exercises.

More often than others, preschool educational institutions use classes in the form of didactic exercises and games that combine gaming and practical methods. Games and exercises in such classes are its separate parts, which are consistently combined.

Visibility in FEMP in the senior group according to the Federal State Educational Standard

The key condition for efficiency FEMP classes in the senior group is the use of visualization methods, which, when properly selected, contribute to the assimilation of knowledge, increasing the effectiveness of training. Preschoolers think concretely, because it is easier for them to deal with things, and only after with words, because in the older group the principle of visibility plays a big role in teaching mathematics.

Principles of use visual material:

Visualization is effective only in combination with a verbal explanation, highlighting the essence. The teacher directs the observation of children, helping them to master the shape of objects or counting. Using visual material, preschoolers do not deepen their knowledge of balls, apples or hedgehogs, but learn to abstract, highlighting the shape, color or number of objects.
The framework for using visualization is important: after mastering the method of action, cards, pictures or figures will distract the child, interfere with his independence. After showing the sample, the children must complete the task, following the verbal instructions.

Educators should carefully consider the place and method of using visualization, the nature of the material, so that preschoolers learn to independently use it to find an answer or control the correct execution. Demonstration and didactic tools are separated very conditionally, since the same materials can be used in practical tasks, and to explain the new.

There are two types of visual material in the FEMP classes:

Small dispenser. As visual material, small handouts are used, which each child receives, and demonstration tools that are printed on a magnetic board or flannelgraph. All of them must be understandable and attractive in appearance in order to arouse interest in children, provoke the interaction of logical and sensual thinking. It is important for educators to remember the availability of spare material so that demonstration and distribution tools are in the classroom in sufficient quantities for each pupil.
Demonstrative and didactic. Counting sticks, cards, small toys, three-dimensional numbers, labyrinths, cards, geometric lotto, dominoes, entertaining cubes, geometric shapes for counting, tables, cards with images of objects or seasons, board games act as didactic material in kindergarten in FEMP classes. and much more. To study the quantities (thickness, width, height and length), objects of different sizes are used; spatial relationships help to master sets of didactic aids; a calendar or a clock layout is the best way to introduce time, graduated test tubes or jars demonstrate the difference in depth and volume.

It is important that the size handout allowed each pupil to freely place it on the table without disturbing others. Demo material is shown frontally, therefore it should be much larger and larger. To provide one senior group for FEMP sessions, 25 sets of handouts and one or two sets of demonstration material will be required.

In working with older preschoolers, teachers use visual aids that model mathematical concepts and develop deductive thinking. A flannelograph or other canvas measuring 60x30 cm is used with special strips for laying out cards and images. Musical instruments and any objects that make sounds that will help in establishing the power by ear (spoons, tambourines, drums, watches and even drops of water) can be used. Information Technology- presentations and tables - serve as one of the forms of visibility, which contributes to the development of mental abilities in preschoolers.

An alternative to the visual is entertaining mathematical material, which is distinguished by its variety and systematic use. The tasks involve increasing complexity of exercises and games, so that in the process of their implementation conditions for independent searches are created and direct teaching methods are used. Entertaining material comprehensively affects the development of mathematical abilities of pupils, positively influencing purposefulness, logical thinking, spatial imagination, the ability to find ways of action to solve cognitive and practical tasks. For these purposes, the following types of entertaining material can be involved in kindergarten:

Puzzle toys - Rubik's "Pyramid", "Snake", "Unicube" and others, which consist of folding or rotating three-dimensional geometric shapes.
Geometric constructors - "Pythagoras", "Tangram", "Magic Circle", where from flat geometric figures, according to a plan or a model, you need to add a plot image.
Logic exercises, tasks for finding a missing figure or finding signs of similarity / differences, recognizing parts in a whole or restoring a whole from parts.
Labyrinths are exercises that require mental and visual analysis to find the shortest path from point to point.

Game complexes in the assimilation of elementary mathematical knowledge

Methodology Pomoraeva and Pozina on conducting proved that game complexes that increase efficiency and contribute to the development of knowledge in full by children, developing thinking, logic and memory, are of fundamental importance in obtaining the simplest mathematical knowledge. Classes in the traditional form provoke rapid fatigue of children and the development of physical inactivity, because active forms learning and gaming activities are an effective alternative to the usual lessons. Game complexes contribute to the development of attention and ingenuity (through puzzles and joke tasks), logical thinking(through reasoning over the course of solving the task), independence and memory.

Examples of practical application of gaming activities:

Mastering the concepts of equality and inequality - didactic games "Fix the mistake", "What number is missing?", "Confusion", "Name the neighbors", with the help of which children learn to perform operations with numbers within 10 and explain their actions.
The development of memory and thinking - the game "Which toy is missing?" and "Make a number."
The study of the days of the week and their names is an observation during which children designate multi-colored circles every day to make it easier for them to understand the sequence; games “Live Week” and “Days of the Week” are held to consolidate knowledge.
Getting to know the calendar and months - games "All year round", "Twelve months" and others.
Orientation skills in space - didactic exercises to determine your position in space, the position of objects.
Acquaintance with geometric shapes- a game to search for squares, triangles or circles in the surrounding objects.

Game situations in educational process should be appropriate to the time and place and not be random. Having mastered the simplest mathematical representations, pupils will be able to transfer knowledge to non-standard situations. A variety of classes in FEMP are classes-holidays or lessons-entertainment, which are based on the entertainment component, but also perform educational tasks. They stimulate the intellectual activity of children, and the competitive nature motivates them to work effectively.

Didactic manuals on FEMP in the senior group

To form preschoolers' skills in elementary mathematics, teachers of preschool institutions use proven didactic aids, among which the logical sticks and blocks of X. Kuzener and 3. Gyenesh proved their effectiveness, as well as lesson plans for FEMP in the senior group authorship I.A. Pomoraeva and V.A. Pozina.

Logic blocks and sticks - a set of flat and voluminous geometric bodies, where properties (thickness, size, color and shape) can be distinguished for each block. To work with 3. Gyenesh blocks, children receive task cards, which symbolically indicate the sequence in which you need to make a chain of geometric bodies, and the pattern that needs to be taken into account. With the help of X. Kusener's sticks, which are called "colored numbers", you can simulate numbers by composing the treasured numbers from cubes and parallelepipeds, thus getting acquainted with their composition.

The methodological developments of V.A. Pozina and I.A. Pomoraeva are designed to help educators not only in developing the topics and tasks of classes, but also in achieving their goals. Plans-summaries of classes, taking into account the principles of consistency and consistency, combine and solve all the tasks assigned to teachers by the program. At the game lessons according to the method of Pomoraeva and Pozina, didactic material is used, physical education sessions are held, the study of elementary mathematics takes place in a fun way without boring memorization, since fairy-tale characters, wizards and kind animals give tasks to kids.

V.A. Pomoraeva and I.A. Pozina: plans-summaries of classes on FEMP in the senior group

Methodology lessons Pozina and Pomoraeva is based on gaming and visual-practical methods of work and does not involve direct training. On the contrary, the developed principles make it possible to stimulate the mental activity of children, and educators to show their creative potential.

Since in the older group, acquaintance with elementary mathematics takes place once a week and involves the study of the simplest numbers and the performance of elementary calculations, familiarity with geometric shapes, the study of ways to visually display figures, numbers and mathematical elements, the approximate distribution of program material is as follows:

FEMP classes in the senior group according to the methodology Pomoraeva and Pozina are most effective if elementary mathematical knowledge is consolidated at home, for which educators conduct explanatory conversations with parents, give methodical material, speak at parent meetings, since the development of mathematical representations takes place not only in the conditions of the corresponding lesson in the preschool educational institution, but also in everyday situations and at home. It has been proven that the interaction of parents and teachers helps children to master the simplest mathematics faster and better.

You can learn more about the formation of elementary mathematical knowledge in preschool educational institutions in the articles:
1. FEMP classes in the middle group
2. Techniques for the development of spatial representations in preschool children
3. Summary of the lesson on the formation of elementary mathematical representations for children of middle preschool age "Saving the Snowman"

Foreword

This manual is addressed to educators working under the "Program of Education and Training in Kindergarten" edited by M. A. Vasilyeva, V. V. Gerbova, T. S. Komarova, to organize mathematics classes in the senior group.
The manual deals with the organization of work on the development of elementary mathematical concepts in children aged 5–6, taking into account the patterns of formation and development of their cognitive activity and age-related capabilities.
The book presents an approximate planning of classes in mathematics for the year. The structure of the classes allows you to combine and successfully solve problems from different sections of the program. The proposed system of classes, which includes a set of tasks and exercises, various methods and techniques of working with children (visual-practical, playful), helps preschoolers to master the methods and techniques of cognition, to apply the acquired knowledge in independent activities. This creates the prerequisites for the formation of a correct understanding of the world, allows for a general developmental orientation of education, a connection with mental, speech development and various activities.
Game situations with elements of competitions used in the classroom motivate children's activities and direct their mental activity to find ways to solve the tasks. The methodology of conducting classes does not imply direct teaching, which can negatively affect the comprehension and independent performance of mathematical tasks by the child, but implies the creation of situations of community, collaboration. Activation of mental activity develops the active position of the child and forms the skills of learning activities.
The volume of classes allows educators to realize their creative potential and take into account the characteristics of a particular group of children.
The knowledge gained in the classes on the formation of elementary mathematical representations must be consolidated in everyday life. To this end, special attention should be paid to role-playing games, in which conditions are created for the application of mathematical knowledge and methods of action.
When working with children both in a preschool institution and at home, you can use the workbook for the “Program of Education and Training in Kindergarten” “Mathematics for Preschoolers: Senior Group” (M .: MOZAIKA-SINTEZ, 2009).
The manual includes additional material compiled in accordance with the recommendations of modern psychologists, teachers and methodologists, which allows expanding the content of work with children of the sixth year of life.

Approximate distribution of program material for the year