Olga Vakulenko
Development of elementary mathematical representations in children 6–7 years old
Development of elementary mathematical concepts in children 6-7 years old.
Preschool institutions solve an important social problem - comprehensive education developed personality. Educators and educators must prepare a thinking and feeling child who can apply his knowledge in life.
Important role in education children belongs to mathematics. It contains enormous opportunities for development of children's thinking in the process of their education from early childhood.
Formation and development logical structures of thinking must be implemented in a timely manner. You need to choose the right path leading to the acceleration of intellectual child development.
From my experience working with children, I can conclude that successful learning mathematics is determined the degree of formation of the child’s mental operations and speech, the ability and desire to think. Possession of counting skills and the ability to solve counting problems is necessary for children to begin successful education at school. Every child strives to be active. It is important that the desire does not disappear. Therefore, it is necessary to help the child express himself in a more intimate, natural and accessible form of activity - play. It is in this type of activity that intense intellectual, emotional and personal development occurs. child development, which again is the basis for successful schooling.
:In my opinion, development of mathematical abilities occupies a special
place in the intellectual child development, the proper level of which determined qualitative features of children’s assimilation of such initial mathematical representations and concepts,how to count, number, measurement, magnitude, geometric figures, spatial relations. Hence it is obvious that the content of training should be aimed at developing children of these basic mathematical concepts and concepts and arming them with techniques mathematical thinking comparison, analysis, reasoning, generalization, inference.
Guided by an idea developmental education, I strive to focus not on the level reached by children development, but looking ahead a little so that children can make some effort to master mathematical material.
The goal of my work was: create a condition for intellectual and cognitive development of preschool children, formations children mathematical abilities .
For myself I set the following tasks:
1. Form children's performance about the importance of numbers, space-time relationships, size and shape in human life subject.
2. To carry out the formation of visual-figurative and logical
Conceptual forms of thinking, develop perception, imagination, spatial performance, attention, memory (verbal, semantic, visual).
3. Develop mental capacity, find dependencies and patterns, possess systematic perception, generalized and forms of thinking (generalize objects and actions) and basic logical operations (comparison, classification, generalization).
4. Develop quality of mind: flexibility, criticality, logic and independence.
Based on the identified tasks, I divided the work into 3 stages. On the first
carried out diagnostics mathematical abilities of children 6-7 years old. Assessed skills development of mental arithmetic, the degree of mastery of visually figurative and logical thinking, spatiotemporal relations.
At the second stage, I studied and generalized the teaching experience in development of children's mathematical abilities scientists and practicing teachers. Developed a long-term work plan for the following age categories.
3-4 years. The main result should be the formation of children's interest in learning, developing their attention, memory, speech, mental operations. At the same time, they must have developed the following basic knowledge, skills and skills:
1. The ability to identify and explain signs of similarity in the simplest cases
and the differences between the two items(by color, shape, size).
2. The ability to continue a series made up of items or figures with one changing characteristic. The ability to independently compose similar series.
items by length and width.
4. Quantitative and ordinal counting within 1О.
S. Ability to recognize simple geometric shapes (square, circle, triangle). Find in the environment objects similar in shape.
items arranged in a row.
2. The ability to answer questions “how much in total >>”, “which (Which)"according to the account.
3. Learn to compare two groups items and form based on the account
idea of equality(inequality).
4. Improve skills children compare two objects according to
size (length, width, height).
5. Introduce children with rectangle, teach to recognize and name it.
Continue learning to recognize and name a circle, square, triangle.
b. Define direction of movement away from you (right, left, forward,
back, up, down, know right and left hand.
1. The ability to identify and express in speech signs of similarity and difference
individual objects and aggregates.
2. Ability to unite groups items, select part, install
relationship between part and whole.
use ordinal and cardinal numbers.
4. Ability to name each number in within 10 previous and
subsequent numbers.
5. The ability to recognize and name geometric shapes and bodies.
6. The ability to name parts of the day, the sequence of days in the week,
sequence of months in a year.
2. The ability to compare numbers in within 10 using visual material and install, how much one number is greater or less than another.
3. Ability to directly compare items by length, mass, volume (capacity, area.
4. The ability to practically measure length and volume using various standards.
5. The ability to recognize and name geometric shapes and find them in the environment objects similar in shape.
At the third stage I I envision the creation of a subject-development environment. My work is based on the principle from simple to complex. I I offer children games saturated with logical and mathematical content: "geometric lotto", “choose according to shape”, <<заполни квадрат», “match pictures to numbers”. While playing, children do not notice that they are being taught something, but unbeknownst to themselves, in the game the children learn to compare (didactic games “how are they similar and how are they different”, "Find differences",
"find two identical subject» , analyze ( "find the pairs", "what first, what then", generalize ( "name objects in one word» , "what common"), classify items("stripped items no indication» ,
“choose according to shape”, learn to formulate simple conclusions. To enhance mental activity children, I try to ask questions: For what? Why? For what? how else?
My teaching experience was is provided in consultations for parents on the topic "features of thinking children 6-7 years old» , in the conversation “games and game exercises in teaching children mathematics».
At the final stage of working with children, I conducted an open frontal lesson and summed up result: 85o/o coped, 15% had difficulties. Thus, the result of my work was the creation of conditions that ensure children's mathematical development, integration of tasks according to development of elementary mathematical concepts in different types of activities. U children a high level has been formed development mental abilities - mastering generalized forms of thinking, the ability to find dependencies and patterns.
Prospects for my professional activity I see:
In the implementation of new projects based on interests and needs children
and their parents.
Dissemination and generalization of my work experience among educators
working under the program "Community".
Method of express diagnostics of intellectual abilities of children 6-7 years old (MEDIS)
E. I. SHCHBLANOVA, I. S. AVERINA, E. N. ZADORINA
Currently, a large number of schools have appeared in which education is conducted according to accelerated programs, with in-depth study of certain subjects, under special programs for gifted children, etc. In connection with this, the problem of selecting students capable of such training has arisen. Unfortunately, the solution to this problem is often arbitrary, without any psychological and pedagogical justification.
As a rule, an experienced teacher can quite competently determine a child’s readiness to enter the first grade of school and distinguish normally developed children from children with one or another developmental delay. The issue of children's readiness for school education is covered in sufficient detail in the literature.
The problem of selecting capable and gifted children requires a completely different approach to be solved. This approach should first of all take into account the complexity and versatility of the phenomenon of giftedness itself, which includes both cognitive (intellectual and creative abilities) and non-cognitive (motivational and personal characteristics) factors of development.
Therefore, first of all, it is necessary to clearly formulate the objectives of the training program for which children are being selected, and the requirements that are presented to children within the framework of this program. When making such a selection, the main attention should be paid to the interests of the child: whether studying at a given school will be optimal for his development. To resolve this issue, among many other factors, determining the level of intellectual development of the child is of great importance.
Diagnosis of the level of intellectual development of children requires a thorough and comprehensive analysis by a qualified specialist - a psychologist. However, the practical implementation of such an individual examination of each child upon admission to school is not possible. At the same time, even to make an approximate judgment about the intelligence of children, it is necessary to have a methodology that would allow one to meet a number of conditions required for diagnosing intelligence.
Among them, first of all, it is necessary to mention the standardization of tests, which allows, to a certain extent, to avoid subjectivity in the selection of tasks and ensure equal opportunities for all children. The tasks in the method must be selected in such a way that it is possible to assess different aspects of the child’s intelligence and at the same time reduce the influence of his training (“training”). In addition, the technique must be sufficiently reliable and valid with comparative ease of use and little time consumption.
The development of this methodology was carried out on the basis of well-known foreign tests of cognitive abilities - KFT 1-3 by K. Heller and co-workers. KFT tests 1-3, developed at the University of Munich and intended for gifted first-graders.
Each MEDIS form consists of 4 subtests with 5 tasks of increasing difficulty. Before completing each subtest, two tasks similar to the test ones are performed in training. During this training, performing tasks together with the experimenter, the child must understand what he must do and find out everything that is not clear to him. Training tasks can be repeated if necessary.
MEDIS tasks, as in foreign tests, are presented in the form of pictures, which makes it possible to test children regardless of their reading ability. When completing tasks, the child is only required to choose the correct answer (cross out the oval under it) from several proposed ones. Before presenting the tasks, the child is shown an image of an oval, a crossed out oval under the selected picture, and a training exercise is carried out in crossing out the oval on command. All instructions and explanations are given orally by the experimenter.
First subtest aims to identifygeneral student awareness, their vocabulary. Among five to six images of objects, you need to mark the one named by the experimenter. The first tasks include the most common and familiar objects, such as "boot", and the last - rarer and lesser-known objects, such as "statue".
Second subtest provides an opportunity to assess the child's understandingquantitative and qualitative relationshipsbetween objects and phenomena: more - less, higher - lower, older - younger, etc. In the first tasks these relationships are unambiguous - the largest, the farthest, while in the last tasks the child needs, for example, to choose a picture where one object more than another, but less than a third.
The third subtest reveals level of logical thinking, analytical and synthetic activity of the child. Moreover, in tasks to eliminate the superfluous, both images of specific objects and figures with different numbers of elements are used.
Fourth subtestsent for diagnosismathematical abilities. It includes mathematical tasks for intelligence, which use various materials: arithmetic tasks, tasks for spatial thinking, identifying patterns, etc. To complete these tasks, the child must be able to count to ten and perform simple arithmetic operations (addition and subtraction) .
Thus, the variety of tasks in MEDIS makes it possible to cover different aspects of a child’s intellectual activity in minimal periods of time and obtain information both about his ability to learn in primary school and about the individual structure of his intelligence. This gives grounds for using MEDIS as the main part of a battery of methods for determining the readiness of children to learn in schools with educational programs of increased difficulty.
MEDIS can be used individually and in groups of 5-10 people. When examining children in groups, the experimenter needs the help of an assistant. The environment during testing should be calm and serious, without unnecessary tension. Each test taker must have his own test book, on the cover of which his first and last name must be indicated. During testing, monitoring of children is of great importance. In group testing, this task is performed primarily by the experimenter's assistant. This observation allows us to avoid cases of the child misunderstanding the instructions and at the same time obtain additional information about the readiness of children to learn at school and the individual characteristics of their behavior.
It should be taken into account that the group testing environment may be extremely unfavorable for some children: those with increased anxiety, confused by the new environment, etc. In such cases, it is recommended to repeat the testing using a different form of test or supplement it with an individual psychological and pedagogical examination.
All MEDIS tasks are completed without a time limit. The pace at which the experimenter reads the tasks should depend on the speed at which the children complete the tasks; it may differ in different groups. At the same time, children should not be forced to complete the task at a certain pace. Children who work quickly need 15 seconds to complete each task. Children who work slowly may need 20-25 seconds. The speed of reading tasks should not remain constant when moving from one task to another in different test parts.
When planning testing, it is important to take into account not only the time required to complete the tasks of the corresponding part of the methodology, but also the time required to distribute test materials, explain how to perform the test, and work with children on the training examples given at the beginning of each subtest. The total test time is on average 20-30 minutes.
When interpreting the results of this technique, it should be taken into account that, like any other test, MEDIS cannot serve as the only criterion for making decisions about the level of intellectual development of a child, about his selection for training in special programs, about the profile of his abilities. Test results should be considered in conjunction with other indicators: data from an interview with the child, information from parents, indicators of the child’s interests, etc.
Instructions: All test tasks are spoken no more than 2 times!
Task 1 - awareness.
1- show the rodent (correct answerin the 5th picture),
2- acrobat (4),
3- edible (2),
4- plane (2),
5- biceps (4).
Task 2 - mathematical abilities.
1- show the bed where the flowers were planted before everyone else (3),
2- a picture in which the girl stands closer to the tree than the boy and the dog (4),
3- a picture in which a duck flies the lowest, but fastest (2),
4-degree thermometer, in which the temperature is higher than the lowest, but lower than all the others (4),
5- picture where the boy runs fast, but not faster than everyone else (1).
Task 3 - logical thinking.
In all tasks it is necessary to show the “extra”.
(right answers- 3, 4, 2, 2, 5).
Task 4 - quantitative and qualitative relationships.
1- find a rectangle in which there are more than 6 sticks, but less than 12 (3),
2- We drew a row of dominoes, but forgot to draw one. Which domino do you need to take on the right to continue this row? (2),
3- choose a cube that has one more point than this cube on the left (4),
4- count the sticks in the cubes on the left. Which cube has more sticks? Show how much more (1)
5- show the plate on which the least amount of cake was eaten (3).
FULL NAME. ___________________________________________________________
Research Date ________________________________________________
MEDIS subtests | 5- high | 4- above average |
Parents who want to teach their child mathematics are faced with the question of what exactly needs to be taught to the child. What abilities can and should be developed in preschool age to ensure successful completion of the school curriculum.
What abilities are considered mathematical in children under 7 years of age?
You should not think that mathematical abilities only mean the ability to count quickly and accurately. It's a delusion. Mathematical abilities include a whole range of skills aimed at creativity, logic, and counting.
The speed of counting and the ability to memorize a large array of numbers and data are not genuine mathematical abilities, since even a slow and thorough child who studies thoughtfully can successfully comprehend mathematics.
Mathematical abilities include:
- Ability to generalize mathematical material.
- The ability to see what different objects have in common.
- The ability to find the main thing in a large amount of different information and exclude what is not necessary.
- Use numbers and signs.
- Logical thinking.
- The child's ability to think in abstract structures. The ability to distract yourself from the task at hand and see the resulting picture as a whole.
- Think both forward and backward.
- The ability to think independently without using templates.
- Developed mathematical memory. Ability to use acquired knowledge in various situations.
- Spatial thinking – confident use of the concepts of “up”, “down”, “right” and “left”.
How are mathematical abilities formed?
All abilities, including mathematical ones, are not a predetermined skill. They are formed and developed through training and reinforced by practice. Therefore, it is important not only to develop this or that ability, but also to improve it through practical exercises, bringing it to automatism.
Any ability goes through several stages in its development:
- Cognition. The child gets acquainted with the subject and learns the necessary material;
- Application. Applies new knowledge in independent play;
- Consolidation. Returns to classes and repeats what was previously learned;
- Application. Using fixed material when playing independently;
- Extension. There is an expansion of knowledge about the subject or ability;
- Application. The child supplements independent play with new knowledge;
- Adaptation. Knowledge is transferred from the game situation to life.
Any new knowledge must go through the application stage several times. Give your child the opportunity to use the received data in independent play. Children need some time to comprehend and consolidate every minor change in knowledge.
If a child cannot master the acquired skill or knowledge through independent play, there is a high probability that it will not be consolidated. Therefore, after each lesson, let your baby go out to play or take a break and play with him. During the game, show how to use new knowledge.
How to develop mathematical abilities in a child
You need to start mathematical development in the form of a game and use things that will interest your baby. For example, toys and household items that he encounters every day.
From the moment the child shows interest in a particular object, the parent begins to show the child that the object can not only be examined and touched, but also perform various actions with it. By focusing on some features of an object (color, shape), in an unobtrusive manner, you can show the difference in the number of objects and introduce the first concepts of plurality and spatial position.
After the child learns to separate objects into groups, you can show that they can be counted and sorted. Pay attention to geometric features.
The development of mathematical abilities must go simultaneously with the basics of number operations.
Any new knowledge should be presented with the child’s clear interest in learning. If there is no interest in the subject and its study, the child should not be taught. It is important to maintain a balance in your child's learning to develop a love for mathematics. Almost all problems associated with studying the foundations of this discipline have their origin in the initial lack of desire to know.
What to do if your child is not interested
If your child gets bored every time you try to teach him the basics of mathematics, then you need to:
- Change the form of presentation of the material. Most likely, your explanations are too complex for the child to understand and do not contain game elements. Preschool children cannot perceive information in the classical form of a lesson; they need to be shown and told new material during games or entertainment. Dry text is not perceived by a child. Use it in teaching or try to involve the child directly in teaching;
- Show interest in the subject without your child's participation. Young children are interested in everything that interests their parents. They love to imitate and copy adults. If the child does not show interest in any activity, then try to start playing with the selected objects in front of the child. Talk out loud about what you are doing. Show your own interest in the game process. The child will see your interest and join;
- If the child still quickly loses interest in the subject, you need to check whether the knowledge and skills that you want to instill in him are too difficult or easy;
- Keep in mind the length of classes for different ages. If a child under 4 years old loses interest in a subject after 5 minutes, then this is normal. Since at this age it is difficult for him to concentrate on one subject for a long time.
- Try introducing one element at a time into your lesson. For children 5-7 years old, the duration of classes should not exceed 30 minutes.
- Don't be upset if your child doesn't want to study on a particular day. You need to try to involve him in training after some time.
The main thing to remember:
- The material must be adapted to the age of the child;
- The parent must show interest in the child’s material and results;
- The child must be ready for class.
How to develop mathematical thinking
The order of teaching a child mathematical thinking consists of interconnected activities that are presented in order of increasing complexity of the material.
1. You need to start learning with concepts about the spatial arrangement of objects
The child must understand where right is left. What is “above”, “below”, “before” and “behind”. Having this skill allows you to perceive all subsequent activities easier. Orientation in space is fundamental knowledge not only for the development of mathematical abilities, but also for teaching a child to read and write.
You can offer your child the following game. Take a few of his favorite toys and place them at different distances in front of him. Ask him to show which toy is closer, which is further, which is to the left, etc. If you have any difficulty choosing, please tell me the correct answer. Use different variants of words in this game that determine the location of objects relative to the baby.
Use this approach to learning and repetition not only in class, but also in everyday life. For example, ask your child to determine the spatial arrangement of objects on the playground. More often in everyday life, ask for something, orienting the baby in space.
In parallel with spatial thinking, they teach generalization and classification of objects according to their external features and functionality.
2. Explore the concept of set of objects
The child must distinguish between the concepts many - few, one - many, more - less and equally. Offer different types of toys in different quantities. Offer to count them and say how many or few there are, which toys are fewer and vice versa, also show the equality of toys.
A good game to reinforce the concept of set is “What’s in the Box.” The child is offered two boxes or drawers containing different numbers of items. By moving objects between boxes, the child is asked to make the number of objects more or less, to equalize. Under the age of 3 years, the number of objects should not be large so that the child can clearly assess the difference in objects without counting.
3. It is important to teach a child simple geometric shapes in early childhood.
Teach your child to see them in the world around them. It is good to use applications from mathematical shapes to develop knowledge of geometric shapes. Show your child a drawing of an object with clear contours (house, car). Offer to make an image of an object from prepared triangles, squares and circles.
Show and explain what the angle of the figures is, invite the child to guess why the “triangle” has such a name. Offer your child to familiarize himself with figures with a large number of angles.
Consolidate geometric knowledge by drawing the studied material, folding different figures from other objects (sticks, pebbles, etc.). You can use plasticine and other materials to create different shapes.
Ask them to draw a number of different types of shapes and count them with your child. Ask which figures are many and which are few.
When walking with your child, pay attention to the shape of houses, benches, cars, etc. Show how combining different shapes can create new and familiar objects.
4. The ability to navigate in space and classify objects allows you to teach measuring the size of an object
Early learning to measure length with a ruler and using centimeters is not recommended, as this will be difficult to understand material. Try measuring objects with your child using sticks, ribbons and other materials at hand. This training does not involve the measurement itself, but the principle of its implementation.
Most teachers advise teaching your child to measure using counting sticks. They justify this by convenience for the child and teaching him to use special material. These sticks will come in handy when learning units of counting. They can also be used as visual material when working with books (putting a stick aside according to the number of characters), studying geometric shapes (a child can lay out the desired shape with chopsticks), etc.
5. Quantitative measurements
After learning basic math concepts, you can move on to quantitative measurements and studying numbers. The study of numbers and their written notation occurs from an early age according to a certain system.
6. Addition and subtraction
Only after mastering quantitative measurements and numbers should you introduce addition and subtraction. Addition and subtraction are introduced at the age of 5-6 years and are the simplest one-step operations with small numbers.
7. Division
Division in preschool age is introduced only at the level of shares, when the child is asked to divide an object into equal shares. The number of such parts should not exceed four.
Examples of activities with a child to develop mathematical abilities
To solve this problem, you don’t need any sophisticated methods, you just need to make some additions to your everyday life.
- When walking outside, invite your child to count any items or objects (tiles, cars, trees). Point to many objects, ask to find a generalizing feature;
- Encourage your child to solve problems to find the correct answer by guiding him. For example, Masha has 3 apples, and Katya has 5, Lena has one more apple than Masha and one less than Katya. The problem can be simplified by asking what number is between 1 and 3;
- Clearly explain to your child what addition and subtraction are. Do this on apples, toys or any other objects. Let your child touch objects and show these simple operations by adding or subtracting an object;
- Ask your child what the differences between objects are;
- Show what scales are and how they work. Explain that weight can not only be felt by holding an object in your hands, but can also be measured in numbers;
- Teach how to use a clock with hands;
- Pay special attention to the spatial arrangement of objects;
- You can study shapes not only on cards, but also look for them in objects around;
- Show your child that mathematics is in everything around him, if you just look closely.
What additional materials will help teach your child mathematics?
- Cards and pictures with different numbers of objects, with numbers and mathematical symbols, geometric figures;
- Magnetic or chalk board;
- Clock with hand and scales;
- Counting sticks;
- Construction sets and puzzles;
- Checkers and chess;
- Lotto and dominoes;
- Books that contain counting and allow you to carry out mathematical operations;
- Methodological aids for the development of logic and other abilities according to the child’s age.
Tips for parents who want to teach their child the basics of mathematics
1. Encourage your child to find answers. Help him find them by reasoning. Don't scold for mistakes or laugh at incorrect answers. Each child’s attempt to draw a conclusion or solve a problem trains his abilities and allows him to consolidate knowledge;
2. Use your playtime to develop essential skills. Focus on what has been studied previously, show how new and already learned material can be used in practice. Create situations in which the child will need to use knowledge to achieve a certain result;
3. Do not overload your child with a large amount of new information. Give him time to comprehend the acquired knowledge through free play;
4. Combine the development of mathematical abilities with spiritual and physical development. Introduce counting into physical education classes and logic into reading and role-playing games. Diversified development of the child - the path to the full development of the baby. A physically and spiritually developed child comprehends mathematics much easier;
5. When teaching a child, try to use all channels of information absorption. In addition to the oral story, show this on various objects, give the opportunity to touch and evaluate the weight and texture. Use a variety of forms of presenting information. Show how you can use the acquired knowledge in life;
6. Any material should be in the form of a game that will interest the child. Excitement and involvement in the process are good for remembering. If your child is not interested in the material, stop. Think about what was done wrong and correct it. Each child is individual. Find a method that suits your baby and use it;
7. The ability to concentrate on a task and remember the conditions is important for the successful development of mathematical fundamentals. Ask a question about what the child understood from the given task after each condition. Work to improve concentration;
8. Before asking your child to decide on his own, show an example of how to reason and decide. Even if the child has carried out a certain calculation operation more than once, remind him of the procedure. It is better to show the correct course of action than to allow the child to reinforce the wrong approach;
9. Don't force your child to study if he doesn't want to. If the baby wants to play, then give him this opportunity. Offer to study after some time;
10. Try to diversify knowledge in one lesson. The best option would be if during the day you pay a little attention to a variety of areas of mathematical knowledge than if you memorize the same type of material, bringing it to automatism;
11. The task of a parent in preschool age is not to teach counting and calculations, but to develop abilities. If you don’t teach your child to add and subtract before school, it’s okay. If a child has mathematical thinking and knows how to draw conclusions, then he will be able to comprehend any complex operations quickly and at school.
What books help develop mathematical abilities?
The solution to the issue of teaching mathematics to a child under 7 years old with the help of books begins from an early age. For example, the fairy tale “Teremok”. In it, the appearance of various characters occurs as they increase in size. Using this example, you can teach your child the concepts of big and small. Try playing this fairy tale in a paper theater. Invite your child to place the figures of the fairy tale characters in the correct order and tell the story. The fairy tale “Turnip” also teaches the child the concepts of more and less, but its plot develops from the opposite (from large to small).
It will be useful from a mathematical point of view to study the fairy tale “The Three Bears” through the concepts of large, medium and small; the child can easily master counting to three.
When choosing books to read to your child, pay attention to the following:
- The presence of an account in the book and the possibility of comparing heroes according to certain criteria;
- The images in the book should be large and interesting. Using them, you can show your child what geometric shapes are used to create different objects (a house is a triangle and a square, the hero’s head is a circle, etc.);
- Any plot should develop linearly and contain certain conclusions at the end. Avoid books with complex plots that do not develop linearly. Teach your child that any action has its consequences and how to draw conclusions. This approach will help you more easily understand the principles of logical thinking;
- Books should be selected according to age.
There are a large number of different publications on sale that allow you to familiarize yourself with most mathematical operations and terms using the examples of heroes. The main thing is to discuss the material read with your child and ask leading questions that will stimulate the development of mathematical abilities.
Buy methodological books for developing your child’s mathematical abilities according to his age. Now there are a large number of different materials that contain tasks for the development of a child’s mathematical abilities. Bring such publications into the game. Remind your child of the tasks he previously completed using this publication to solve new problems.
Developing a child's mathematical abilities is not a difficult task. A child under 7 years old seeks new knowledge on his own and is happy when it is presented to him in a playful way. Find a lesson option that suits your child and have fun learning math basics.
Topic 6.
DIAGNOSTICS OF MATHEMATICAL ABILITIES OF SENIOR PRESCHOOL CHILDREN
There is a significant variety of types of giftedness that can manifest themselves already in preschool age. Among them is intellectual giftedness, which largely determines a child’s aptitude for mathematics and develops intellectual, cognitive, and creative abilities.
Children with intellectual giftedness are characterized by the following features:
- highly developed curiosity, inquisitiveness; the ability to “see” yourself, find problems and the desire to solve them, actively experimenting; high (relative to age-related capabilities) stability of attention when immersed in cognitive activity (in the area of his interests); early manifestation of the desire to classify objects and phenomena, discover cause-and-effect relationships; developed speech, good memory, high interest in new and unusual things; the ability to creatively transform images and improvise; early development of sensory abilities; originality of judgment, high learning ability; desire for independence.
The main areas of work with children with a penchant for mathematics include: determining the child’s aptitude, developing individual programs for the development of the child’s abilities, and additional education.
I want to focus on the first stage - determining the child’s aptitude for mathematics.
In view of the implementation of the Federal State Educational Standard in the educational process of preschool educational institutions, the issue of monitoring the quality of preschool education has become especially acute. It is necessary to competently approach the issue of diagnosing the levels of development of children. In the modern understanding, pedagogical diagnostics is a system of methods and techniques, specially developed pedagogical technologies, test tasks that allow us to determine the level of professional competence of teachers and the level of development of a preschool child. Its main purpose is to analyze and eliminate the causes that give rise to shortcomings in work, accumulate and disseminate teaching experience, stimulate creativity and pedagogical skill.
Purpose of diagnosis: tracking achievements in a child’s mastery of the means and methods of cognition, identifying gifted children in the field of mathematical development.
Form of organization: problem-game situations conducted individually with each child.
We have proposed several diagnostic situations: “Enter the hut”, “Let’s restore the ladder”, “Correct the mistakes”, “Which days are missed” and “Whose backpack is heavier”.
Diagnostic situation “Enter the hut”
Goal: to identify the practical skills of children 5-6 years old in composing numbers from 2 smaller ones and in carrying out search actions.
On three huts located in a row, the numbers (6, 9,7 respectively) indicate the number of gold coins. Traces lead to the huts. Only the one who opens the door can take the coins. To do this, you need to step on the left and right footprints together as many times as the number shows. (Mark with pencil).
Teacher: Which hut did you choose? What tracks will you step on? If you want, then enter other huts?
Diagnostic situation “Correct the mistakes and name the next move”
The goal is to identify children’s ability to follow the sequence of moves, offer options for correcting mistakes, reason, and mentally justify the course of their actions.
The situation is being organized without practical action. The child watches the adult’s progress, comments on his own move, and corrects mistakes.
Teacher: Imagine that you and I are playing dominoes. Some of us made mistakes. Find them and fix them. The first move was mine (left).
As errors are discovered, the child is asked the question: “Which of us made mistakes? How can I fix them using additional chips?”
As a result, generally low results were obtained for the group. At the beginning of the school year, the use of these methods turned out to be inappropriate. The knowledge of most children is not sufficiently formed, the ability to reason and justify actions is poorly expressed. In addition, the proposed situations are not enough to diagnose all areas of children’s mathematical development.
After the diagnosis, teachers were given the following recommendations:
1. Analyze the subject-game development environment
2. Initiate the creative cognitive activity of individual children (personal participation of the teacher in children's activities, creation of gaming communities, motivation)
3. Select games and gaming materials necessary for independent mastery of the actions necessary in a given period (knowledge of the dependencies between numbers, quantities in the conditions of a serial series)
4. Practice organizing and conducting leisure activities, children's games, projects, and joint events with parents.
5. Develop your own pedagogical creative potential. (accompanied by slide)
To carry out repeated diagnostics in September, the author’s diagnostic methods of Anna Vitalievna Beloshistaya were chosen, since it was her developments, in my opinion, that are most accessible, feasible and understandable to children and teachers. The positive aspects of these diagnostic methods are their simplicity, small amount of handouts, which significantly speeds up the diagnostic procedure, especially since all types of diagnostics must be carried out during scheduled moments, and most of them, according to the instructions, are carried out individually. The author focuses on aspects of developmental learning and the personal-activity successive approach.
1. Diagnostic situation of analytical-synthetic activity
(adapted technique)
Goal: to identify the maturity of the analysis and synthesis skills of children aged 5-6 years.
Objectives: assessment of the ability to compare and generalize objects based on characteristics, knowledge of the shape of the simplest geometric figures, the ability to classify material according to an independently found basis.
Presentation of the task: the diagnosis consists of several stages, which are offered to the child one by one. Conducted individually.
Material: set of figures - five circles (blue: large and two small, green: large and small), small red square. (Slide “Circles”)
diagnostic situation
Assignment: “Determine which of the figures in this set is extra. (Square.) Explain why. (All the rest are circles.).”
Material: the same as for No. 1, but without the square.
Assignment: “The remaining circles were divided into two groups. Explain why you divided it this way. (By color, by size.).”
Material: the same and cards with numbers 2 and 3.
Assignment: “What does the number 2 mean on circles? (Two big circles, two green circles.) Number 3? (Three blue circles, three small circles.).”
Assignment rating:
Slide with a photo of a child
2. Diagnostic situation “What is unnecessary”
(methodology)
Purpose: to determine the development of visual analysis skills in children aged 5-6 years.
Option 1.
Material: drawing of figurines-faces. (slide “Faces”)
diagnostic task
Assignment: “One of the figures is different from all the others. Which? (Fourth.) How is it different?”
Option 2.
Material: drawing of human figures.
diagnostic task
Assignment: “Among these figures there is an extra one. Find her. (Fifth figure.) Why is she extra?”
Assignment rating:
Level 1 – task completed completely correctly
Level 2 – 1-2 mistakes made
Level 3 – task completed with the help of an adult
Level 4 – the child finds it difficult to answer the question even after prompting
3. Diagnostic situation for analysis and synthesis
for children 5 – 7 years old (methodology)
Goal: to determine the degree of development of the skill of isolating a figure from a composition formed by superimposing some forms on others, to identify the level of knowledge of geometric figures.
Presentation of the task: individually with each child. In 2 stages.
Material: 4 identical triangles. (slide)
diagnostic task
Assignment: “Take two triangles and fold them into one. Now take the other two triangles and fold them into another triangle, but of a different shape. What is the difference? (One is tall, the other is low; one is narrow, the other is wide.) Is it possible to make a rectangle out of these two triangles? (Yes.) Square? (No.)".
Material: drawing of two small triangles forming one large one. (slide)
diagnostic task
Assignment: “There are three triangles hidden in this picture. Find them and show them."
Assignment rating:
Level 1 – task completed completely correctly
Level 2 – 1-2 mistakes made
Level 3 – task completed with the help of an adult
Level 4 – the child did not complete the task
4. Diagnostic test.
Initial mathematical representations (methodology)
Purpose: to determine children’s ideas about relationships more than; less by; about quantitative and ordinal counting, about the shape of the simplest geometric figures.
Material: 7 any objects or their images on a magnetic board. Items can be either the same or different. The task can be offered to a subgroup of children. (slide “Yula”)
diagnostic task
Method of execution: the child is given a sheet of paper and a pencil. The task consists of several parts that are offered sequentially.
A. Draw as many circles on the sheet as there are objects on the board.
B. Draw 1 more squares than circles.
B. Draw 2 less triangles than circles.
D. Draw a line around 6 squares.
D. Color in the 5th circle.
Assignment rating:
Level 1 – task completed completely correctly
Level 2 – 1-2 mistakes made
Level 3 – 3-4 mistakes made
Level 4 – 5 mistakes were made.
During diagnostics, visual material can be provided to children in a multimedia version or on a magnetic board, if the instructions for conducting it do not require practical actions with it. The material should be colorful, age-appropriate, aesthetically designed, appropriate for the number of children.
The proposed methods No. 1 – 2 are carried out in September, as one of the stages of initial monitoring. Methods No. 3-4 – in May, to determine the result of children’s mathematical development.
Only after carrying out several diagnostics is a conclusion drawn up about the maturity of the child’s knowledge, skills and abilities, the results of which are entered into the table: (slide of an empty table)
As a result of the work carried out over the year in accordance with these recommendations for teachers to enrich the group environment in the field of mathematical development, as well as thanks to the diagnostic methods selected in accordance with the tasks of the educational educational institution in May, we came to the following results: (tables)
Analysis-synthesis | Concept of form | Initial mat. representation | |||||||
Total for the group |
As can be seen from the above data, the level of knowledge, both individually and in the group as a whole, has increased significantly. During the diagnostic process, gifted children were identified who easily coped with the situations proposed by the teacher and quickly and accurately found the right solutions.
In order to further develop the mathematical abilities of gifted children, teachers were asked to continue working with these children individually: in special moments, in joint targeted activities with the teacher in the field of mathematical development.
Bibliography:
1. Monitoring in kindergarten. Scientific and methodological manual. – SPb.: PUBLISHING HOUSE “CHILDHOOD-PRESS”, 2011. – 592 p.
2. Management of the educational process in preschool educational institutions. Toolkit/ , . – M.: Iris-press, 2006. – 224 p.
3. Formation and development of mathematical abilities of preschoolers. Toolkit. / . – M.: Arkti, 2004.
· Make sure that the child is emotionally positive about communication.
·Tasks are offered in strict accordance with the instructions.
· An assessment of a child’s mathematical development is made based on the results of several diagnostics.
· The choice of a specific diagnostic technique is made in accordance with the basic and basic general education program of the preschool educational institution.
· When summing up, you should take into account the results of short-term observations of the child, his behavior in a new game, in a creative or problematic situation.
Summary: Development of mathematical abilities in children. More than twenty exercises for the development of logical and mathematical thinking in a child. Training in the ability to compare, classify, analyze and summarize the results of one’s activities.
Both parents and teachers know that mathematics is a powerful factor in the intellectual development of a child, the formation of his cognitive and creative abilities. It is also known that the success of teaching mathematics in primary school depends on the effectiveness of a child’s mathematical development in preschool age.
Why do many children find mathematics so difficult not only in elementary school, but even now, during the period of preparation for educational activities? Let's try to answer this question and show why generally accepted approaches to the mathematical preparation of a preschool child often do not bring the desired positive results.
In modern primary school educational programs, important importance is attached to the logical component. The development of a child’s logical thinking implies the formation of logical techniques of mental activity, as well as the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build simple conclusions based on cause-and-effect relationships. So that the student does not experience difficulties literally from the first lessons and does not have to learn from scratch, already now, in the preschool period, it is necessary to prepare the child accordingly.
Many parents believe that the main thing in preparing for school is to introduce the child to numbers and teach him to write, count, add and subtract (in fact, this usually results in an attempt to memorize the results of addition and subtraction within 10). However, when teaching mathematics using textbooks of modern developmental systems (L. V. Zankov’s system, V. V. Davydov’s system, the “Harmony” system, “School 2100”, etc.), these skills do not help the child in mathematics lessons for very long. The stock of memorized knowledge ends very quickly (in a month or two), and the lack of development of one’s own ability to think productively (that is, to independently perform the above-mentioned mental actions based on mathematical content) very quickly leads to the appearance of “problems with mathematics.”
At the same time, a child with developed logical thinking always has a greater chance of being successful in mathematics, even if he was not previously taught the elements of the school curriculum (counting, calculations, etc.). It is no coincidence that in recent years, many schools working on developmental programs have conducted interviews with children entering first grade, the main content of which is questions and tasks of a logical, and not just arithmetic, nature. Is this approach to selecting children for education logical? Yes, it is natural, since the mathematics textbooks of these systems are structured in such a way that already in the first lessons the child must use the ability to compare, classify, analyze and generalize the results of his activities.
However, one should not think that developed logical thinking is a natural gift, the presence or absence of which should be accepted. There is a large number of studies confirming that the development of logical thinking can and should be done (even in cases where the child’s natural abilities in this area are very modest). First of all, let's figure out what logical thinking consists of.
Logical techniques of mental actions - comparison, generalization, analysis, synthesis, classification, seriation, analogy, systematization, abstraction - are also called logical thinking techniques in the literature. When organizing special developmental work on the formation and development of logical thinking techniques, a significant increase in the effectiveness of this process is observed, regardless of the initial level of development of the child.
It is most advisable to develop the logical thinking of a preschooler in line with mathematical development. The process of a child’s assimilation of knowledge in this area is further enhanced by the use of tasks that actively develop fine motor skills, that is, tasks of a logical and constructive nature. In addition, there are various methods of mental action that help enhance the effectiveness of using logical-constructive tasks.
Seriation is the construction of ordered increasing or decreasing series based on a selected characteristic. A classic example of seriation: nesting dolls, pyramids, insert bowls, etc.
Series can be organized by size, by length, by height, by width if the objects are of the same type (dolls, sticks, ribbons, pebbles, etc.), and simply by size (with an indication of what is considered size) if the objects different types (seat toys according to height). Series can be organized by color, for example, by the degree of color intensity (arrange jars of colored water according to the degree of color intensity of the solution).
Analysis is the selection of the properties of an object, or the selection of an object from a group, or the selection of a group of objects according to a certain criterion.
For example, the attribute is given: “Find all sour”. First, each object in the set is checked for the presence or absence of this attribute, and then they are isolated and combined into a group based on the “sour” attribute.
Synthesis is the combination of various elements (signs, properties) into a single whole. In psychology, analysis and synthesis are considered as mutually complementary processes (analysis is carried out through synthesis, and synthesis is carried out through analysis).
Tasks to develop the ability to identify the elements of a particular object (features), as well as to combine them into a single whole, can be offered from the very first steps of the child’s mathematical development. Let us give, for example, several such tasks for children two to four years old.
1. A task to select an object from a group based on any criterion: “Take the red ball”; “Take the red one, but not the ball”; "Take the ball, but not the red one."
2. A task to select several objects according to the specified criterion: “Choose all the balls”; “Choose round balls, but not balls.”
3. A task to select one or more objects based on several specified characteristics: “Choose a small blue ball”; "Pick a big red ball." The last type of task involves combining two characteristics of an object into a single whole.
Analytical-synthetic mental activity allows the child to consider the same object from different points of view: as big or small, red or yellow, round or square, etc. However, we are not talking about introducing a large number of objects, quite the contrary, in a way organizing a comprehensive review is the technique of setting various tasks for the same mathematical object.
As an example of organizing activities that develop a child’s ability to analyze and synthesize, we will give several exercises for children five to six years old.
Exercise 1
Material: set of figures - five circles (blue: large and two small, green: large and small), small red square.
Assignment: “Determine which of the figures in this set is extra. (Square.) Explain why. (All the rest are circles.).”
Exercise 2
Material: the same as for Exercise 1, but without the square.
Assignment: “Divide the remaining circles into two groups. Explain why you divided them this way. (By color, by size.).”
Exercise 3
Material: the same and cards with numbers 2 and 3.
Assignment: “What does the number 2 mean on the circles? (Two large circles, two green circles.) The number 3? (Three blue circles, three small circles.).”
Exercise 4
Material: the same didactic set (a set of plastic figures: colored squares, circles and triangles).
Assignment: “Remember what color was the square that we removed? (Red.) Open the box, Didactic set.” Find the red square. What other colors are there squares? Take as many squares as there are circles (see exercises 2, 3). How many squares? (Five.) Can you make one big square out of them? (No.) Add as many squares as needed. How many squares did you add? (Four.) How many are there now? (Nine.)".
The traditional form of tasks for the development of visual analysis are tasks for choosing an “extra” figure (object). Here are a few tasks for children five to six years old.
Exercise 5
Material: drawing of figurines-faces.
Assignment: “One of the figures is different from all the others. Which one? (The fourth one.) How is it different?”
Exercise 6
Material: drawing of human figures.
Task: “Among these figures there is an extra one. Find it. (Fifth figure.) Why is it extra?”
A more complex form of such a task is the task of isolating a figure from a composition formed by superimposing some forms on others. Such tasks can be offered to children five to seven years old.
Exercise 7
Material: drawing of two small triangles forming one large one.
Assignment: “There are three triangles hidden in this picture. Find and show them.”
Note. You need to help the child show the triangles correctly (circle with a small pointer or finger).
As preparatory tasks, it is useful to use tasks that require the child to synthesize compositions from geometric shapes at the material level (from material material).
Exercise 8
Material: 4 identical triangles.
Assignment: “Take two triangles and fold them into one. Now take two other triangles and fold them into another triangle, but of a different shape. How are they different? (One is tall, the other is low; one is narrow, the other is wide.) You can Is it possible to make a rectangle out of these two triangles? (Yes.) A square? (No.)."
Psychologically, the ability to synthesize is formed in a child earlier than the ability to analyze. That is, if a child knows how it was assembled (folded, designed), it is easier for him to analyze and identify its component parts. That is why such serious importance is given in preschool age to activities that actively form synthesis - construction.
At first, this is a patterned activity, that is, performing tasks of the “do as I do” type. At first, the child learns to reproduce the object, repeating the entire construction process after the adult; then - repeating the process of construction from memory, and finally moves on to the third stage: independently restores the method of constructing a ready-made object (tasks like “make the same one”). The fourth stage of tasks of this kind is creative: “build a tall house”, “build a garage for this car”, “build a rooster”. The tasks are given without a sample, the child works according to the idea, but must adhere to the given parameters: a garage specifically for this car.
For construction, any mosaics, construction sets, cubes, cut-out pictures are used that are suitable for this age and make the child want to tinker with them. An adult plays the role of an unobtrusive assistant; his goal is to help bring the work to completion, that is, until the intended or required whole object is obtained.
Comparison is a logical method of mental action that requires identifying similarities and differences between the characteristics of an object (object, phenomenon, group of objects).
Performing a comparison requires the ability to identify some features of an object (or group of objects) and abstract from others. To highlight various characteristics of an object, you can use the game “Find it using the specified characteristics”: “Which (of these objects) is big yellow? (Ball and bear.) What is big yellow and round? (Ball.)”, etc.
The child should use the role of the leader as often as the answerer, this will prepare him for the next stage - the ability to answer the question: “What can you tell about him? (The watermelon is large, round, green. The sun is round, yellow, hot.)” . Or: “Who will tell you more about this? (The ribbon is long, blue, shiny, silk.).” Or: “What is this: white, cold, crumbly?” etc.
Types of comparison tasks:
1. Tasks to separate a group of objects according to some criteria (large and small, red and blue, etc.).
2. All games of the “Find the same” type. For a child two to four years old, the set of characteristics by which similarities are sought should be clearly defined. For older children, exercises are offered in which the number and nature of similarities can vary widely.
Let us give examples of tasks for children five to six years old, in which the child is required to compare the same objects according to various criteria.
Exercise 9
Material: images of two apples, a small yellow one and a large red one. The child has a set of shapes: a blue triangle, a red square, a small green circle, a large yellow circle, a red triangle, a yellow square.
Assignment: “Find one that looks like an apple among your figures.” An adult offers to look at each image of an apple in turn. The child selects a similar figure, choosing a basis for comparison: color, shape. “Which figure can be called similar to both apples? (Circles. They are similar in shape to apples.).”
Exercise 10
Material: the same set of cards with numbers from 1 to 9.
Assignment: “Put all the yellow figures to the right. What number fits this group? Why 2? (Two figures.) What other group can be matched to this number? (A blue and red triangle - there are two of them; two red figures, two circles; two square - all options are analyzed.)". The child makes groups, uses a stencil frame to sketch and paint them, then signs the number 2 under each group. “Take all the blue figures. How many are there? (One.) How many colors are there in total? (Four.) Figures? (Six.) ".
The ability to identify the characteristics of an object and, focusing on them, to compare objects is universal, applicable to any class of objects. Once formed and well developed, this skill will then be transferred by the child to any situations requiring its use.
An indicator of the maturity of the comparison technique will be the child’s ability to independently apply it in activities without special instructions from an adult on the signs by which objects need to be compared.
Classification is the division of a set into groups according to some criterion, which is called the basis of classification. Classification can be carried out either according to a given basis, or with the task of searching for the basis itself (this option is more often used with children six to seven years old, as it requires a certain level of formation of the operations of analysis, comparison and generalization).
It should be taken into account that when classifying a set, the resulting subsets should not intersect in pairs and the union of all subsets should form this set. In other words, each object must be included in only one set, and with a correctly defined basis for classification, not a single object will remain outside the groups defined by this basis.
Classification with preschool children can be carried out:
By name (cups and plates, shells and pebbles, skittles and balls, etc.);
- by size (large balls in one group, small ones in another, long pencils in one box, short pencils in another, etc.);
- by color (this box has red buttons, this one has green buttons);
- in shape (this box contains squares, and this box contains circles; this box contains cubes, this box contains bricks, etc.);
- based on other non-mathematical characteristics: what can and cannot be eaten; who flies, who runs, who swims; who lives in the house and who in the forest; what happens in summer and what happens in winter; what grows in the garden and what in the forest, etc.
All of the examples listed above are classifications based on a given basis: the adult communicates it to the child, and the child carries out the division. In another case, classification is performed on a basis determined by the child independently. Here, the adult sets the number of groups into which many objects (objects) should be divided, and the child independently looks for the appropriate basis. Moreover, such a basis can be determined in more than one way.
For example, tasks for children five to seven years old.
Exercise 11
Material: several circles of the same size, but different colors (two colors).
Assignment: “Divide the circles into two groups. By what criteria can this be done? (By color.).”
Exercise 12
Material: several squares of the same colors are added to the previous set (two colors). The figures are mixed.
Assignment: “Try to divide the figures into two groups again.” There are two options for separation: by shape and by color. An adult helps the child clarify the wording. The child usually says: “These are circles, these are squares.” The adult generalizes: “So, they divided it according to shape.”
In exercise 11, the classification was unambiguously specified by the corresponding set of figures on only one basis, and in exercise 12, the addition of a set of figures was deliberately made in such a way that classification on two different grounds became possible.
Generalization is the presentation in verbal form of the results of the comparison process.
Generalization is formed in preschool age as the identification and fixation of a common feature of two or more objects. A generalization is well understood by a child if it is the result of an activity carried out by him independently, for example, classification: these are all big, these are all small; these are all red, these are all blue; these all fly, these all run, etc.
All of the above examples of comparisons and classifications ended with generalizations. For preschoolers, empirical types of generalization are possible, that is, generalization of the results of their activities. To lead children to this kind of generalization, the adult organizes work on the task accordingly: selects objects of activity, asks questions in a specially designed sequence to lead the child to the desired generalization. When formulating a generalization, you should help the child construct it correctly, use the necessary terms and verbiage.
Here are examples of generalization tasks for children five to seven years old.
Exercise 14
Material: set of six figures of different shapes.
Assignment: “One of these figures is extra. Find it. (Figure 4.).” Children of this age are unfamiliar with the concept of a bulge, but they usually always point to this shape. They can explain it like this: “Her corner went inward.” This explanation is quite suitable. “How are all the other figures similar? (They have 4 corners, these are quadrilaterals.).”
When selecting material for a task, an adult must ensure that the child does not end up with a set that focuses the child on unimportant features of objects, which will encourage incorrect generalizations. It should be remembered that when making empirical generalizations, the child relies on external visible signs of objects, which does not always help to correctly reveal their essence and define the concept.
For example, in exercise 14, figure 4, in general, is also a quadrilateral, but non-convex. A child will become acquainted with figures of this kind only in the ninth grade of high school, where the definition of the concept “convex flat figure” is formulated in a geometry textbook. In this case, the first part of the task was focused on the operation of comparing and identifying a figure that differs in external shape from other figures in a given group. But the generalization is made based on a group of figures with characteristic features, frequently occurring quadrangles. If a child becomes interested in figure 4, an adult can note that it is also a quadrangle, but of an unusual shape. Forming in children the ability to independently make generalizations is extremely important from a general developmental point of view.
Next, we give an example of several interrelated exercises (tasks) of a logical and constructive nature on the formation of an idea of a triangle for five-year-old children. For modeling constructive activities, children use counting sticks, a stencil frame with slots in the shape of geometric shapes, paper, and colored pencils. The adult also uses sticks and figures.
Exercise 15
The purpose of the exercise is to prepare the child for subsequent modeling activities through simple constructive actions, to update counting skills, and to organize attention.
Assignment: “Take from the box as many sticks as I have (two). Place them in front of you the same way (vertically side by side). How many sticks? (Two.) What color sticks do you have (the sticks in the box are of two colors: red and green)? Make them different colors. What color are your sticks? (One is red, one is green.) One and one. How many are together? (Two.)."
Exercise 16
The purpose of the exercise is to organize constructive activities according to the model. Counting exercises, development of imagination, speech activity.
Material: counting sticks of two colors.
Assignment: “Take another stick and put it on top. How many sticks are there? Let’s count. (Three.) What does the figure look like? (Like a gate, the letter “P.”) What words start with “P”?”
Exercise 17
The purpose of the exercise is to develop observation, imagination and speech activity. Formation of the ability to evaluate the quantitative characteristics of a changing structure (without changing the number of elements).
Material: counting sticks of two colors.
Note: the first task of the exercise is also preparatory to the correct perception of the meaning of arithmetic operations. Assignment: “Move the top stick like this (the adult moves the stick down so that it is in the middle of the vertical sticks). Has the number of sticks changed? Why hasn’t it changed? (The stick has been rearranged, but not removed or added.) What does the figure look like now? ( With the letter "N".) Name the words starting with "N".
Exercise 18
The purpose of the exercise is to develop design skills, imagination, memory and attention.
Material: counting sticks of two colors.
Assignment: “What else can be put together from three sticks? (The child puts together figures and letters. Names them, comes up with words.).”
Exercise 19
The purpose of the exercise is to form an image of a triangle, a primary examination of the triangle model.
Material: counting sticks of two colors, a triangle drawn by an adult.
Task: “Make a figure out of sticks.” If the child does not fold the triangle himself, an adult helps him. “How many sticks were needed for this figure? (Three.) What kind of figure is this? (Triangle.) Why is it called that? (Three corners.).” If the child cannot name the figure, the adult suggests its name and asks the child to explain how he understands it. Next, the adult asks to trace the figure with a finger, count the corners (vertices), touching them with a finger.
Exercise 20
The purpose of the exercise is to consolidate the image of the triangle on the kinesthetic (tactile sensations) and visual level. Recognition of triangles among other figures (volume and stability of perception). Outlining and shading triangles (development of small muscles of the hand).
Note: the task is problematic because the frame used has several triangles and figures similar to them with sharp corners (rhombus, trapezoid).
Material: stencil frame with figures of different shapes.
Assignment: “Find a triangle on the frame. Circle it. Color in the triangle along the frame.” The shading is done inside the frame, the brush moves freely, the pencil “knocks” on the frame.
Exercise 21
The purpose of the exercise is to consolidate the visual image of a triangle. Recognition of the desired triangles among other triangles (perceptual accuracy). Development of imagination and attention. Development of fine motor skills.
Assignment: “Look at this drawing: here is a mother cat, a father cat and a kitten. What shapes are they made of? (Circles and triangles.) What triangle is needed for a kitten? For a mother cat? For a father cat? Draw your cat ". Then the child completes the drawings of the remaining cats, focusing on the sample, but independently. The adult draws attention to the fact that the father cat is the tallest. “Place the frame correctly so that the daddy cat turns out to be the tallest.”
Note: this exercise not only helps the child accumulate reserves of images of geometric figures, but also develops spatial thinking, since the figures on the stencil frame are located in different positions, and to find the one you need, you need to recognize it in a different position, and then rotate the frame to find it drawing in the position required by the drawing.
It is obvious that the child’s constructive activity in the process of performing these exercises develops not only the child’s mathematical abilities and logical thinking, but also his attention, imagination, trains motor skills, eye, spatial concepts, accuracy, etc.
Each of the above exercises is aimed at developing logical thinking techniques. For example, exercise 15 teaches the child to compare; exercise 16 - compare and generalize, as well as analyze; exercise 17 teaches analysis and comparison; exercise 18 - synthesis; exercise 19 - analysis, synthesis and generalization; exercise 20 - actual classification by attribute; exercise 21 teaches comparison, synthesis and elementary seriation.
The logical development of a child also presupposes the formation of the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build simple conclusions based on cause-and-effect relationships. It is easy to see that when completing all the above examples of tasks and task systems, the child practices these skills, since they are also based on mental actions: analysis, synthesis, generalization, etc.
Thus, two years before school it is possible to have a significant impact on the development of a preschooler’s mathematical abilities. Even if your child does not become an indispensable winner of mathematical Olympiads, he will not have problems with mathematics in elementary school, and if he does not have them in elementary school, then there is every reason to expect that he will not have them in the future.
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