First of all, you should evaluate natural talent trainee. The choice of further teaching methods will depend on this.
Natural affinity for mathematics
There are several important criteria ability assessments:
- knowledge of numerical and symbolic symbols;
- ability for logical thinking;
- ability for abstract thinking.
The lack of these abilities does not mean that you should give up learning. Just training should be carried out with a specialist and using special techniques.
Mathematical through testing, both in paper and electronic versions.
Development of mathematical abilities in a child
If you want to develop your child's ability to exact sciences, then you should submit the material to game form and under no circumstances force you to study. Contact with the teacher during the learning process is of great importance, as is the teacher’s ability to interest the student.
It should be remembered that children cannot sit in one place for a long time, so trying to force a child to sit and learn the material can only lead to a reluctance to learn. Today there are special techniques learning for children. And remember that the knowledge base laid down in childhood is the foundation of future abilities.
Ways to develop mathematical abilities
Having assessed the student’s natural abilities, mathematical abilities should be developed in accordance with his capabilities. While pursuing mathematics, a person must follow several rules.
- Regular brain training, solving problems and examples in the mind, performing calculations without computing devices, solving non-standard problems, building logical chains help develop mathematical abilities.
- Studying new products in the field of programming, mathematics, and biographies of famous personalities will help to intensify interest in mathematics.
- Look for leisure activities that will help develop logic, thinking, and memory. Crosswords and numbers, tasks, puzzles, board games and many other activities make you think, do mental calculations, and memorize numbers.
- Spend more time walking outdoors.
- Lead healthy image life: smoking, alcoholism and others bad habits negatively affect brain function.
- Compliance with the study and rest regime helps to stay in good shape, not get tired and make progress on the path to studying any subjects, including the exact sciences.
During development mathematical abilities should also be given great attention process independent search decisions and development of the student’s memory. The age of the child also plays an important role when choosing teaching methods. If children preschool age very easily perceive everything new and learn, then an adult is less receptive to new material and remembers worse. Methods preschool development are as efficient as possible; This is not only memorizing numbers, but solving problems on logical thinking, as well as the development of the child’s fine motor skills.
It is worth considering the fact that the development of mathematical abilities is also necessary for a child with pronounced humanitarian talents. After all modern man must be comprehensively developed to adapt to living conditions in the world of innovative technologies.
One of the most significant species activity in preschool age is play. Moreover, the child begins not only to take part in actions, but also to obey certain algorithms, rules, etc. This allows you to complicate the conditions over time, adding more and more new practical tasks.
Teaching numbers in a playful way can begin at 2-3 years of age.
Learning mathematics in a game
Educational games conducted by the parent for the purpose of development cognitive activity child, allow him to learn new knowledge and acquire the skills he needs in a simple and unobtrusive form. They perfectly develop fantasy and imagination, help the child remember and successfully put into practice forms of behavior. Thus, the child’s mental development reaches a qualitatively new level.
A game for a preschool child (especially when we're talking about about educational games) are not just entertainment. This is both labor and creative activity simultaneously. Its role in the development of a child as an emerging personality cannot be overestimated. By directing and organizing the game, the parent can also include it in pedagogical process, controlling all aspects social development child. A properly organized game is distinguished by the fact that it always contains specific goal, as well as the means necessary to achieve it.
The role of games in teaching preschoolers This is especially evident in didactic games, which, among other things, have the goal of developing the child’s basic cognitive processes: attention, memory, total stock ideas about the surrounding world. And despite the fact that the educational value of the didactic game is extremely small, it is indispensable for the prevention of socio-pedagogical neglect, preparing the child for school, etc.
Development mathematical representations must be carried out strictly step by step. You need to move on to learning new material only after the previously learned material has been completely consolidated. In addition, the development of mathematical abilities and skills in preschool children must obey the strict principle of conformity with nature (each age has its own load).
Principles of organizing play activities for preschoolers
- A game for a preschooler should be based on generally accepted standards of morality and morality, and respect for the child’s personality.
- In no case should gaming activities in any way degrade the dignity of participants (including losers).
- A didactic game should help a child to comprehend the world around him as deeply as possible, assimilating the laws that it obeys.
Game activity in mathematics with kindergarten In particular, the purpose of didactic games may be to develop mathematical abilities in preschool children. It will be much easier to do this through gaming activities.
How to use educational games to teach your child the basics of counting
Modern pedagogy is developing at a rapid pace. And more and more schools are beginning to use developing technologies in the learning process using computer technology, recruiting experimental classes. And the same can be safely said about family education.
Didactic games help develop mathematical abilities Early introduction of the child to high technology It is no coincidence: computer and information literacy is a requirement of the modern rhythm of life. That is why, already in the preschool period, it is necessary to pay maximum attention to the formation of mathematical concepts and the basics of computer science. All these skills will definitely be useful to your child at school.
What should a child know by the time he enters first grade?
Despite the fact that mathematics is one of the basic school subjects, as well as the basis of many sciences that the child will begin to study in the future, it is this discipline that in many cases causes considerable difficulties for children. This is largely due to the fact that the mathematical mindset, which greatly facilitates the child’s perception of information of this type, is not inherent in all children.
However, there is a strictly defined system of knowledge and mathematical concepts that must be formed by the time the child enters school.
- Ability to count from zero to ten in both ascending and descending order
- Developed skill of recognizing numbers in a series (even if they are placed separately)
- Formed ideas about cardinal and ordinal numbers
- Formed ideas about the “previous” and “next” number within ten
- Knowledge of basic geometric shapes and the skill of recognizing them (understanding the features that distinguish a triangle, circle, square, etc.)
- Having an idea of the whole and the parts; the ability to divide an object into 2 and 4 equal parts.
- Ability to use sticks, strings and some other measuring devices to estimate body parameters such as length, width and height
- The ability to compare objects according to the categories “more-smaller”, “higher-lower”, “wider-narrower”.
Does a preschooler need computer science?
Despite the fact that today computer science is an optional discipline that is not included in the category of compulsory subjects, some ideas about computer science should be formed in the child by this time. For example:
- Knowledge about algorithms.
- An initial introduction to computers.
- Understanding the program used to control a computation.
- Basic skill in using algorithms and logical operations using the commands “And”, “Or”, “Not”.
Initial acquaintance with computers for preschoolers Basics of mathematical concepts in preschool age
Assimilation mathematical knowledge impossible without the child understanding the basics of science such as quantity, number, etc. However, given that for a child they remain abstract for a long time, understanding even the simplest categories at first glance can be significantly difficult.
In these cases, it is possible to develop mathematical abilities in preschool children through play activities.
Simple didactic games give the child the opportunity to understand what “digit” and “number” are, and form adequate spatio-temporal ideas. In order for games to have maximum effect, it is necessary to build them on the basis of the following principles.
For effective absorption In order for the child to acquire skills acquired during games, it is necessary that visual material be used in classes: bright pictures, toys, cubes, etc. This is explained by voluntary attention preschoolers are not yet well developed. And to activate it, it is necessary that the object be distinguished by such qualities as brightness, novelty and contrast. In addition, favorite toys used during classes will make them even more interesting and exciting.
Geometric cards develop spatial understanding For example, if a child has some difficulty in counting, you can put in front of him several geometric shapes painted in different colors and sequentially count the objects in each of them. To prevent the child from becoming attached to specific things and could transfer the acquired knowledge to various items, it is very advisable to use new toys in the learning process, supplementing the existing stock with new ones.
IN Everyday life You should also encourage the child to name the number of objects on the table, the number of cars in the yard, children on the playground, etc.
After a child learns to count, parents will be able to significantly expand his stock of everyday knowledge by explaining the purpose of certain objects. For example, thanks to counting skills, it will not be difficult for a child to explain why a person needs a watch or a thermometer. And subsequently - to understand by the clock, at any moment, telling the time or measuring the temperature.
By school almost all children can count A fairy tale is also an indispensable tool for developing mathematical concepts in a child. You can use lesson elements in an unobtrusive form, including them in the process: for example, while reading a fairy tale, you can ask the child how many characters he counted in it; how many animals, birds, trees are shown in the picture of the illustrated book. It is also useful to invite the child to compare characters, pointing out their similarities and differences; indicating who is more or less of them, higher or lower, etc. Operations with numerals can be performed within the first ten.
A significant role in the development of addition and subtraction skills in the future will be played by the child’s ability to divide a whole object into parts.
In order for the child to effectively learn the concept of quantity, as well as the “previous” and “next” number, you can play with him, for example, by inviting him to guess the number within certain limits and giving him hints with the words “more” or “less.” This will allow the child to better navigate numbers and compose complete number series in his mind.
Children love to play with counting sticks Ordinary objects can also make a significant contribution to the development of a child’s mathematical understanding. counting sticks.
Here are just some examples of didactic games using these items:
- Lay out the counting sticks in front of the child and invite him to first choose any two, and then distribute them on two sides. After this, the child must say how many sticks are on each side.
- Over time, the conditions of the game can be slightly complicated by asking the child to divide four sticks into two parts. And then suggest other ways to divide the four sticks into two groups. Subsequently, the number of sticks can be increased to 10. Increasing the number of sticks will give the child more scope for imagination, offering more and more new ways of division.
- From sticks you can make simplest geometric shapes, thereby explaining to the child what a “triangle”, “rectangle”, “square” is. Once your child has an understanding of angles, you can explain the differences between shapes in more detail. And also invite him to fold them from sticks on his own.
- Over time, classes on forming simple geometric concepts can be complicated by asking the child to fold, for example, a rectangle with a side of 3 or 4 sticks. Or make different shapes from the same number of sticks.
- It is also useful to offer the child a fixed number of sticks, from which he could assemble two figures, or figures that have one common side.
- Counting sticks are also great for making simple numbers and letters. Using this method also prepares the child well for working with the lined surface of a notebook.
Preparing your hand for writing. Working with notebooks
Before you start teaching your child how to write numbers, you need to spend some time with him preliminary preparation. In particular, he must clearly understand what a notebook cell is, what its boundaries are, and find the corners, middle and sides.
After the child begins to freely navigate the lined surface, it will be possible to move on to drawing simple ornaments, for example, connecting opposite angles cells, or points located in the middle.
Preparation for writing includes various exercises No matter how strong the parent’s desire to teach the child to write as quickly as possible and prepare his hand for writing numbers, it is very desirable that in one lesson he learns no more than one or two patterns. The benefit of such activities is not only that the child prepares to write more complex elements, but also develops perfectly fine motor skills.
Logic games in preschool age
The development of mathematical abilities in preschool children through gaming activities is impossible without the use of logical games. Among other things, logic games encourage the child to look for non-standard and unusual solutions, develop in it creative thinking, support his desire to continue learning.
Logic game for preschoolers Entertaining ones are valuable because they unobtrusively lead the child to the conclusion that in order to complete a task that is interesting to him, concentration and concentration are necessary. This makes it possible not only to develop thinking, but also to polish voluntary attention. This will give the child the opportunity to perceive the conditions of the task and look for a possible catch in it. Thus, the development of mathematical abilities of preschool children through gaming activities is carried out as unobtrusively and correctly as possible.
You need to read the problems out loud, slowly and clearly so that the child can draw conclusions from each sentence and understand it correctly. It is very undesirable to give the child too many explanations: he must independently assimilate the train of thought. This will greatly enhance the joy of discovery.
Simple and familiar riddles from childhood will also play an irreplaceable role in the process of logic development: this will give the child the opportunity to learn to distinguish key features objects and recognize them by them.
Games for mastering the basics of computer science
Despite the fact that computer science is still not a subject compulsory for study at primary school age, studying its fundamentals greatly contributes to the development of forms abstract thinking. It also helps to master such actions as classifying objects according to certain signs, ranking, highlighting the main and secondary. The child begins to learn to assimilate established rules and strictly adhere to them.
To master basic concepts of computer science, you can use board games, which are sold today in all children's stores.
Computer games for preschoolers develop abilities The meaning of most board games for children is quite simple: with the help of chips and a cube, the child moves around the playing field. Thanks to this, spatio-temporal relationships are formed, the ability to follow given instructions, and carry out sequential actions. The child learns the simplest conditions and algorithms. It is desirable that board games be complemented by a plot that is interesting for the child, thoughtful design and interesting graphics.
Conclusion
Despite the fact that not every child has a mathematical mind and learning science can present difficulties for him even at initial stages, special exercises, carried out in a playful way, can significantly facilitate it. And at the same time, turn it into an interesting and exciting game.
Classes conducted in a playful way allow the child to accustom himself to controlled activities, instilling in him an interest in learning. Also math games have a beneficial effect on the development of memory, thinking, speech, as well as creativity. And then they help to master more complex categories, such as numbers, numbers, counting, etc. The child prepares his hand for writing and learns to navigate in space.
Comments 2 Share:The development of mathematical abilities in preschool children begins... Conduct a diagnosis of a preschooler in order to select an individual...
Mathematical ability is the ability to think logically. Is it possible to develop mathematical abilities in preschool children? Yes, it's possible. A person is born with an underdeveloped left hemisphere of the brain. It is responsible for logic and is activated gradually, along with the acquisition of new skills. The success of this process largely depends on the baby’s environment. At the right approach can be achieved good results in the development of his intellect, and therefore his mathematical abilities.
Modern theories and technology mathematical development Preschool children are expected to:
- formation of elementary mathematical concepts in preschoolers;
- development of their logical thinking;
- usage modern means and teaching methods.
It is advisable to first diagnose the development of each preschooler in order to select an individual educational program for him.
Mathematical representations
The development of mathematical abilities in preschool children begins with their immersion in a mathematical environment. In order to later feel comfortable among mathematical formulas and problems, they must in preschool age;
- find out what a figure and a number are;
- learn ordinal and quantitative calculations;
- learn to add and subtract within tens;
- find out what the shape of an object and volume are;
- learn to measure the width, height and length of objects;
- distinguish between temporal concepts “earlier”, “later”, “today”, “tomorrow”, etc.;
- navigate in space, understanding the concepts of “further”, “closer”, “ahead”, “behind”, etc.;
- be able to compare: “narrower - wider”, “lower - higher”, “less - more”.
Don't be scared! Mathematical concepts can be mastered at home, casually, in a playful way. How to do it?
Count objects out loud whenever possible or involve your child in doing so. (How many flowers do we have in the vase?, How many plates do we need to put?) Ask your child to follow your instructions: “Please bring me two pencils.”
Are you walking down the street together? Count to ten and back: in a duet, alternately, then let him count alone.
Teach your child to find the following and previous number. (Do you know which number is greater than 3 and less than 5?)
Help him understand addition and subtraction operations. IN primary school There are children who find it difficult to solve problems because they do not understand the meaning of these mathematical operations. If in one problem the boxes were folded, then in all other problems about boxes these students try to fold them, regardless of the conditions of the problem. Prepare your child before school. Take candy, apples, cups and clear example Explain to him what addition means and what subtraction means.
Teach him to compare objects. (Look, a magpie! Is it bigger than a sparrow or smaller?) Draw his attention to the fact that there can be objects different quantities. (There are a lot of apples and few pears in the vase. What can you do to make the fruits equal?)
Introduce your child to scales. It's great if you have a mechanical kitchen scale with weights. Let the child weigh the apple, an empty mug, or a mug of water.
Explain how to tell the time using a clock with hands.
Place toys on the table. Teach your child to distinguish which toy is closer to him, which is further away, which is in between.
Draw a quadrilateral, triangle, circle, oval. Let him try to explain how the first two figures differ from the second two. Show him where the angle is in the triangle. Count the angles, and the child himself will guess why the triangle has such a name.
Teach your preschooler easily, unobtrusively, and he will become friends with mathematics.
Formation of logical thinking
For successful mastery mathematical science it is necessary to be able to perform operations on given objects: find similarities or differences, regroup them according to given characteristic. Start mastering these wisdom before your child enters school. This will help him in deciding mathematical problems, and in everyday life.
Techniques for developing mathematical abilities in preschool children:
- The ability to identify an object or group of objects based on a given characteristic (analysis).
- Bringing together some elements, properties or characteristics into a single whole (synthesis).
- Arranging any objects in ascending or descending order according to a given criterion.
- Comparison with the aim of finding similarities or differences between objects (comparison).
- Distribution of objects into groups by name, color, size, shape, etc. (classification).
- Conclusion, comparison result (generalization). This technique is given special significance.
Analysis tasks for children 5-7 years old
Mathematical development of preschool children using simple exercises.
Exercise 1
In Figure 1, find the extra figure. (This is a red square)
Picture 1
Task 2
In Figure 1, distribute the circles into two groups. Explain your decision. (You can distribute by color, or by size).
Task 3
In Figure 2, show three triangles. (Two small and one along the outer contour)
Synthesis problems
Combining elements, sides of an object into unified system.
Exercise 1
Do what I do. In this task, an adult and a child construct identical objects. The child repeats the actions of the adult.
Task 2
Repeat the same from memory.
Task 3
Build a tower, design a scooter, etc. This is a creative activity. It is done without a sample.
Figure 2
Organizing tasks
Collecting and sorting items from smallest to largest or vice versa.
Exercise 1
Build the nesting dolls according to height, starting with the smallest one.
Task 2
Put on the pyramid rings, starting from the largest to the smallest.
Analysis tasks for children 2-4 years old
Performed with toys or pictures.
Exercise 1
Choose a blue car. Choose a car, but not a blue one.
Task 2
Select all the small cars. Select all the cars, but not the small ones.
Task 3
Choose the little blue car.
Comparison tasks for children 2-4 years old
The difference and similarity of elements according to some characteristic.
Exercise 1
What's round like a ball? (Apple, orange)
Task 2
Play with your child: first you describe the characteristics of the object, and the child guesses, then vice versa.
Example: Small, gray, can fly. Who is this? (Sparrow)
Comparison problems for older children
Same as the previous task, only for older children.
Exercise 1
In Figure 3, find a figure similar to the sun. (Circle)
Task 2
In Figure 3, show all the red shapes. What number corresponds to them? (Number 2)
Figure 3
Task 3
What else corresponds to the number 2 in Figure 3? (Number of yellow pieces)
A task on the ability to classify objects for children 2-4 years old
The adult names the animals, and the child says which of them can swim and which cannot. Then the child chooses what to ask about (about fruits, cars, etc.), and the adult answers.
Task for a child 5-7 years old
In Figure 3, highlight the polygons in separate group and separate them by color. (All shapes except the circle. The square and triangle will be in one group, and the rectangle in the other)
Generalization task
Figure 4 shows geometric shapes. What do they have in common? (These are quadrilaterals)
Figure 4
Entertaining games and tasks
For independent games preschoolers invented modern construction sets - puzzles. These are flat construction sets “Pythagoras”, “Magic Circle” and others, as well as volumetric construction sets “Snake”, “Magic Balls”, “Pyramid”. All of them teach the child to think geometrically.
Fun tasks like:
- There were 3 pears on the table. One was cut in half. How many pears are left on the table? (3)
- A team of dogs ran 4 km. How far did each dog run? (4)
Offering the child similar tasks, you will teach him to listen carefully to the condition and find the catch. The child will understand that mathematics can be very interesting.
Read and tell your child something from the history of mathematics: how ancient people believed, who invented the numbers we use, where geometric shapes came from...
Don't neglect simple riddles. They also teach you to think.
Tools to help parents of young mathematicians
First of all, this is visual didactic material:
- images of objects drawn on cards;
- household items, toys, etc.;
- cards with numbers and arithmetic signs, geometric figures;
- magnetic board;
- ordinary and hourglass;
- scales;
- counting sticks.
Buy educational games, construction sets, puzzles, counting materials, checkers and chess.
Everyone knows board games with dice, chips and a playing field. This is useful and interesting game. She teaches the child to count and perform tasks carefully. In addition, the whole family can take part in it.
Buy children's educational books with good illustrations.
- Encourage your child's curiosity.
- Look for answers to his questions together. Reason with him.
- Don't complain about lack of time. Talk and play while walking together, before bed.
- Great importance have a trusting relationship between an adult and a preschooler. Never laugh at your child's mistakes.
- Do not overload your baby with activities. This will harm his health and discourage him from learning.
- Pay attention not only to the development of mathematical abilities in preschool children, but also to their spiritual and physical development. Only then will your child become a harmonious personality.
Svetlana Zubkova
Formation of mathematical abilities: ways and forms
5 areas are defined.
Formation of elementary mathematical performances of preschoolers,
falls into the educational field "Cognition" and involves the development in children
cognitive interests, as well as intellectual advancement, through
development educational and research activities, FCCM.
According to curriculum work in every age group By mathematical
development consists of five sections: "Quantity and Counting", "Value", "Geometric
figures", "Orientation in space", "Orientation in time"
Mathematics- one of the most difficult educational subjects but she has
unique developmental effect. Her study promotes memory development, speeches,
imagination, emotions; builds perseverance, patience, creativity
personality.
Children need to be taught not only to calculate and measure, but also to reason.
The potential of a teacher does not lie in the transfer of certain mathematical knowledge and
skills, and in introducing children to material giving food to the imagination,
affecting not only the purely intellectual, but also emotional sphere child.
The teacher's task: do a lesson on femp entertaining and unusual. Want
remind you of the ancient proverb: “I hear - I forget, I see - and I remember, I
I do - and I understand"
The teacher must make the child feel that he can understand and learn not
only private concepts, but also general patterns. And the main thing is to know the joy of
overcoming difficulties.
Full mathematical development is ensured by organized
purposeful activity during which the teacher puts children in front of
cognitive tasks and helps to solve them, and this is both GCD and activities in everyday life
During directly educational FEMP activities are being decided on a number of
software tasks.
1) educational
2) developing
3) educational,
4) speech
When moving from one software task to another, it is very important to constantly
return to the topic covered, which ensures correct assimilation material.
There must be a surprise moment fairy-tale heroes, connection between everyone
didactic games.
The entire lesson on FEMP is based on clarity.
The teacher must remember that visibility is not an end in itself, but a means of learning.
Poorly chosen visual material distracts children's attention and interferes with learning
knowledge, correctly selected increases the effectiveness of learning.
Two types of visuals are used material(Demonstration, handout.)
Both demonstration and distribution material must meet aesthetic
requirements: attractiveness has great value in learning – with beautiful aids it is more interesting for children to study. And the brighter and deeper the children’s emotions, the more complete
the interaction of sensory and logical thinking, the more intensively it takes place
activity, and children acquire knowledge more successfully.
In progress formation of elementary mathematical representations
For preschoolers, the teacher uses the choice of optimal methods training: practical,
visual, verbal, playful.
When choosing a method, a number of factors are taken into account factors: software problems solved using
at this stage, age and individual characteristics children, availability of necessary
didactic means.
The leading method is practical method– these are exercises, game tasks,
educational games, didactic exercises. The child must not only listen,
perceive, but must also participate in the performance of a particular task. Most
educational games are widely used; they are effective means And
method formation of elementary mathematical concepts. Game as a method
training involves the use of individual elements of different types of games in the classroom
(plot, moving, gaming techniques (competition, search).
Subject and word games are carried out in and outside of class.
And the more the child plays educational games and completes tasks, the more
will learn better material on FEMP.
Didactic tools should change not only taking into account age
features, but depending on the relationship between the concrete and the abstract at different
stages of children's assimilation of software material. Didactic the material must be
artistically issued.
For example: real objects can be replaced by numerical figures, and they
In kindergarten it is widely techniques are used:show (demonstration, instruction,
explanation, clarification, instructions, questions for children.
Modeling is a visual and practical technique, including the creation of models and their
use for the purpose formation of elementary mathematical concepts in
Mathematics is an exact science, and it is necessary for children to learn to express accurately and coherently
your thoughts. Formation correct speech is component mental
raising a child. The richer the speech, the wider the opportunities for knowledge
reality, full communication, development of correct thinking.
Model of educational activities according to FMEP:
1. The teacher’s competence in the field of educational activities.
2. The teacher’s readiness for direct educational activities.
3. Selection of optimal methods and techniques
4. Correct selection of demonstration and distribution materials material.
5. Grammatically correct speech teacher
Conclusion.
Mathematics- one of the most difficult subjects in school. They talk about this too
parents and teachers and the students themselves. And preschoolers don’t know that mathematics-
difficult discipline. And they should never know about it.
Our task is to teach the child to comprehend mathematics with interest and pleasure and
always believe in yourself.
Publications on the topic:
Relevance Mathematics is one of the most difficult academic subjects. Teacher's potential preschool does not consist in transferring those.
Formation and development of logical and mathematical abilities in preschool children Formation and development of logical and mathematical abilities in preschool children and the problem psychological readiness to learning.
Abstract of GCD on the formation of elementary mathematical abilities in the senior group “Tsvetik-Semitsvetik” SUMMARY OF NODS IN THE EDUCATIONAL FIELD “COGNITIVE DEVELOPMENT” Formation of elementary mathematical abilities. Integration with others.
“Without play there is not and cannot be full-fledged mental development. The game is a huge bright window through which spiritual world child.
Mathematics manual for flannelgraph. The manual turned out to be multifunctional, so the goals and objectives are varied. This manual contains.
Summary: Development of mathematical abilities in children. More than twenty exercises for the development of logic - mathematical thinking The child has. 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 intellectual development 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 is mathematics so difficult for many children, not only in elementary school, but even now, in preparation for educational activities? Let's try to answer this question and show why generally accepted approaches to mathematical training preschool children often do not bring the desired positive results.
In modern primary school educational programs important is given a 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, now, in preschool period, you need to prepare your 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 formation own skill Thinking productively (that is, independently performing 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 more chances be successful in mathematics even if he was not taught the elements beforehand school curriculum(counting, calculations, etc.). It is no coincidence that last years in many schools working on developmental programs, an interview is conducted with children entering the 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 techniques mental actions 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. Classic example series: 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 - connection 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 look at the same object with various points vision: how big or small, red or yellow, round or square, etc. However, this is not about introducing large quantity objects, on the contrary, the method of organizing a comprehensive consideration is the method 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 circles? (Two large circle, two green circles.) 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?”
More complex shape 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 tall house", "build a garage for this car", "build a rooster". The tasks are given without a sample, the child works according to an 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 signs object, you can use the game “Find it by the indicated signs”: “Which (of these objects) is big yellow? (Ball and bear.) What is big yellow round? (Ball.)”, etc.
The child should use the leading role as often as the responding role, this will prepare him for next stage- the ability to answer the question: “What can you tell about it? (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 formation of 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. high school, where the definition of the concept “convex” is formulated in a geometry textbook flat figure". IN in this case the first part of the task was focused on the operation of comparing and selecting a figure that differs in external form from other figures in this group. But the generalization is made for a group of figures with characteristic features, frequently occurring quadrilaterals. If a child becomes interested in figure 4, an adult can note that this is also a quadrilateral, but 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 action, update counting skills, 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, imagination development, 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 quantitative characteristics changing design (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 shapes similar to them 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 visual image 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's obvious that constructive activity In the process of performing these exercises, the child 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 make sure 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 you can provide significant impact on the development of mathematical abilities of a preschooler. 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.
|
