Formation of mathematical representations according to GEF. We form elementary mathematical ideas from preschoolers of different ages. The history of the appearance of a FMP in preschool education
The game is a huge bright window through which spiritual world The child is poured by a lifeful flow of representations, concepts about the world around.
The game is a spark, lighting the light of inquisitiveness and curiosity.
(In A. Sukhomlinsky)
Purpose: Increased knowledge of teachers for the formation of elementary mathematical representations
Tasks:
1. To introduce teachers with non-traditional technologies for the application of games in the work on the FMP.
2. Arm teachers by practical skills of mathematical games.
3. Submit a complex of didactic games to form elementary mathematical ideas in children preschool age.
The relevance of the problem: in mathematics there are tremendous opportunities for the development of children's thinking in the process of their training from the very early age.
Dear Colleagues!
Development of mental abilities of preschool children is one of the actual problems of modernity. A preschooler with developed intelligence fasterly remembers the material, more confident in its abilities, is better prepared for school. The main form of the organization is a game. The game contributes to the mental development of the preschooler.
The development of elementary mathematical ideas is an extremely important part of the intellectual and personal development of the preschooler. In accordance with the Gos, the pre-school educational institution is the first educational stage and the kindergarten performs an important function.
Speaking about the mental development of the preschooler, I wanted to show the role of the game as a means of forming a cognitive interest in mathematics in preschool children.
Games with mathematical content are developing logical thinking, cognitive interests, creative abilities, speake independence, initiative, perseverance in achieving the goal, overcoming difficulties.
The game is not only a pleasure and joy for the child, which in itself is very important, with its help you can develop attention, memory, thinking, the imagination of the kid. Playing, the child can acquire, new knowledge, skills, skills, develop abilities, sometimes not guessing about it. The most important properties of the game include the fact that in the game the children act as they act in the most extreme situations, at the limit of the forces of overcoming difficulties. Moreover, such a high level of activity is achieved by them, almost always voluntarily, without coercion.
You can highlight the following features of the game for preschoolers:
1.Iigra is the most affordable and leading activity of children of preschool age.
2. The game is also an effective means of forming the identity of the preschooler, its moral and volitional qualities.
3. All psychological neoplasms originate in the game.
4. The signal contributes to the formation of all parties to the child's personality, leads to significant changes in his psyche.
5. The game is an important means of mental education of a child, where mental activity is associated with the work of all mental processes.
At all the steps of preschool childhood, a big role is given to the game method during educational activities.
Didactic games are included directly into the maintenance of educational activities as one of the means of implementing the software tasks. The site of the didactic game in the structure of OD on the formation of elementary mathematical representations is determined by the age of children, the purpose, the purpose, the content of OD. It can be used as a learning job, exercise aimed at performing a specific task of forming representations.
In the formation of the children of mathematical ideas, entertaining in the form and content of various didactic gaming exercises are widely used.
Didactic games are divided into:
Games with objects
Pictures
Verbal games
Didactic formation games mathematical representations Conditionally divided into the following groups:
1. Games with numbers and numbers
2. Time Travel Games
3. Games for orientation in space
4. Games with geometric shapes
5. Games for logical thinking
We present to your attention the game made by your own hands, on the formation of elementary mathematical ideas.
Simulator "Beads"
Purpose:assistant in solving the simplest examples and tasks for addition and subtraction
Tasks:
- develop the ability to solve the simplest examples and tasks for addition and subtraction;
- bring up care, preferabity;
- develop a shallow motility of hands.
Material: rope, beads (no more than 10), color gamut for your taste.
- Children may first calculate all beads on the simulator.
- Then solve the simplest tasks:
1) "Five apples hung on the tree." (Five apples are counted). Two apples fell. (Take two apples). How many apples are left on the tree? (recalculate beads)
2) Three birds were sitting on the tree, three more birds flew to them. (How many birds left to sit on the tree)
- Children solve the simplest tasks as for addition and subtraction.
Simulator "Colored palms"
Purpose:formation of elementary mathematical representations
Tasks:
- develop color perception, orientation in space;
- teach a bill;
- develop the ability to use schemes.
Tasks:
1. How many palms (red, yellow, green, pink, orange) color?
2. How many squares (yellow, green, blue, red, orange, violet) color?
3. How many palms in the first row looks up?
4. How many palms in the third row looks down?
5. How many palms in the third row on the left looks right?
6. How many palms in the second row on the left looks to the left?
7. The palm of green in the red square looks at us, if you make three steps to the right and two down, where will we find ourselves?
8. Specify the route
The manual is made of multicolored colored cardboard with the help of children's handles
Dynamic pauses
Exercises to reduce muscle tone
We are legs - top top,
We are hands - clas-clap.
We are my eyes - MiG Mig.
We shoulders - chik chick.
Once - here, two - there,
Turn around yourself.
Once - sat down, two-engines,
Hands up all raised.
Sat down, got up,
Vanka-stand like steel.
Hands to the body all pressed
And swelling to do steel
And then they set off,
As if my elastic ball.
Happy two, only two,
Do we have time!
Movement to perform the text content.
Hands on the belt. Blink your eyes.
Hands on belt, shoulders up and down.
Hands on the belt, deep turns to the right and left.
Movement to perform the text content.
Standing in place, raise hands through the sides up and lower down.
Exercises for the development of the vestibular apparatus and feelings of equilibrium
On a roving track
On a roving track,
On a roving track
Our legs are walking,
Once or twice, only two.On pebbles, on pebbles,
On pebbles, on pebbles,
Once or twice, only two.On a roving track,
On a roving track.
Tired of our legs,
Tired of our legs.
Here is our home,
We live in it. Walking with highly raised knees on a flat surface (possibly on line)
Walking on uneven surfaces (ribbed path, walnuts, peas).
Walking on a flat surface.
To squat.
Fold your palms, raise your hands above your head.
Exercises on the development of the perception of rhythms of the surrounding life and sensations of their own body
Big feet
Walked on the road:
Top, top, top. T.
OP, top, top.
Little feet
Ran along the track:
Top, top, top, top, top,
TOP, TOP, TOP, TOP, TOP.
Mom and the child move at a slow pace, with the power of pouring into the beat with words.
The pace of movement increases. Mom and the child are poured 2 times faster.
Dynamic exercise
The text is pronounced prior to the start of exercise.
- Up to five we believe, the Giri is squeezing, (and
- How many points will be in a circle, raise your hands so many times (on the board - a circle with dots. Adult indicates them, and children think how many times you need to raise your hands)
- How many times he hit the tambourine, so many times the firewood crammed, (and. N. - Standing, legs on the width of shoulders, hands in the castle up sharp sloping forward - down)
- How many Christmas trees are green, so much to perform the slopes, (and. N. - Standing, legs apart, hands on the belt. Tops are performed)
- How many cells up to the line, so many times joined you (3 5 times), (on the board depicted 5 cells. Adult indicates them, children jump)
- Sat as many times how many butterflies with us (and. P. - Standing, legs slightly put. During the arms of the arms forward)
- on the socks stand up, get the ceiling (and. N. - Main rack, hands on the belt. Lifting on the socks, hands up - to the sides, stretch)
- How many drops to the point, so much stand on the socks (4-5 times), (and. N. - Basic rack. When lifting on socks, hands on the sides - up, palm below the shoulder level)
- I leaned as many times as clarified with us. (and. n. - Standing, Pour Out, when there are no legs, not bend)
- How much I will show the circles, so much you will run jumps (5 3 times), (and. N. - Standing, hands on the belt, jumping on socks).
Dynamic exercise "Charging"
Leaned first
To the bottom of our head (tilt forward)
Right - Left we are with you
Show your head, (slopes to the sides)
Hands behind the head, together
We start running on the spot, (imitation of running)
I will remove and me and you
Hands because of the head.
Dynamic exercise "Masha-Crayman"
The text of the poem is pronounced, and at the same time accompanying movements are performed.
Looking for things Masha (turn one way)
Masha-crawling. (turn to the other side, at the start)
And there is no on the chair, (hands forward, to the sides)
And under the chair there, (sit down, dilute your hands to the sides)
There is no on the bed
(Hands lowered)
(head slopes left - right, "pursue" index finger)
Masha-crawling.
Dynamic exercise
The sun looked in the crib ... Once, two, three, four, five. We all make charging, stretch your hands, time, two, three, four, five. Bend - three, four. And jump in place. On the sock, then on the heel, we all make charging.
"Geometric figures"
purpose: Formation of elementary mathematical skills.
Educational tasks:
- Secure the ability to distinguish geometric shapes in color, shape, size, teach children to systematize and classify geometric shapes on features.
Developing tasks:
- Develop logical thinking, attention.
Educational challenges:
- Emotional responsiveness, curiosity.
At the initial stage, we familiarize children with the name of volumetric geometric shapes: a ball, cube, pyramid, parallelepiped. You can replace the names to more familiar to children: a ball, a cube, a brick. Then we introduce the color, then gradually familiarize with geometric figures: a circle, square, triangle, and so on according to the educational program. The tasks can be given different depending on the age, the abilities of children.
Task for children aged 2-3 years (color correlation)
- "Find flower and shapes of the same color as the ball."
Task for children aged 3-4 years (correlation in form)
- "Find the shapes similar to the cube."
Task for children aged 4-5 years (correlation in form and color)
- "Find the figures similar to the pyramid of the same color."
Task for children aged 4-7 years (correlation in form)
- "Find objects similar to the parallelepiped (brick)."
Didactic game "Week"
Purpose:familiarization of children with a week, as a unit of time measurement and names of the days of the week
Tasks:
- form an idea of \u200b\u200ba week, as a unit of measurement of time;
- be able to compare the number of items in the account based group;
- develop visual perception and memory;
- create a favorable emotional atmosphere and conditions for active gaming activities.
There are 7 dwarfs on the table.
How many gnomes?
Name the colors in which the dwarfs are dressed.
Monday comes first. This gnome loves everything red. And his apple is red.
The second comes Tuesday. This gnome is all orange. Cap and jacket is orange.
The third comes Wednesday. The favorite color of this gnome is yellow. And your favorite toy yellow chicken.
Thursday appears the fourth. This gnome is dressed in all green. He treats all green apples.
Friday comes fifth. This gnome loves all blue. He loves to look at the blue sky.
Saturday appears sixth. This gnome is all blue. He loves blue flowers, and the fence is painting in blue.
The seventh comes Sunday. This is a gnome in all violet. He loves his purple jacket and his purple cap.
So that the gnomes do not confuse when they replace each other, Snow White gave them a special color clock in the form of a flower with multi-colored petals. Here they are. Today we have Thursday, where do you need to turn the arrow? - Right on the green petal of hours.
Guys, and now it's time and relax on the island of "warm-up".
Physical traffic.
On Monday we played,
And on Tuesday we wrote.
On Wednesday, the shelves wrapped.
All Thursday dishes soap
Friday candies bought
And on Saturday, Morse welded
Well, on Sunday
There will be a noisy birthday.
Tell me, is there a middle of the week? We'll see. Guys, and now you need to decompose the cards so that all the days of the week went in the right order.
Children lay seven cards with numbers in order.
Clever, all the cards laid out correctly.
(Account from 1 to 7 and the name of each day of the week).
Well, now everything is in order. Sick your eyes (remove one of the numbers). Guys, what happened, one day disappeared. Name it.
We check, call all the numbers in order and days of the week, and is lost day. I change the numbers in some places and suggest children to clean up.
Tuesday today, and we will go to visit in a week. What day will we go to visit? (Tuesday).
Birthday at Mom on Wednesday, and today Friday. How much days will go to the mother's holiday? (1 day)
We will go to my grandmother on Saturday, and today Tuesday. After how many days, we will go to your grandmother? (3 days).
Nastya wiped dust 2 days ago. Today is Sunday. When did Nastya rubbed dust? (Friday).
What before Wednesday or Monday?
Our journey continues, you need to jump from the bump on the bump, only the numbers are posted, on the contrary, from 10 to 1.
(Suggest circles of different colors corresponding to the days of the week). That child comes out, the color of the circle of which, corresponds to the mandated day of the week.
The first day of our week, a difficult day, he ... (Monday).
The child gets a red circle.
Here the giraffe comes slim says: "Today ... (Tuesday)."
A child is getting up with an orange circle.
So the heron came up and said: now ...? ... (Wednesday).
A child gets up, who has a circle of yellow.
We cleaned the snow on the fourth day in ... (Thursday).
A child gets up with a circle of green.
And on the fifth day they gave me a dress, because it was ... (Friday).
Rises a baby with a blue circle
For the sixth day, Dad did not work, because it was ... (Saturday).
A child gets up with a blue circle.
I brother asked for forgiveness on the seventh day in ... (Sunday).
A child who has a circle of purple color.
Clever, with all the tasks coped.
The development of elementary mathematical representations in preschoolers is a special area of \u200b\u200bknowledge, in which, subject to consistent training, it is possible to purposefully form abstract logical thinking, increase the intellectual level.
Mathematics has a unique developing effect. "Mathematics, Queens of all sciences! It puts in order the mind! ". Its study contributes to the development of memory, speech, imagination, emotions; Forms perseverance, patience, creative personality potential.
Forms of control
Intermediate Certification - Offset
Compiler
Gougetova Natalia Valerievna, Senior Lecturer of the Department of Technologies of Psychological and Pedagogical and Special Education OGU.
Adopted abbreviations
DOU - pre-school educational institution
Zun - Knowledge, skills, skills
MMR - Mathematical Development Method
RAMM - the development of elementary mathematical representations
Timmar - Theory and Mathematical Development Methodology
FMP - the formation of elementary mathematical representations.
Topic number 1 (4 h-lek., 2 h-practicals., 2 times, 4 h - s. Broadcast
General issues Learning mathematics children with developmental deviations.
Plan
1. Objectives and objectives of mathematical development of preschoolers.
in preschool age.
4. Principles of learning mathematics.
5. Methods of the FMP.
6. FAMP receptions.
7. FAMPs.
8. Forms of work on the mathematical development of preschoolers.
The goals and objectives of the mathematical development of preschoolers.
Under the mathematical development of preschoolers should understand the shifts and changes in cognitive activity Persons that occur as a result of the formation of elementary mathematical ideas and related logical operations.
The formation of elementary mathematical representations is a focused and organized process of transferring and learning knowledge, techniques and methods of mental activity (in the field of mathematics).
Tasks of the methodology of mathematical development as a scientific field
1. Scientific justification Software requirements
formation of mathematical ideas from preschoolers in
Each age group.
2. Determination of the content of mathematical material for
Child learning in Dow.
3. Development and implementation in the practice of effective didactic means, methods and various forms of organization of work on the mathematical development of children.
4. Implementation of continuity in the formation of mathematical ideas in the DOU and at school.
5. Development of the preparation of highly specialized personnel capable of working on the mathematical development of preschoolers.
The purpose of the mathematical development of preschoolers
1. Comprehensive child education.
2. Preparation for successful school education.
3. Correctional and educational work.
Tasks of mathematical development of preschoolers
1. Formation of a system of elementary mathematical representations.
2. Formation of backgrounds of mathematical thinking.
3. Formation of sensory processes and abilities.
4. Extension and enrichment of the dictionary and improvement
associated speech.
5. Formation of initial forms of training activities.
Summary sections of the FMP program in Dow
1. "Number and score": ideas about the set, number, account, arithmetic action, textual tasks.
2. "Value": representations about various quantities, comparisons and measurements (length, width, height, thickness, area, volume, mass, time).
3. "Form": ideas about the form of objects, on geometric figures (flat and voluminous), their properties and relationships.
4. "Orientation in space": orientation on your body, relative to ourselves, relative to items, relative to another person, orientation on the plane and in space, on a sheet of paper (pure and in a cell), orientation in motion.
5. "Orientation in time": an idea of \u200b\u200bparts of the day, days of the week, months and seasons; The development of the "sense of time".
3. The value and possibility of the mathematical development of children
in preschool age.
The importance of learning children mathematics
Training is developing, is a source of development.
Training should go ahead of development. It is not necessary to navigate the fact that the child himself can already do, but on what he can do with the help and under the leadership of an adult. L. S. Profitable emphasized that it is necessary to focus on the "zone of the nearest development".
Ordered views, correctly formed first concepts, in time developed mental abilities, serve as a key to further successful learning children at school.
Psychological studies are convinced that in the learning process, qualitative changes in the mental development of the child occur.
From an early age, it is important not only to report to children ready-made knowledge, but also to develop the mental abilities of children, to teach them on their own, consciously receive knowledge and use them in life.
Training B. everyday life It is episodic. For mathematical development, it is important that all knowledge is systematically and consistently. Knowledge in the field of mathematics should be complicated gradually taking into account the age and level of development of children.
It is important to organize the accumulation of the child's experience, teach it to use the references (forms, values, etc.), rational ways of action (accounts, measurements, calculations, etc.).
Considering the minor experience of children, training is mainly inductive: first accumulate with the help of adult specific knowledge, then they are generalized in the rules and patterns. It is necessary to use a deductive method: first assimilation of the rules, then its use, concretization and analysis.
To carry out competent training of preschoolers, their mathematical development, the educator must know the subject of science of mathematics, the psychological features of the development of mathematical ideas of children and the work technique.
Opportunities for the full development of the child in the process of the FMP
I. Sensory development (sensation and perception)
The source of elementary mathematical ideas is the surrounding real reality that the child knows in the process of diverse activities, in communication with adults and under their training guidance.
At the heart of the knowledge of the small children of high-quality and quantitative signs of objects and phenomena, there is sensory processes (movement of the eye, tracing shape and size of the subject, feeling with their hands, etc.). In the process of various perceptual and productive activities, the children begin to form about the world around them: about the various features and properties of objects - color, form, magnitude, their spatial location, quantity. The touch experience is gradually accumulating, which is a sensual basis for mathematical development. In the formation of elementary mathematical representations at the preschooler, we rely on various analyzers (tactile, visual, auditory, kinesthetic) and at the same time develop them. The development of perceptions is by improving perceptual action (viewing, feeling, listening, etc.) and the assimilation of systems of sensory standards produced by mankind (geometric shapes, measures of magnitude, etc.).
II. Development of thinking
Discussion
Name the types of thinking.
As in the work of the educator on the FMP, the level is taken into account
Development of the child's thinking?
What logic operations do you know?
Give examples of mathematical tasks for each
logical operation.
Thinking is the process of conscious reflection of reality in ideas and judgments.
In the process of forming elementary mathematical representations, all types of thinking are developing in children:
vividly effective;
visual-shaped;
wonder-logical.
| Logical operations | Examples of assignments of preschool children |
| Analysis (decomposition of the whole to composite parts) | - What geometric figures made up the machine? |
| Synthesis (knowledge of the whole in unity and interrelation of its parts) | - Make a house of geometric shapes |
| Comparison (comparison for the establishment of similarities and differences) | - What are these subjects similar? (Form) - What are the difference between these items? (size) |
| Specification (clarification) | - What do you know about the triangle? |
| Generalization (the expression of the main results in general) | - How can you call the square, rectangle and rhombus as one word? |
| Systematization (location in a certain order) | Put the nesting dolls |
| Classification (distribution of objects by groups depending on their general features) | - Spread out the figures into two groups. - What kind of sign did you do it? |
| Abstraction (distraction from a number of properties and relationships) | - Show items round shape |
III. Memory development, attention, imagination
Discussion
What includes the concept of "memory"?
Offer children a mathematical task for the development of memory.
How to intensify the attention of children when forming elementary mathematical representations?
Word the task for children to develop imagination using mathematical concepts.
Memory includes memorization ("Remember is a square"), remember ("What is this figure called?"), Reproduction ("Draw a circle!"), Recognition ("Find and name familiar figures!").
Attention does not act as an independent process. Its result is the improvement of any activity. To activate attention, the ability to put the task and motivate it. ("Kati one apple. Masha came to her, it is necessary to divide the apple equally between two girls. Carefully look at how I will do it!").
Images of imagination are formed as a result of the mental design of objects ("Present a five-corn figure").
IV. Detergery
Discussion
How in the process of the formation of elementary mathematical representations, is a child's speech?
What gives mathematical development to develop a child's speech?
Mathematical classes have a huge positive impact on the development of the child's speech:
enrichment of the dictionary (numeral, spatial
Prepositions and adverbs, mathematical terms characterizing the form, value, etc.);
matching words in the only and multiple number ("one bunny, two bunny, five bunnies");
formulation of responses with a complete proposal;
logic arguments.
The wording of thought in the Word leads to a better understanding: formulating, thought is formed.
V. Development of special skills and skills
Discussion
- What special skills and skills are formed in preschoolers in the process of forming mathematical representations?
In mathematical classes, children are formed special skills and skills necessary for them in life and studies: account, calculation, measurement, etc.
Vi. Development of cognitive interests
Discussion
What is the meaning of a child of cognitive interest in mathematics for its mathematical development?
What are the ways of excitement of cognitive interest in mathematics from preschoolers?
As can be excited cognitive interest To work on FMPS in Dow?
Meaning of cognitive interest:
Activates perception and mental activity;
Broadens the mind;
Contributes to mental development;
Improves the quality and depth of knowledge;
Contributes to the successful application of knowledge in practice;
Encourages independently acquire new knowledge;
Changes the nature of the activity and related experiences (activity becomes active, independent, versatile, creative, joyful, effective);
Has a positive effect on personality formation;
It has a positive effect on the health of the child (excites energy, increases vitality, makes life happier);
Ways of excitement of interest in mathematics:
· Communication of new knowledge with children's experience;
· Opening of new parties in the former experience of children;
· Literal excitation;
· Stimulation.
Psychological prerequisites of interest in mathematics:
Creating a positive emotional attitude to the teacher;
Creating a positive attitude to classes.
Ways of excitement of cognitive interest in the exercise on the FAMP:
§ Explanation of the meaning of the work performed ("Doll nowhere to sleep. Let's build a bed for her! What size should it be? Let's die!");
§ Work with your favorite attractive objects (toys, fairy tales, pictures, etc.);
§ Connection with close to children situation ("Misha has a birthday. When is your birthday, who comes to you?
Misha also came guests. How many cups need to put on the table for the holiday? ");
§ Interesting for children Activity (game, drawing, design, applique, etc.);
§ Eat tasks and assistance in overcoming difficulties (the child must at the end of each lesson, to experience satisfaction from overcoming difficulties) ", a positive attitude towards the activities of children (interest, attention to each child's answer, goodwill); Initiative, etc.
Methods FMP.
Methods of organization and implementation of educational activities
1. Perceptual aspect (transmission methods educational information Pedagogue and perception of her children through a hearing, observation, practical actions):
a) verbal (explanation, conversation, instruction, questions, etc.);
b) visual (demonstration, illustration, view, etc.);
c) practical (subject-work and mental actions, didactic games and exercises, etc.).
2. Gnostic aspect (methods characterizing the assimilation of new material by children - by actively memorizing, by independent reflection or a problem situation):
a) illustratively explanatory;
b) problem;
c) heuristic;
d) research and others.
3. Logical aspect (methods characterizing mental operations when applying and assimilating educational material):
a) inductive (from private to general);
b) deductive (from total to private).
4. Management aspect (methods characterizing the degree of independence of educational activities of children):
a) work under the guidance of the teacher,
b) independent work of children.
Features of the practical method:
ü performing a variety of subject-practical and mental actions;
ü widespread use of didactic material;
ü The emergence of mathematical representations as a result of action with the didactic material;
ü Development of special mathematical skills (accounts, measurements, calculations, etc.);
ü The use of mathematical ideas in everyday life, game, work, etc.
Types of visual material:
Demonstration and distribution;
Scene and immutty;
Volumetric and plane;
Special countable (countable sticks, abacus, scores, etc.);
Factory and homemade.
Guidelines for the use of visual material:
· New software task is better to start with a plot volumetric material;
· As the learning material is assimped, proceed to plot-plane and inconsistency;
· One program task is explained on a large variety of visual material;
· New visual material better to show children in advance ...
Requirements for improvised visual material:
Hygienicity (paints are covered with varnish or film, velvet paper is used only for demonstration material);
Aesthetics;
Reality;
Diversity;
Homogeneity;
Strength;
Logic connectedness (hare - carrots, protein - bump, etc.);
A sufficient number ...
Features of the verbal method
All work is built on a dialogue caregiver - a child.
Requirements for the teacher's speech:
Emotional;
Competent;
Affordable;
Loud enough;
Friend;
In the younger groups, the tone is mysterious, fabulous, mysterious, pace of non-burst, multiple repetitions;
In the older groups, the tone is interested, using problem situationsThe tempo is quite fast, approaching the lesson at school ...
Children's speech requirements:
Competent;
Understandable (if a child has a bad pronunciation, the teacher welcomes the answer and asks to repeat); full offers;
With the necessary mathematical terms;
Loud enough ...
Famp techniques
1. Demonstration (usually used when reporting new knowledge).
2. Instruction (used in preparing for independent operation).
3. Explanation, indication, clarification (used to prevent, detect and eliminate errors).
4. Questions for children.
5. Clean reports of children.
6. Subjective and mental actions.
7. Control and evaluation.
Requirements for teacher issues:
accuracy, concreteness, laconicism;
logical sequence;
variety of wording;
small but enough;
avoid prompting questions;
skillfully use additional issues;
to give children time to think ...
Requirements for children's answers:
brief or complete depending on the nature of the issue;
on the question;
independent and conscious;
accurate, clear;
loud enough;
grammatically correct ...
What if the child is responsible wrong?
(In the younger groups it is necessary to correct, ask to repeat the correct answer and praise. In the elders - you can make a note, call another and praise the correctly answered.)
FAMPS
Equipment for games and classes (set of canvas, countable ladder, flannelugaph, magnetic board, board for writing, TSO, etc.).
Kits of didactic visual material (toys, designers, construction material, demonstration and distribution material, ledge sets, etc.).
Literature ( methodical manuals For educators, collections of games and exercises, books for children, working notebooks, etc.) ...
8. Forms of work on the mathematical development of preschoolers
| The form | Tasks | time | Coverage of children | Main role |
| Occupation | Give, repeat, consolidate and systematize knowledge, skills and skills | Systematic, regularly, systematically (durability and regularity in accordance with the program) | Group or subgroup (depending on age and development problems) | Educator (or defecat) |
| Didactic game | Consolidate, apply, expand zun | In class or out of occupation | Group, subgroup, one child | Educator and children |
| Individual work | Clarify zun and eliminate gaps | In class and out of occupation | One child | Educator |
| Leisure (mathematical matinee, holiday, quiz, etc.) | Mature mathematics, sum up | 1-2 times a year | Group or several groups | Educator and other specialists |
| Independent activities | Repeat, apply, work out zun | During regime processes, household situations, daily activities | Group, subgroup, one child | Children and educators |
Task for independent work of students
Laboratory work number 1: "Analysis of" Education and training programs in children's garden»Section" Formation of elementary mathematical representations ".
Topic number 2 (2 hr., 2 ppm., 2 hours, 2 h - s. Broad
PLAN
1. Organization of classes in mathematics in a preschool institution.
2. Exemplary classes in mathematics.
3. Methodical requirements for classes in mathematics.
4. Ways to maintain the good performance of children in class.
5. Formation of work skills with handouts.
6. Formation of training skills.
7. Meaning and place of didactic games in mathematical development of preschoolers.
1. Organization of classes in mathematics in a preschool institution
Classes are the main form of organizing the training of children in kindergarten.
The occupation begins not outside the parties, but from the collection of children around the educator who checks them appearance, attracts attention, deals with individual characteristics, taking into account the problems in the development (vision, hearing, etc.).
In younger groups: the subgroup of children can, for example, to dissolve in the chairs with a semicircle in front of the tutor.
In the senior groups: a group of children is usually seated by the desks along two, face to the tutor, as work with handouts is carried out, training skills are developed.
The organization depends on the content of the work, age and individual characteristics of children. The occupation can begin and take place in the game room, in the sports or music hall, on the street, etc., standing, sitting and even lying on the carpet.
The beginning of the classes must be an emotional, interest, joyful.
In younger groups: Surprise moments are used, fabulous plots.
In senior groups: it is advisable to use problem situations.
In the preparatory groups, the work of the duty officers is organized, discussed what they were engaged in the past (in order to prepare for school).
Approximate structure of classes in mathematics.
Organization of classes.
Travel course.
Outcome.
2. Trucking
Exemplary parts of stroke mathematical lesson
Mathematical workout (usually from the older group).
Work with demonstration material.
Work with dispensing material.
Fizkultminutka (usually from the middle group).
Didactic game.
The number of parts and their order depend on the age of children and the associated tasks.
IN junior group: At the beginning of the year, there can be only one part - didactic game; In the second half of the year - up to three hours of the Ray (usually work with demonstration material, work with dispensing material, mobile didactic game).
IN medium group: Usually four parts (regular work begins with a handouting material, after which physkultminutka is necessary).
In the senior group: up to five parts.
In the preparatory group: up to seven parts.
The attention of children is preserved: 3-4 minutes from younger preschoolers, 5-7 minutes from senior preschoolers - this is an approximate duration of one part.
Types of Physkultminuts:
1. The poetic form (children are better not to vote, but to breathe properly) - is usually carried out in the 2nd youngest and middle groups.
2. A set of exercise for the muscles of the hands, legs, backs, etc. (better to do for music) - it is advisable to spend in the older group.
3. With mathematical content (apply if the occupation does not carry a large mental load) - more often used in the preparatory group.
4. Special gymnastics (finger, articulation, for eyes, etc.) - is regularly held with children with problems in development.
Comment:
if the occupation is movable, physical attachment can not be carried out;
instead of physical attacks, you can carry out relaxation.
3. Outcome classes
Any occupation must be completed.
In the younger group: the teacher sums up after each part of the classes. ("How well we played. Let's collect toys and we will dress for a walk.")
Central I. senior groups: At the end of the classes, the teacher himself sums up, entrying children. ("What did we know the new today? What did you talk about? What played?"). In the preparatory group: children themselves draw conclusions. ("What did we do today?") The work of the duty officers is organized.
It is necessary to evaluate the work of children (including individually praise or make a remark).
3. Methodical requirements for classes in mathematics (depend on the principles of training)
2. Educational tasks are taken from different sections of a program to form elementary mathematical representations and are combined in relationships.
3. New tasks are served in small portions and are specified for this lesson.
4. In one lesson, it is advisable to solve no more than one new task, the rest on repetition and consolidation.
5. Knowledge are systematically and consistently in an affordable form.
6. Used diverse visual material.
7. The connection of the knowledge gained with life is demonstrated.
8. Individual work with children is carried out, an intereted approach to the selection of tasks is carried out.
9. Regularly monitors the level of learning the material by children, identifying gaps in their knowledge and their elimination.
10. All work has a developing, correctional orientation.
11. Mathematics classes are held in the first half of the day in the middle of the week.
12. Mathematics classes are better to combine with classes that do not require a large mental load (physical education, music, drawing).
13. You can carry out combined and integrated classes for different methodsIf tasks are combined.
14. Each child should actively participate in each lesson, perform mental and practical actions, reflect their knowledge in speech.
PLAN
1. Stages of formation and content of quantitative representations.
2. The value of the development of quantitative ideas from preschoolers.
3. Physiological and psychological mechanisms of perception of quantity.
4. Features of the development of quantitative ideas in children and guidelines To their formation in the Dow.
1. Stages of formation and content of quantitative representations.
Stages formation of quantitative representations
("Accounting Stages" by A.M. Leushina)
1. DOBER ACTIVITIES.
2. Accounts.
3. Computational activity.
1. Daughter activity
For the correct perception of the number, for the successful formation of counting activities, it is necessary to first teach children to work with sets:
See and called significant signs of objects;
See many completely;
Select the elements of the set;
Call a set ("generalizing word") and list it elements (set the set in two ways: indicating the characteristic property of the set and listed
all elements of the set);
Make a set of separate elements and from subsets;
Share many classes;
Organize the elements of the set;
Compare the sets in the amount by the correlation "one to one" (establishing mutually unambiguous compliance);
Create equitable sets;
Combine and disconnect the set (the concept of "whole and part").
2. Accounting activity
The ownership of the account includes:
Knowledge of words-numeral and invoking them in order;
The ability to correlate the numeral elements of the set "one to one" (setting a mutually unique correspondence between the elements of the set and the segment of the natural row);
Allocation of the final number.
Possession of the concept of the number includes:
Understanding the independence of the result of a quantitative account from its direction, the location of the elements of the set and their qualitative signs (size, form, colors, etc.);
Understanding of the quantitative and sequence value of the number;
The idea of \u200b\u200ba natural number of numbers and its properties includes:
Knowledge of the sequence of numbers (direct and reverse order, the recording of the previous and subsequent number);
Knowledge of the formation of adjacent numbers from each other (by adding and subtracting a unit);
Knowledge of connections between adjacent numbers (more, less).
3. Computational activity
Computational activity includes:
· Knowledge of connections between adjacent numbers ("more (less) per 1");
· Knowledge of the formation of adjacent numbers (P ± 1);
· Knowledge of the composition of numbers from units;
· Knowledge of the composition of numbers from two smaller numbers (the folding table and the corresponding cases of subtraction);
· Knowledge of numbers and signs +, -, \u003d,<, >;
· The ability to compile and solve arithmetic tasks.
To prepare for the assimilation of the decimal system, it is necessary:
o possession of oral and written numbering (typing and record);
o ownership of arithmetic actions of addition and subtraction (climbing, calculation and recording);
o Possession of account with groups (pairs, three, heels, tens, etc.).
Comment. Data and skills of the preschooler must qualitatively seize within the first ten. Only with the complete assimilation of this material you can start working with the second tent (it is better to do it in school).
About values \u200b\u200band measure
PLAN
2. The importance of development in preschoolers ideas about values.
3. Physiological and psychological mechanisms of perception of objects.
4. Features of the development of ideas about children and methodical recommendations for their formation in DOU.
Preschoolers get acquainted with various values: length, width, height, thickness, depth, area, volume, weight, time, temperature.
The initial idea of \u200b\u200bthe magnitude is associated with the creation of a sensual basis, the formation of ideas about the size of items: show and call length, width, height.
The main properties of the value:
Comparability
Relativity
Measurement
Variability
The definition of the value is possible only on the basis of comparison (directly or comparing with some way). The characteristic of the value is relative and depends on the objects selected to compare (< В, но А > FROM).
The measurement makes it possible to characterize the value of the number and move from comparison directly to the comparison of the numbers, which is more convenient, as it is done in the mind. Measurement is a comparison of the value with the size of the same genus adopted per unit. The purpose of the measurement is to give a numerical characteristic value. The variability of magnitudes is characterized by the fact that they can be added, deduct, multiply by the number.
All these properties can be comprehended by preschoolers in the process of their actions with objects, isolation and comparison of values, measuring activities.
The concept of the number occurs during the account and measurement process. Measuring activities expands and deepens children's ideas about the number that have already developed in the process of counting activities.
In the 60-70s of the XX century. (P. Ya. Galperin, V. V. Davydov) there was an idea about measuring practice as the basis of the formation of the concept of a child. Now there are two concepts:
The formation of measuring activities based on the knowledge of the number and account;
Formation of the concept of a number based on measuring activity.
The account and measurement should not be opposed to each other, they mutually complement each other in the process of mastering the number as an abstract mathematical concept.
In kindergarten, first learn children to allocate and call different parameters of sizes (length, width, height) based on eye comparison sharply contrasting items. Then we form the ability to compare the method of application and the imposition of slightly differ and equal items with a pronounced one value, then by several parameters at the same time. Work on the layout of seriation series and special exercises for the development of the chammere is consolidating the ideas about the values. Acquaintance with the conditional measure, equal to one of the compaable items in size, is preparing children to measuring activities.
The measurement activity is quite complex. It requires certain knowledge, specific skills, knowledge of the generally accepted system of measures, the use of measuring instruments. Measuring activities can be formed in preschoolers under the condition of targeted leadership of adults and great practical work.
Measurement scheme
Before you get acquainted with generally accepted references (centimeter, meter, liter, kilogram, etc.), it is advisable to first teach children to use conditional standards when measuring:
Length (length, width, height) with strips, sticks, ropes, steps;
Volume of liquid and bulk substances (the amount of cereals, sand, water, etc.) with glasses, spoons, cans;
Square (figures, sheet of paper, etc.) by cells or squares;
Mass objects (for example: apple - acorns).
The use of conditional measurements makes the measurement available for preschoolers, simplifies activity, but does not change its essence. The essence of measurement in all cases is the same (although objects and tools are different). Typically, training starts from measuring the length, which is more familiar to children and come in handy in school first.
After this work, you can introduce preschoolers with references and some measuring instruments (ruler, weights).
In the process of forming measuring activities, preschoolers are able to understand that:
o measurement gives an accurate quantitative characteristic value;
o for measurement it is necessary to choose an adequate measure;
o The number of measure depends on the measured value (the greater
The value, the greater its numerical value and vice versa);
o The measurement result depends on the selected measurement (the greater the measure, the less numerical value and vice versa);
o For comparison, the values \u200b\u200bmust be measured by the same measurements.
The measurement makes it possible to compare the values \u200b\u200bnot only on a touch basis, but on the basis of mental activity, forms an idea of \u200b\u200bthe value of both mathematical
Integration of the formation of elementary mathematical representations (FMP)
in different educational areas
(Slide 1)
Mathematics is one of the most difficult school subjects at school. Preschoolers do not know about it and should not learn. Therefore, our task is to give the child the opportunity to feel that he will be able to understand, to learn not only private concepts, but also common patterns. And most importantly, it is to know the joy when overcoming difficulties.
A distinctive feature of modern pedagogy is its aspiration into the future. Nowadays, not only new methods of studying mathematics appeared, but the Mathematics itself is a powerful factor in the development of the child, the formation of his cognitive and creative abilities.
(Slide 2)
Integration (by Ozhegov) - parts of one whole. The integrated approach complies with one of the principles of preschool didactics: education should be small in volume, but capacious.
Reforming the pre-school education system in connection with the adoption (GEF to) of the Federal State Educational Standard of Preschool Education Ensure the content, methods and forms of work with children involves revised in theory and practice. In the new conditions it is necessary to use flexible models and technologies educational processSupposing the activation of independent actions of children and their creative manifestations, a humane, dialogical style of communication of the teacher and a child.
(Slide 3)
Integrated classes are not an innovation, but a well-forgotten old and familiar, especially experienced educators. After all, the term "integrated" classes appeared in 1973, but this question was not enough at that time.
(Slide 4)
According to GEF, the program should be built on the basis of the principle of integrating educational areas: (slide)
- social and communicative development,
-Conal development,
-checheny development
-Exterative-aesthetic development,
Physical development in accordance with their specificity and age capabilities of pupils.
(Slide 5)
(FAMP) formation of elementary mathematical representations of preschoolers enters the educational area "cognitive development" and is aimed at obtaining primary (slide 6) of ideas about the properties and relations of the objects of the world (about form, color, size, number, numbers, parts, and whole, space and time). (Slide 7)
It is when acquiring mathematical ideas that a child receives a fairly sensual orientation experience in a variety (slide 8) properties of objects and relations between them, mastering the techniques and methods of knowledge, applies knowledge and skills in practice formed during training.
(Slide 9)
Integration mental I. exercise It can be carried out in the process of filling physical culture activities in mathematical content. (Slide 10) during (NOD) direct educational significance physical culture Children meet with mathematical relationships: compare the subject in size and form or determine, (slide 11) where the left side, and where is the right. In class we use various flat and volumetric geometric shapes and numbers. (Slide 12-2rd) Much work is based on orientation in space and relative to its body.
When fixing the quantitative account, the pupils perform various exercises: (slide 13) "bounce on one leg", "running 10 times on the left leg, 10 times on the right", (slide 14) "take a house of a certain color or form"). Children not aware of the load believe, reflect on, think. (Slide 15)
(FAMP) formation of elementary mathematical representations (slide 18) directly related to the educational area " Speech development"Where the main task is to develop a mathematical dictionary in children. (Slide 19 - 2r) In the process of integration, a practical assimilation of lexico-grammatical categories is carried out and the correct sound is practiced.
(Slide 20) The process of forming a mathematical dictionary involves a systematic learning assimilation, gradually its expansion. Thus, qualitative relations (slide 21) must be realized in practical actions compared to the aggregates and individual items;
In class, children learn not only to recognize the magnitude of objects, but, and correctly reflect their views; (slide 23) to distinguish between changes in total; find more complex orientations in the value of items (slide 24); To master nouns, denoting objects, geometric shapes, (slide 25) as well as spatial relationships and temporary notation.
(Slide 26)
Familiarization with literary works and small forms of folklore contributes to the formation of ideas from a child about features different properties and relations that exist in natural and social world; (Slide 27) It develops the thinking and imagination of the child, enriches emotions, gives samples of the live Russian language. Many works contribute to the formation of ideas about the quantitative relations, parts of the day, days of the week, the days, the size and orientation in space.
(Slide 28)
During reading fiction And the preparation of small stories, we paid attention to the number of parts of a particular work. (Slide 29) in any of the fairy tales, whether it is a folk or author, there is a number of mathematical concepts. Tale of "Kolobok", "Teremok", "Repka", "Winter" and "Phone" introduces quantitative and ordinal account, and also the foundations arithmetic action.
(slide 30)
In this work, such small folklore forms, proverbs, sayings, sweat, booms, readings, and of course riddles are widely used.
(slide 31)
Mathematics penetrates "artistic aesthetic development" and help solve problems through their methods and techniques. Visual, (Slide 32) Related guidelines will help children remember in more detail, feel some kind of mathematical concepts (slide 33)
(Slide 34)
We pay attention to how many parts and what size should be divided by a piece of plasticine or paper strip. (Slide 35) How can I get a subject of one form or another, fixing not only the color, (slide 36) form, size of the item, but also its spatial location. (Slide 37) When drawing plants, nature, (slide 38-2r), mark the location of the items, consider how many parts and where, you need to portray the object (slide 39), (slide 40) (slide 41-2r)
At musical activities, we use musical and didactic games to develop a sense of rhythm, which contribute to the development and consolidation of some mathematical definitions.
Children find out that the sound is long and short, high and low (slide 42-2r) musical moving games contribute to the consolidation of color knowledge, the form of the subject. As well as the skill of orientation in space is fixed.
Thus, elementary mathematical representations in preschoolers are absorbed, fixed and evolved through a musical material.
(slide 43)
The development of mathematical ideas continues in everyday life. During duty, children call how many dishes are missing on the tables, for which the number of children there are tables today, etc. (Slide 44) While walking, we celebrated this day, month, season. (Slide 45)
We consider objects alive inanimate nature, Call color, shape, size of the subject or object. (Slide 46) (Find the highest or low plant on the site, etc.).
In independent activities, children use "Cubes Nikitina", "Geocont", various mosaics, puzzles, didactic games (slide 47)
When you meet children with scales, familiarize (slide 48) with measuring the mass of the subject. We tell what hours are: (slide 49-2r) (slide 50)
Integration made it possible to combine together all types of activity (slide 51) of a child in kindergarten, one topic flows from one educational area to another, (slide 52-2r) and each solve their training, fixing and educational tasks.
(Slide 53)
Practice shows that senior preschoolers show an increased cognitive interest in classes only in the event that (slide 54) when intrigued and amazed by something unknown. In this case, information looks interesting in their eyes, almost magical. (Slide 55) The task of the teacher is to make classes on the formation of elementary mathematical ideas in entertaining and unusual. (slide 56-2r)
(Slide 57)
The eyelid of the computer is boldly walks around the country, so we introduce (slide 58-2r) new technologies to their work and use multimedia equipment - as a visual material.
(slide 59-2r)
From this we can conclude that the integration is deeply rebuilding the content of education leads to changes in the work methodology and creates conditions and new training technologies. As well as provides a completely new psychological climate for a child and teacher in the learning process. (Slide 60)
Nuca Marina Gennadievna
Position: Educator
Educational institution: Madoum Murmansk №96
Locality: Murmansk
Name of material: Didactic games as a means of developing mathematical abilities of preschoolers
Subject: The formation of elementary mathematical representations in accordance with GEF to
Publication date: 14.05.2017
Section: preschool education
Nuca Marina Gennadievna
educator Madoum Murmansk № 96
Didactic games as a means of development
mathematical abilities pupils
senior pre-school age in preschool
"From how laid down
elementary mathematical
submissions
depends on the further path
mathematical development
successful child promotion in
of this area of \u200b\u200bknowledge "
L.A. Wenger
One of the most important tasks of educating the child of preschool
age is the development of his mind, the formation of such mental skills and
abilities that allow you to easily explore a new one.
For the modern educational system, the problem of mental
education (but the development of cognitive activity is one of
the tasks of mental education) is extremely important and relevant. So important
learn to think creatively, non-standard, independently find the right
mathematics
capaches
develops
flexibility
thinking, teaches logic, forms memory, attention, imagination, speech.
mastering
elementary
mathematical
representations
attractive
unobtrusive
joyful.
Mathematical development of preschoolers - positive changes in
cognitive sphere of personality that occur as a result of development
mathematical ideas and related logical operations.
The formation of elementary mathematical representations is
the purposeful process of transferring and learning knowledge, techniques and methods
mental activity provided for by software requirements.
Basic
preparation
successful
mastering
mathematics at school, but also the comprehensive development of children.
Mathematical education of the preschooler is a focused
learning
elementary
mathematical
representations
fashion
knowledge
mathematical
reality
preschool
institutions
whom
is an
education
culture
thinking and mathematical development of the child.
Organization of educational activities in mathematical
development of children of senior preschool age
preschool age.
In accordance with GEF to the main objectives of mathematical
development of preschool children are:
1. Development of logical and mathematical ideas about mathematical
properties
relationships
objects
(concrete
values
geometric Figures, dependencies, laws);
Development of sensory, objective and effective ways of knowledge
mathematical
relationship:
survey
comparison
grouping, streamlining, partition);
Development of children of experimental research methods
knowledge
mathematical
(e COP PE E R I M E N T I R O VO N E,
modeling, transformation);
Development in children logical methods knowledge of mathematical
relationship
abstraction
negation,
comparison,
classification);
Mastering
mathematical
methods
knowledge
reality: account, measurement, simple calculations;
Development
intellectual-creative
manifestations
resourcefulness, smelting, guesses, intelligence, desire for the search
non-standard solutions;
Development
agmented
evidence
enrichment of the child's dictionary;
8. Education of the readiness of children for school training,
activity,
initiative
independence, responsibility, perseverance in
overcoming difficulties, coordination of eye movements and shallow motors
hands, self-control skills and self-esteem.
All objectives of the mathematical development of senior preschoolers
solved
training
entertaining.
initial
learning
exacerbate
emotional testing
procea sys
forcing
watch,
compare,
talk
argue
prove
right
performed
actions.
adult
support
Try
line up
educational
activity
actively and enthusiastically engaged. Offering children mathematical tasks
consider
individual
abilities
preferences
various
learning
mathematical content is of a purely individual character.
Mastering mathematical ideas will be effective and
perfect only when children do not see what they are taught. Them
it seems that they only play. Not noticeable for himself in the process of gaming
actions with gaming material are considered to be folded, deducted, decide
brain teaser
Capabilities
organizations
activities
expand subject to the creation of a developing garden in a kindergarten group
solid spatial environment. Therefore, I make every effort for
creation in the group properly organized subject-spatial
medium that allows each child to find a lesson in the shower, believe
in their strength and abilities, learn to interact with teachers and with
peers, understand and evaluate feelings and deeds, argument
your conclusions.
in mathematical
development of senior children
preschool
age
diverse
using
concrete task, mode, developing medium, etc.:
organized educational activities, didactic games, experiments,
experiments, Mathematical Holidays, Leisure, Casual Domestic
situations, conversations, independent activities of children.
The fundamental principle of the development of modern pre-school
about b r and zo n i i
p r ... n n n s
Fed E R A flask
g O S UD A R S T N E N N S M
educational
standard
preschool
education
integration
educational
regions.
Development
mathematical
presentations of children, the acquisition of the main mathematical knowledge in
accordance with the software requirements and age characteristics
implemented
educational
socio
communicative
development,
cognitive
development,
development,
artistic and aesthetic development, physical development. Necessary
pedagogical
conditions
mathematical
development
preschool children
integrated
are:
thoughtful
organized
educational
activities,
in k l yuch and yu u and i
integrated
rational
combination
valid
activities (game, visual, cognitive, research
activation
cognitive
interest
mathematics
preschoolers and the desire to absorb new knowledge.
Novikova
"Mathematics
allows
realize
educational work on the formation of mathematical representations
integrated
most
activities. I use when working on this program a variety
methodical
combination
practical
activities,
solution of problem-gaming and search situations. All obtained during
classes of knowledge, skills, skills are fixed in didactic games, because
each script of classes in mathematics has a section "Let's play",
value
formation
mathematical
representations
preschool children
technologies, in particular, such a component such as didactic game.
2. The value of the didactic game as a component of the game
technologies in the mathematical development of children of senior preschool
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methods
actions.
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mathematical
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organized
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Development
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formation
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mastering
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preschool
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training
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preschool
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development
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