Exercises for the development of thinking of younger students

Tasks, exercises, games that contribute to the development of thinking

1. Making proposals

This game develops the ability to quickly install variousdifferent, sometimes completely unexpected connections between familiarmetas, to creatively create new integral images from individualdisparate elements.

3 words are taken at random that are not related in meaning, for example, “lake-ro", "pencil" and "bear". Gotta make as many as possible.sentences that would necessarily include these 3 words (you can change their case and use other words). Answerscan be banal (“The bear dropped a pencil into the lake”),complex, with going beyond the situation indicated by three initial words and introducing new objects (“The boy took a pencil and drew a bear swimming in the lake”), and creativekimi, including these objects in non-standard connections (“Mal-a chik, thin as a pencil, stood near the lake, which roared likebear").

2. Exclusion of superfluous

Any 3 words are taken, for example, “dog”, “tomato”, “sun-tse". It is necessary to leave only those words that mean in somethingsimilar objects, and one word, superfluous, not possessing this common feature, should be excluded. Find as many as possibleoptions for excluding superfluous words, and most importantly - more recognitionkov, uniting each remaining pair of words and not inherentexcluded, superfluous. Without neglecting the options thatit begs to be (delete "dog", and "tomato" and "sun-tse "leave, because they are round), it is advisable to look for non-standard and at the same time very well-aimed solutions. winsthe one with the most answers.

This game develops the ability not only to establish unexpectedgiven connections between phenomena, but it is also easy to move from oneconnections to others without focusing on them. The game also teaches one thingtemporarily hold several objects in the field of thought at onceand compare them with each other.

It is important that the game forms an attitude to the fact that it is possiblewe have completely different ways of combining and dismembering somesecond group of objects, and therefore you should not be limited to oneit is the only "correct" solution, but you need to look for the wholethere are many of them.

3. Search for analogues

An object or phenomenon is called, for example, a helicopterm. It is necessary to write out as many of its analogues as possible, i.e.other objects similar to it in various essential featuressigns. It is also necessary to systematize these analogs into groups, depending on which property of a given pre-meta they were selected. For example, in this case a bird, a butterfly can be called (they fly and sit down); bus, train (vehicles); corkscrew (important parts rotate), etc. Winsthe one who named the largest number of groups of analogues.

This game teaches you to highlight the most diverse properties in an object.properties and operate with each of them separately, forms the ability tothe ability to classify phenomena according to their features.

4. Ways to use the item

A well-known object, such as a book, is named. It is necessary to name as many different ways of using it as possible: a book can be used as a stand for a movie projector;le, etc. A ban should be introduced on naming immoral, barbaric ways of using an object. The one who points out winsa greater number of different functions of the subject.

This game develops the ability to concentrate thinking onone subject, the ability to introduce it into a variety of situations and relationships, to discover unexpected possibilities in an ordinary subjectness.

5. Making up the missing parts of the story

Children are read a story in which one of the parts is omitted(beginning of the event, middle or end). The task is to-to guess the missing part. Along with the development of logicalof his thinking, the compilation of stories is extremely importantfor the development of the child’s speech, enrichment of his vocabularystock, stimulates the imagination and fantasy.

6. Logic puzzles and tasks

A. Numerous examples of tasks of this kind can be found in various teaching aids. For example, the well-knownnaya riddleabout the wolf, goat and cabbage:“The peasant needs to re-carry a wolf, goat and cabbage across the river. But the boat is such that in ita peasant can fit, and with him either only a wolf, or onlygoat, or just cabbage. But if you leave the wolf with the goat, thenthe wolf will eat the goat, and if you leave the goat with cabbage, then the goat will eatempty. How did the peasant transport his cargo?

Answer:“It is clear that we have to start with a goat. Peasant, pe-carrying a goat, he returns and takes a wolf, which he transports to anothergoy shore, where he leaves him, but then he takes and carries him back tofirst coast goat. Here he leaves her and transports the cabbage to the wolf. After that, returning, he transports a goat, and crosseswa ends happily.”

B.Divide task: "How to divide 5 apples between 5 people so thateveryone got an apple, but one apple was left in the basket?

Answer:"One person takes an apple along with a basket."

Ways to develop divergent thinking.

B dullness of thought

1. Come up with words with a given letter:

a)beginning with the letter "a"

b)ending with the letter "t";

in)in which the third letter from the beginning is "c".

2. List objects with a given attribute:

a)red (white, green, etc.) color;

b)round shape.

3. List all possible uses ofpizza in 8 minutes.

If the children's answers are something like this: constructionhouse, barn, garage, school, fireplace - this will be a witnesstalk about good fluency of thinking, but its insufficientflexibility, since all of the above usesbricks belong to the same class. If the child says that with the help of a brick you can hold the door, makeload paper, hammer a nail or make redpowder, then he will receive, in addition to a high score in muscle fluencyleniya, also a high score on the direct flexibility of theReduction: This subject quickly moves from one class to another.

Fluency of associations — dealing with relationships, understandingmania for the diversity of objects belonging to a certaintogether with this object.

4. List words with the meaning "good" and words with
the opposite meaning of the word "solid".

5. 4 small numbers are given. The question is howso they can be correlated with each other in order to eventually get8: 3+5; 4+4; 2+3+4-1.

6. The first participant calls any word. The second participant adds any of his words. The third participant comes up with a sentence that includes the indicated two words, i.e., looks for possible relationships between these words. Offershould make sense. Then he comes up with a new word, andthe next participant tries to connect the second and third word into a sentence, and so on. The task is to gradually increasechanging the pace of the exercise.

For example: tree, light. "When I climbed a tree, I sawnot far away is the light from the window of the forester's lodge.

fluency of expression - rapid formation of phrases oroffer.

7. Initial letters are given (for example, B-C-E-P), eachday of which represents the beginning of words in a sentenceresearch institutes. It is necessary to form various sentences, for example"The whole family ate cake."

Originality of thinking - changing the meaning in such a wayat once, to get a new, unusual meaning.

8. Make a list of as many titles as possiblefor a short story.

9. It is proposed to create a simple symbol to indicatenoun or verb in a short sentence - other-In other words, it is necessary to invent something like a representationcharacters.For example, "the man went to the forest."

The ability to create a variety of predictions

10. 1 or 2 lines are suggested to be addedother lines to make objects. The more linesadds the participant, the more points he gets (in advancethis condition is not specified).

11. Two simple equalities B - C =D; To= A + D.
From the information received, you need to make as many other equalities as possible.

Ability to establish causal relationships

12. Children are offered the beginning of the phrase. Need to continuethis phrase with the words "due to the fact that ...", "because ...".Today I'm very cold because... it's cold outside

Walked for a long time... forgot to put on a sweater.

Mom is in a good mood because...etc.

Ways to develop convergent thinking.

Ability to Understand the Elements

1. Guess an object or animal by its features.
Children conceive an object in the absence of a driver, and thenlist its features in turn: color, shape, possibleuse or habitat (for animals), etc. ByWith these signs, the driver guesses the intended object.

2. Establishing relationships. On the left is the ratio of two
concepts. From the row of words on the right, choose one so that it
formed a similar relationship with the upper word.

school hospital

Education doctor, student, institution, treatment, patient

song waterthirstpainting

Deaf lame, blind, artist, drawing, sick

table knife

steel fork, wood, chair, food, tablecloth

fish fly

Sieve net, mosquito, room, buzz, cobweb

bird man

Nest people, chick, worker, beast, house

bread house

baker wagon, city, dwelling, builder, door

boot coat

Button tailor, shop, leg, lace, hat

scythe razor

Grass hay, hair, sharp, steel, tool

leg arm

Overshoe boot, fist, glove, finger, brush

water food

Thirst to drink, hunger, bread, mouth, food

3. Exclusion of the 4th superfluous. Identification of significantsigns.

Groups of words are proposed, three of which are combinedessential feature, and the fourth word turns out to be superfluousthem that do not make sense.

For example, truck, train, bus, tram. "Gro-zovik” is an extra word, since the train, bus, tram are passenger transport; apple, blueberry, pear, plum is an extra word - blueberries, since apple, pear, plum -fruits, etc.

4. Sequential pictures.

A certain number of images are presented in disorderexpressions that have a logical sequence. Picture-The expressions can be taken from cartoons. Subject's task- determine the existing logical sequence

5. Restructuring of the word.

From the letters of this word, make as many new ones as possiblewords. In a new word, each letter can be used as manythe number of times it occurs in the original word. For example, fromthe words "coppice" are obtained words: warp, sand, juice, village,armchair, crypt, splash, etc.

6. Deduction.Thinking tasks of this type are proposed:

Ivan is younger than Sergei.Ivan is older than Oleg.Who is older: Sergey or Oleg?

7. Generalizations.

a) to name objects in one word:for example, a fork, a spoon, a knife are ... rain, snow, frost are ...arm, leg, head— this...etc;

b) specify the general concept:fruit is...; transport is...

8. Continue a series of numbers.

A series with a certain sequence of numbers is set.Participants must understand the pattern of building a series and continue it. For example, 1, 3, 5, 7... 1,4, 7... 20, 16, 20... 1 , 3, 9...

9. Shadow game.Purpose of the game: development of observation, pa-wrinkle, inner freedom and looseness.

The soundtrack of calm music sounds. From a group of childrentwo children are selected. The rest are spectators. One child is a “traveler”, the other is his “shadow”. "Traveler" goes throughthe field, and behind it, two or three steps behind, comes the second child,his "shadow". The latter tries to copy exactly the movementzheniya "traveler".

It is desirable to encourage the "traveler" to performmovements: “pick a flower”, “crouch”, “jump onone leg”, “stop to look from under the arm”, etc.You can modify the game by dividing all the children into pairs -"traveler" and his "shadow".-

Exercises for the development of logical thinking and semantic memory.

1. Exercise for the development of logical thinking, complicated by the task of memorization.

Decipher and remember, without writing down, encrypted two-digit numbers.

MA VK EI FROM SA TO

Cipher key:

Memory time 1 minute.

2. Exercise for the development of logical thinking.

Children are offered a table with proverbs written in two columns: in the first - the beginning, in the second - endings that do not correspond to each other.

Exercise: read, compare parts of proverbs and rearrange according to the meaning, remember the correction of the proverb.

Runtime 1 minute.

CALLED A LOAD, WALK BOLDLY.

LOVE TO RIDE, HAVE FUN.

DID THE BUSINESS - CLIMB INTO THE BODY.

IT'S TIME, LOVE TO CARRY SLED.

3. Fit for each pictureword-at-sign and remember it. Write down in pairs words-recognition-ki and names of pictures.

MAC -SCARLETCANDY -SWEETCOAT -WARM

TOMATO -JUICYSOFA -CONVENIENTKIT -HUGE

PEN -BALLPEACOCK -BEAUTIFUL

4. Choose action words for each subject cardtinke. Write in pairs words-actions and namespictures.

Poppy - blossomcandy - treatcoat -put on

Tomato-growsofa - sit

whale -swimpen - writepeacock - put on airs

5. Remember in pairs words-signs and words-actions:

Blossomtreatput ongrow

Scarletsweetwarm juicy

swimwriteput on airssit

huge ball beautiful comfortable

Write these pairs in your notebook.

6. Children are offered a table (on individualnyatiyah - cards), which is the key to the cipher:

One cut 5 - chickens in the fall

What you sow 6 - while it's hot

Count 7 - you reap

Not everything is gold 8 - what glitters

Strike iron 9 - measure seven times.

Make up sentences from these parts.

Using the key to the cipher, encrypt the proverbsin the form of two-digit numbers (90,17,52,38,46). burnthese numbers in notepad.

Runtime 3 minutes.

7. 6 pairs of words are read, interconnected bymeaning. It is necessary to select for each pair according to the meaninglu the third word and write it down.

egg-chicken chick

forest-tree board

house - city the street

river-lake sea

fur coat - cold snow

bird - flight nest

The development of logical thinking of younger schoolchildren is one of the most important areas of teaching students. The importance of this process is indicated by curricula and methodological literature. It is best to improve logical thinking both at school and at home, but not everyone knows which methods will be most effective for this. As a result, logical learning takes the form of spontaneous, which negatively affects the overall level of development of students. It happens that even high school students do not know how to think logically, using the methods of analysis, synthesis, comparison, etc. How to properly develop the logical thinking of younger students - you will learn from our article.

Features of thinking of elementary school students

The thinking of elementary school students has features

By the time the child begins to go to school, his mental development is characterized by a very high level.

“Each age period of a child is characterized by the leading significance of some mental process. In early childhood, the formation of perception plays a leading role, in the preschool period - memory, and for younger students, the development of thinking becomes the main one.

The thinking of elementary school students has its own peculiarities. It was during this period visual-figurative thinking, which previously had the main value, is transformed into a verbal-logical, conceptual. That is why in elementary school it is extremely important to pay attention to the development of logical thinking.

Younger students develop their logical thinking by regularly completing tasks, learning to think when necessary.

The teacher teaches:

• find connections in the environment
• develop correct concepts
• put into practice the studied theoretical provisions
• analyze with the help of mental operations (generalizations, comparisons, classifications, synthesis, etc.).

All this has a positive effect on the development of logical thinking of younger students.

Pedagogical conditions

Properly created pedagogical conditions stimulate the development of logical thinking of schoolchildren

In order to develop and improve the logical thinking of younger students, it is necessary to create pedagogical conditions conducive to this.

Primary school education should be aimed at the teacher helping each student reveal your abilities. This is real when the teacher takes into account the individuality of each. In addition, the disclosure of the potential of the younger student contributes to diverse educational environment.

Consider pedagogical conditions, contributing to the formation of the student's logical thinking:

1. Lesson assignments that encourage children to think. It is better when such tasks are not only in mathematics lessons, but also in everyone else. And some teachers do logical five minutes between lessons.
2. Communication with the teacher and peers - at school and non-school hours. Reflecting on the answer, ways to solve the problem, the students offer different solutions, and the teacher asks them to justify and prove the correctness of their answer. Thus, younger students learn to reason, compare various judgments, and draw conclusions.
3. It is good when the educational process is filled with elements where the student:
   • can compare concepts (objects, phenomena),
   • understand the differences between common features and distinctive (private)
   • identify essential and non-essential features
   • ignore irrelevant details
   • analyze, compare and generalize.

“The success of the full-fledged formation of the logical thinking of a younger student depends on how comprehensively and systematically this is taught.”

Primary school is the best period for purposeful work on the active development of logical thinking. All sorts of things can help make this period productive and productive. didactic games, exercises, tasks and assignments aimed at:

• developing the ability to think independently
• learning to draw conclusions
• effective use of acquired knowledge in mental operations
• search for characteristic features in objects and phenomena, comparison, grouping, classification according to certain features, generalization
• use of existing knowledge in various situations.

Exercises and games for logic

The means of developing the logical thinking of a younger student must be selected taking into account the goals, as well as focusing on the individual characteristics and preferences of the child.

It is useful to use non-standard tasks, exercises, games for the development of mental operations both in the classroom and during homework with children. Today they are not in short supply, as developed a large number of printing, video and multimedia products, various games. All these means can be used, selecting taking into account the goals, as well as focusing on the individual characteristics and preferences of the child.

Video with an example of a tablet game aimed at developing the logical thinking of younger students

Exercises and games for logical thinking

1. "The fourth extra." The exercise is to exclude one item that lacks some feature common to the other three (it is convenient to use picture cards here).
2. "What is missing?". You need to come up with the missing parts of the story, (beginning, middle or end).
3. "Do not snooze! Continue!". The point is for the students to quickly name the answers to the questions.

In reading lessons:

• Who pulled the turnip last?
• What was the name of the boy from "Flower-Semitsvetik"?
• What was the name of the boy with the long nose?
• Who won the fiancé flies-sokotuhi?
• Who scared the three little pigs?

In Russian language lessons:

• Which word contains three "o"s? (trio)
• The name of which city indicates that he is angry? (Terrible).
• What country can be worn on the head? (Panama).
• What mushroom grows under an aspen? (Boletus)
• How can you write the word "mousetrap" using five letters? ("Cat")

In the lessons of natural history:

• Is a spider an insect?
• Do our migratory birds nest in the south? (Not).
• What is the name of a butterfly larva?
• What does a hedgehog eat in winter? (Nothing, he sleeps).

In math class:

• Three horses ran 4 kilometers. How many kilometers did each horse run? (for 4 kilometers).
• There were 5 apples on the table, one of which was cut in half. How many apples are on the table? (5.)
• Name a number that has three tens. (thirty.)
• If Lyuba stands behind Tamara, then Tamara ... (stands in front of Lyuba).

"Advice. To enrich the educational process, as well as for homework, use logical problems and riddles, puzzles, rebuses and charades, numerous examples of which you can easily find in various teaching aids, as well as on the Internet.

Tasks that activate the brain

There are many tasks that activate the brain

Tasks for developing the ability to analyze and synthesize

1. Connecting elements together:

"Cut out the necessary shapes from the various ones proposed in order to get a house, a ship and a fish."

1. To search for different signs of an object:

How many sides, angles and vertices does a triangle have?

“Nikita and Yegor jumped long. On the first attempt, Nikita jumped 25 cm further than Yegor. From the second, Yegor improved his result by 30 cm, and Nikita jumped in the same way as from the first. Who jumped further on the second attempt: Nikita or Egor? How much? Guess!"

1. To recognize or compose an object according to certain characteristics:

What number comes before the number 7? What number comes after the number 7? Behind the number 8?

Tasks for the ability to classify:

"What common?":

1) Borsch, pasta, cutlet, compote.

2) Pig, cow, horse, goat.

3) Italy, France, Russia, Belarus.

4) Chair, desk, wardrobe, stool.

"What's extra?"- a game that allows you to find common and unequal properties of objects, compare them, and also combine them into groups according to the main feature, that is, classify.

"What unites?"- a game that forms such logic operations as comparison, generalization, classification according to a variable attribute.

For example: take three pictures with images of animals: a cow, a sheep and a wolf. Question: "What unites a cow and a sheep and distinguishes them from a wolf?".

The task of developing the ability to compare:

“Natasha had several stickers. She gave 2 stickers to a friend and she has 5 stickers left. How many stickers did Natasha have?

Tasks for the search for essential features:

"Name the attribute of the object." For example, a book - what is it? What material is it made from? What size is it? What is its thickness? What is its name? What subjects does it apply to?

Useful games: “Who lives in the forest?”, “Who flies in the sky?”, “Edible - inedible”.

Tasks for comparison:

Color comparison.

a) blue
b) yellow
c) white
d) pink.

Form comparison. You need to name more items:

a) square
b) round shape
c) triangular
d) oval.

Let's compare 2 things:

a) pear and banana
b) raspberries and strawberries
c) sled and cart
d) car and train.

Compare seasons:

Conversation with students about the features of the seasons. Reading poems, fairy tales, riddles, proverbs, sayings about the seasons. Drawing on the theme of the seasons.

Non-standard logical problems

One of the most effective ways to develop logical thinking in elementary school is to solve non-standard problems.

“Did you know that mathematics has a unique developmental effect? It stimulates the development of logical thinking, in the best way forming the methods of mental work, expanding the intellectual abilities of the child. Children learn to reason, notice patterns, apply knowledge in various fields, be more attentive, observant.

In addition to mathematical problems, the brain of younger students is developed puzzles, different types of tasks with sticks and matches(laying out a figure from a certain number of matches, transferring one of them in order to get another picture, connecting several points with one line without tearing off the hand).

Problems with matches

1. You need to make 2 identical triangles of 5 matches.
2. It is necessary to add 2 identical squares of 7 matches.
3. You need to make 3 identical triangles of 7 matches.

Comprehensive development of thinking is also provided puzzle games: "Rubik's Cube", "Rubik's Snake", "Fifteen" and many others.

Well-developed logical thinking will help the child in learning, making the assimilation of knowledge easier, more enjoyable and more interesting.

The games, exercises and tasks proposed in this article are aimed at developing the logical thinking of younger students. If these tasks are gradually complicated, then the result will be better every day. And flexible, plastic thinking and quick reaction will help the child in his studies, making the assimilation of knowledge easier, more pleasant and more interesting.

INTRODUCTION

At primary school age, children have significant reserves of development. With the child entering school, under the influence of learning, the restructuring of all his cognitive processes begins. It is the primary school age that is productive in the development of logical thinking. This is due to the fact that children are included in new types of activities for them and systems of interpersonal relations that require them to have new psychological qualities.

The problem is that students already in the 1st grade for the full assimilation of the material require the skills of logical analysis. However, studies show that even in the 2nd grade, only a small percentage of students master the techniques of comparison, summing up a concept, deriving consequences, etc.

Primary school teachers often use exercise-type exercises based on imitation, which do not require thinking, in the first place. Under these conditions, such qualities of thinking as depth, criticality, and flexibility are not sufficiently developed. This is what indicates the urgency of the problem. Thus, the analysis carried out shows that it is precisely at primary school age that it is necessary to carry out purposeful work to teach children the basic methods of mental actions.

The possibilities of forming methods of thinking are not realized by themselves: the teacher must actively and skillfully work in this direction, organizing the entire learning process in such a way that, on the one hand, he enriches children with knowledge, and on the other hand, he forms the methods of thinking in every possible way, contributes to the growth of cognitive forces and students' abilities.

Many researchers note that purposeful work on the development of logical thinking of younger schoolchildren should be systematic (E.V. Veselovskaya, E.E. Ostanina, A.A. Stolyar, L.M. Fridman, etc.). At the same time, studies by psychologists (P.Ya. Galperin, V.V. Davydov, L.V. Zankov, A.A. Lyublinskaya, D.B. Elkonin, etc.) allow us to conclude that the effectiveness of the process of developing logical thinking for younger schoolchildren depends on the method of organizing special developmental work.

The object of the work is the process of developing the logical thinking of younger students.

The subject of the work is tasks aimed at developing the logical thinking of younger students.

Thus,the purpose of the work is to study the optimal conditions and specific methods for the development of logical thinking of younger students.

To achieve this goal, we have identified the following tasks:

To analyze the theoretical aspects of the thinking of younger students;

To identify the features of logical thinking of younger students;

Carry out experimental work confirming our hypothesis;

At the end of the work, summarize the results of the study.

Hypothesis - the development of logical thinking in the process of playing activities of a younger student will be effective if:

The psychological and pedagogical conditions that determine the formation and development of thinking are theoretically substantiated;

The features of logical thinking in a younger student are revealed;

The structure and content of the games of younger students will be aimed at the formation and development of their logical thinking;

Criteria and levels of development of logical thinking of a junior schoolchild are determined.

THEORETICAL ASPECTS OF JUNIOR SCHOOLCHILDREN'S THINKING.

1. CONTENT OF THINKING AND ITS TYPES

Thinking is a mental process of reflecting reality, the highest form of human creative activity. Meshcheryakov B.G. defines thinking as a creative transformation of subjective images in the human mind. Thinking is the purposeful use, development and increment of knowledge, which is possible only if it is aimed at resolving contradictions that are objectively inherent in the real subject of thought. In the genesis of thinking, the most important role is played by understanding (by people of each other, the means and objects of their joint activity)

In the Explanatory Dictionary of Ozhegov S.I. thinking is defined as the highest stage of cognition, the process of reflecting objective reality. Thus, thinking is a process of mediated and generalized cognition (reflection) of the surrounding world. Traditional definitions of thinking in psychological science usually fix its two essential features: generalization and mediation.

Thinking is a process of cognitive activity in which the subject operates with various types of generalizations, including images, concepts and categories. The essence of thinking is in performing some cognitive operations with images in the internal picture of the world

The thinking process is characterized by the following features:

Has an indirect character;

Always proceeds based on existing knowledge;

It comes from living contemplation, but is not reduced to it;

It reflects connections and relationships in verbal form;

Associated with human activities.

The Russian physiologist Ivan Petrovich Pavlov, describing thinking, wrote: “Thinking is a tool for the highest orientation of a person in the world around him and in himself.” According to Pavlov: “Thinking does not represent anything other than associations, first elementary, standing in connection with external objects, and then chains of associations. This means that every small, first association is the moment of the birth of a thought.

concept - this is a reflection in the mind of a person of the general and essential properties of an object or phenomenon. The concept is a form of thinking that reflects the singular and special, which is at the same time universal. The concept acts both as a form of thinking and as a special mental action. Behind each concept is hidden a special objective action. Concepts can be:

General and single;

Concrete and abstract;

empirical and theoretical.

Written, out loud or silently.

Judgment - the main form of thinking, in the process of which the connections between objects and phenomena of reality are affirmed or denied. A judgment is a reflection of the connections between objects and phenomena of reality or between their properties and features.

Judgments are formed in two main ways :

Directly, when they express what is perceived;

Indirectly - by inference or reasoning.

Judgments can be: true; false; general; private; single.

True Judgments These are objectively correct statements.False Judgments These are judgments that do not correspond to objective reality. Judgments are general, particular and singular. In general judgments, something is affirmed (or denied) in relation to all objects of a given group, a given class, for example: "All fish breathe with gills." In private judgments, affirmation or negation no longer applies to all, but only to some subjects, for example: "Some students are excellent students." In single judgments - only to one, for example: "This student did not learn the lesson well."

inference is the derivation of a new judgment from one or more propositions. The initial judgments from which another judgment is deduced or extracted are called premises of the inference. In psychology, the following somewhat conditional classification of types of thinking is accepted and widespread on such various grounds as:

1) the genesis of development;

2) the nature of the tasks to be solved;

3) the degree of deployment;

4) degree of novelty and originality;

5) means of thinking;

6) functions of thinking, etc.

According to the nature of the tasks to be solved, thinking is distinguished:

theoretical;

Practical.

theoretical thinking - thinking on the basis of theoretical reasoning and conclusions.

practical thinking - thinking based on judgments and conclusions based on solving practical problems.

theoretical thinking is the knowledge of laws and regulations. The main task of practical thinking is the development of means for the practical transformation of reality: setting a goal, creating a plan, project, scheme.

According to the degree of deployment, thinking is distinguished:

discursive;

Intuitive.

According to the degree of novelty and originality, thinking is distinguished:

reproductive;

Productive (creative).

Reproductive thinking - thinking on the basis of images and ideas drawn from some specific sources.

Productive Thinking - thinking based on creative imagination.

According to the means of thinking, thinking is distinguished:

verbal;

Visual.

visual thinking - thinking on the basis of images and representations of objects.

verbal thinking - thinking, operating with abstract sign structures.

According to the functions, thinking is distinguished:

critical;

Creative.

Critical thinking focuses on identifying flaws in other people's judgments. Creative thinking is associated with the discovery of fundamentally new knowledge, with the generation of one's own original ideas, and not with the evaluation of other people's thoughts.

FEATURES OF LOGICAL THINKING OF YOUNGER SCHOOLCHILDREN

Many researchers note that one of the most important tasks of teaching at school is the formation of students' skills in performing logical operations, teaching them various methods of logical thinking, arming them with knowledge of logic and developing in schoolchildren the skills and abilities to use this knowledge in educational and practical activities. But whatever the approach to solving this issue, most researchers agree that developing logical thinking in the learning process means:

To develop in students the ability to compare observed objects, to find common properties and differences in them;

Develop the ability to highlight the essential properties of objects and distract (abstract) them from secondary, non-essential;

To teach children to dismember (analyze) an object into its component parts in order to cognize each component and to combine (synthesize) objects mentally dissected into one whole, while learning the interaction of parts and the object as a whole;

To teach schoolchildren to draw correct conclusions from observations or facts, to be able to verify these conclusions; to instill the ability to generalize facts; - to develop in students the ability to convincingly prove the truth of their judgments and refute false conclusions;

Make sure that the thoughts of students are stated clearly, consistently, consistently, reasonably.

Thus, the development of logical thinking is directly related to the learning process, the formation of initial logical skills under certain conditions can be successfully carried out in children of primary school age, the process of formation of general logical skills, as a component of general education, should be purposeful, continuous and associated with the process of teaching school disciplines at all levels.

One of the reasons for the emergence of learning difficulties in younger schoolchildren is a weak reliance on the general patterns of child development in a modern mass school. It is impossible to overcome these difficulties without taking into account the age-related individual psychological characteristics of the development of logical thinking in younger schoolchildren. A feature of children of primary school age is cognitive activity. By the time of entering the school, the younger student, in addition to cognitive activity, already has an understanding of the general connections, principles and patterns that underlie scientific knowledge. Therefore, one of the fundamental tasks that the elementary school is called upon to solve for the education of students is the formation of the most complete picture of the world possible, which is achieved, in particular, through logical thinking, the instrument of which is mental operations.

In elementary school, based on the curiosity with which the child comes to school, learning motivation and interest in experimentation develop. The active inclusion of models of various types in teaching contributes to the development of visual-effective and visual-figurative thinking in younger students. Primary schoolchildren show few signs of mental inquisitiveness, of striving to penetrate beyond the surface of phenomena. They express considerations that reveal only the appearance of understanding complex phenomena. They rarely think about any difficulties.

Younger students do not show independent interest in identifying the causes, the meaning of the rules, but they ask questions only about what and how to do, that is, the thinking of a younger student is characterized by a certain predominance of a specific, visual-figurative component, the inability to differentiate the signs of objects on essential and non-essential, to separate the main from the secondary, to establish a hierarchy of signs and cause-and-effect relationships and relationships. There is an objective need to find such pedagogical conditions that would contribute to the most effective development of logical thinking in children of primary school age, a significant increase in the level of mastery of educational material by children, and the improvement of modern primary education, without increasing the educational load on children.

When substantiating the pedagogical conditions for the development of logical thinking of younger students, we proceeded from the following basic conceptual provisions:

Education and development are a single interrelated process, progress in development becomes a condition for deep and lasting assimilation of knowledge (D.B. Elkonin, V.V. Davydov, L.V. Zankova, E.N. Kabanova-Meller, etc.);

The most important condition for successful learning is the purposeful and systematic formation of the trainees' skills to implement logical techniques (S.D. Zabramnaya, I.A. Podgoretskaya, etc.);

The development of logical thinking cannot be carried out in isolation from the educational process, it must be organically connected with the development of subject skills, take into account the peculiarities of the age development of schoolchildren (L.S. Vygotsky, I.I. Kulibaba, N.V. Shevchenko, etc.). The most important condition is to ensure the motivation of students to master the logical operations in learning. On the part of the teacher, it is important not only to convince students of the need for the ability to carry out certain logical operations, but in every possible way to stimulate their attempts to generalize, analyze, synthesize, etc.

THEORETICAL FOUNDATIONS FOR THE USE OF DIDACTIC GAME TASKS IN THE DEVELOPMENT OF LOGICAL THINKING IN YOUNGER SCHOOLCHILDREN

Recently, the search for scientists (3.M. Boguslavskaya, O.M. Dyachenko, N.E. Veraks, E.O. Smirnov, etc.) has been directed towards creating a series of games for the full development of children's intellect, which are characterized by flexibility, initiative mental processes, the transfer of formed mental actions to new content.

According to the nature of cognitive activity, didactic games can be classified into the following groups:

1. Games that require executive activity from children. With the help of these games, children perform actions according to the model.

2. Games that require action to be played. They are aimed at developing computational skills.

3. Games with which children change examples and tasks into others that are logically related to it.

4. Games that include elements of search and creativity.

This classification of didactic games does not reflect all their diversity, however, it allows the teacher to navigate the abundance of games. It is also important to distinguish between actual didactic games and game techniques used in teaching children. As children "enter" a new activity for them - educational - the value of didactic games as a way of learning decreases, while game techniques are still used by the teacher. They are needed to attract the attention of children, relieve their stress. The most important thing is that the game is organically combined with serious, hard work, so that the game does not distract from learning, but, on the contrary, contributes to the intensification of mental work.

In the situation of a didactic game, knowledge is acquired better. Didactic game and lesson cannot be opposed. The relationship between children and the teacher is determined not by the learning situation, but by the game. Children and the teacher are participants in the same game. This condition is violated - and the teacher takes the path of direct teaching.

Based on the foregoing, a didactic game is a game only for a child. For an adult, it is a way of learning. In the didactic game, the assimilation of knowledge acts as a side effect. The purpose of didactic games and game learning techniques is to facilitate the transition to learning tasks, to make it gradual. The foregoing allows us to formulate the main functions of didactic games:

The function of forming a sustainable interest in learning and relieving stress associated with the process of adapting the child to the school regime;

The function of the formation of mental neoplasms;

The function of forming the actual educational activity;

Functions of formation of general educational skills, skills of educational and independent work;

The function of forming skills of self-control and self-esteem;

The function of forming adequate relationships and mastering social roles.

So,didactic game is a complex, multifaceted phenomenon. A child cannot be forced, forced to be attentive, organized. The following principles should be at the heart of any game technique conducted in the classroom: The relevance of didactic material (actual formulations of mathematical problems, visual aids, etc.) actually helps children perceive tasks as a game, feel interested in getting the right result, strive for the best possible solutions. Collectivity allows you to rally the children's team into a single group, into a single organism, capable of solving tasks of a higher level than those available to one child, and often more complex. Competitiveness creates a desire in a child or a group of children to complete a task faster and better than a competitor, which reduces the time to complete the task, on the one hand, and achieve a realistically acceptable result, on the other.

The game is not a lesson. A game technique that includes children in a new topic, an element of competition, a riddle, a journey into a fairy tale and much more - this is not only the methodological wealth of the teacher, but also the general work of children in the classroom, rich in impressions. Summing up the results of the competition, the teacher draws attention to the friendly work of team members, which contributes to the formation of a sense of collectivism. Children who make mistakes must be treated with great tact. A teacher may tell a child who has made a mistake that he has not yet become the "captain" in the game, but if he tries, he will certainly become one. The game technique used should be in close connection with visual aids, with the topic under consideration, with its tasks, and not be exclusively entertaining. Visualization in children is, as it were, a figurative solution and design of the game. It helps the teacher to explain new material, to create a certain emotional mood.

Play is essential in elementary school . After all, only she knows how to make difficult - easy, accessible, and boring - interesting and fun. The game can be used both when explaining new material, and when consolidating, when practicing counting skills, to develop the logic of students.

Subject to all the above conditions, children develop such necessary qualities as:

a) a positive attitude towards the school, to the subject;

b) the ability and desire to be involved in collective educational work;

c) voluntary desire to expand their capabilities;

e) disclosure of one's own creative abilities.

Classes were held with the whole group of children in the form of extracurricular activities on the basis of O.A. Kholodov’s “Young clever and clever girls”, some of the tasks were performed by children at the main mathematics lessons, or they did it as homework.

Children are already familiar with the term "feature" and it was used when completing tasks: "Name the features of an object", "Name similar and different features of objects."

For example, when studying the numbering of numbers within 100, children were offered the following task:

Divide these numbers into two groups so that each contains similar numbers:

a) 33, 84, 75, 22, 13, 11, 44, 53 (one group includes numbers written in two identical digits, the other - different ones);

b) 91, 81, 82, 95, 87, 94, 85 (the basis of classification is the number of tens, in one group of numbers it is 8, in another - 9);

c) 45, 36, 25, 52, 54, 61, 16, 63, 43, 27, 72, 34 (the basis of the classification is the sum of the “digits” that record these numbers, in one group it is 9, in the other - 7 ).

Thus, when teaching mathematics, tasks for the classification of various types were used:

1. Preparatory tasks. This also includes tasks for the development of attention and observation: “What object was removed?” and “What has changed?”.

2. Tasks in which the teacher indicated on the basis of the classification.

3. Tasks in which the children themselves identify the basis of the classification.

Tasks for the development of the processes of analysis, synthesis, classification were widely used by us in the lessons, when working with a mathematics textbook. For example, the following tasks were used to develop analysis and synthesis:

1. Connecting the elements into a single whole: Cut out the necessary shapes from the "Appendix" and make a house, a boat, a fish out of them.

2. Search for various features of the object: How many corners, sides and vertices does the pentagon have?

3. Recognition or compilation of an object according to given characteristics: What number comes before the given number when counting? What number follows this number? For the number...?

4. Consideration of this object from the point of view of various concepts. Make different problems according to the picture and solve them.

5. Statement of various tasks for a given mathematical object. By the end of the school year, Lida had 2 blank sheets in her Russian language notebook and 5 blank sheets in her math notebook. Put to this condition first such a question that the problem is solved by addition, and then such a question that the problem is solved by subtraction.

Tasks aimed at developing the ability to classify were also widely used in the classroom. For example, children were asked to solve the following problem:There are 9 episodes in the cartoon about dinosaurs. Kolya has already watched 2 episodes. How many episodes does he have left to watch?

Write two problems inverse to the given one. Select a schematic diagram for each problem. We also used tasks aimed at developing the ability to compare, for example, highlighting features or properties of one object:

Tanya had several badges. She gave 2 pins to a friend and she has 5 pins left. How many badges did Tanya have? Which schematic drawing is suitable for this task?

All the proposed tasks, of course, were aimed at the formation of several thinking operations, but due to the predominance of any of them, the exercises were divided into the proposed groups. It is necessary to further develop and improve techniques and methods for the development of productive thinking, depending on the individual properties and characteristics of each individual student.It is necessary to continue the work begun, using various non-standard logical tasks and tasks, not only in the classroom, but also in extracurricular activities.

CONCLUSION

Activities can be reproductive and productive. Reproductive activity is reduced to the reproduction of perceived information. Only productive activity is connected with the active work of thinking and finds its expression in such mental operations as analysis and synthesis, comparison, classification and generalization. If we talk about the current state of the modern elementary school in our country, then the main place is still occupied by reproductive activity. In lessons in two main academic disciplines - language and mathematics - children almost all the time solve educational and training typical tasks. Their purpose is to ensure that the search activity of children with each subsequent task of the same type gradually curtails and, ultimately, completely disappears. In connection with such a system of teaching, children get used to solving problems that always have ready-made solutions, and, as a rule, only one solution. Therefore, children are lost in situations where the problem has no solution or, conversely, has several solutions. In addition, children get used to solving problems based on the already learned rule, so they are not able to act on their own to find some new way. It is also advisable to use didactic games, exercises with instructions in the lessons. With their help, students get used to think independently, use the acquired knowledge in various conditions in accordance with the task. Primary school age has deep potential for the physical and spiritual development of the child. Under the influence of training, two main psychological neoplasms are formed in children - the arbitrariness of mental processes and an internal plan of action (their implementation in the mind). In the process of learning, children also master the methods of arbitrary memorization and reproduction, thanks to which they can present the material selectively, establish semantic connections. The development of the cognitive processes of the younger student will be formed more effectively under the purposeful influence from the outside. The instrument of such influence are special techniques, one of which is didactic games.

Speech by a primary school teacher

MBOU School No. 108

Yangirova-Elizarieva Yesseniya Vladimirovna

at a meeting of the MO "Primary school teachers"

April 2018

Self-education "Development of logical

thinking of younger students"

Introduction 3

Chapter I

Thinking as a philosophical - psychological - pedagogical category 4

Features of the logical thinking of a younger student 11

Text problems as a means of developing logical thinking 16

Chapter II. A set of tasks for the development of logical thinking of younger students:

2.1. Tasks - jokes, smart (simple) 21

2.2. Tasks in verse, simple - compound 23

2.3. Historical tasks 27

2.4. Puzzles, crosswords, charades 29

2.5. Geometric problems 32

Conclusion 33

References 35

Introduction

The social transformations taking place today in Russia have created certain conditions for perestroika processes in the field of education, including in the first grade school. Modern concepts of primary education proceed from the priority of the development of the student's personality on the basis of the leading activity. It was this understanding of the goals of elementary school that prompted the introduction of the term "developmental education" into didactics.

It cannot be said that the idea of ​​developmental education is new, that earlier the problems of child development in the learning process were not raised or solved.

Primary education at the present stage is not closed, but is considered as a link in the system of basic education, moreover, it is the foundation on which the links of this system are built. In this regard, the primary school has a special responsibility.

The relevance lies in the fact that in modern times, children learn using developing technologies, where logical thinking is the basis. From the beginning of training, thinking moves to the center of mental development (L.S. Vygotsky) and becomes decisive in the system of other mental functions, which, under its influence, become intellectualized and acquire an arbitrary character. Numerous observations of teachers and research by psychologists have convincingly shown that a child who has not learned how to learn, who has not mastered the methods of mental activity in the primary grades of school, usually goes into the category of underachievers in the middle grades.

The study of thinking, the process of mental development was carried out by such prominent scientists as G. Eysenck, F. Galton, J. Ketell, K. Meili, J. Piaget, C. Spearman and others. In domestic science, S.L. Rubinshtein, L.S. Vygotsky, N.A. Podgoretskaya, P.P. Blonsky, A.V. Brushlinsky, V.V. Davydov, A. V. Zaporozhets, G.S. Kostyuk, A.N. Leontiev and others.

One of the important directions in solving this problem is the creation in the primary grades of conditions that ensure the full mental development of children, associated with the formation of stable cognitive processes, skills and abilities of mental activity, the quality of the mind, creative initiative and independence in search of ways to solve problems. tasks. However, such conditions are not yet fully provided in primary education, since a teacher’s organization of students’ actions according to a model is still a common technique in teaching practice: too often teachers offer training-type exercises to children that are based on content and do not require manifestation of invention and initiative.

The formation of independence in thinking, activity in the search for ways, achievement of the set goal involves the solution of non-standard, non-standard tasks by children, sometimes having several ways of solving, although correct, but to varying degrees optimal.

The foregoing determined the topic of the study: "The development of logical thinking of a younger student in solving text problems in mathematics lessons."

Object of study: educational activity of junior schoolchildren.

Subject of study: logical thinking of younger students.

Purpose of the study: to reveal the development of logical thinking of students in mathematics lessons.

To achieve the goal of the study, it is necessary to solve the following tasks:

To reveal the essence of logical thinking and the peculiarity of its formation in a younger student;

Make up a set of tasks (tasks) for the development of logical thinking of a younger student;

ChapterI. Philosophical - psychological - pedagogical feature of the development of thinking of younger students

1. Thinking as a philosophical - psychological - pedagogical category

The information received by a person from the surrounding world allows a person to imagine objects in the absence of their own, to foresee their changes in time, to rush with thought into unimaginable distances and the micro-world. All this is possible through the process of thinking. In psychology, thinking is understood as the process of an individual's cognitive activity, characterized by a generalized and mediated reflection of reality. Thinking expands the boundaries of our knowledge by virtue of its nature, which allows us to reveal indirectly - by inference - what is not given indirectly - by perception.

What is thinking in philosophy? There is such a statement that a person is always thinking about something, even when it seems to him that he is not thinking about anything. A thoughtless state, according to psychologists, is a state in its essence as relaxed as possible, but still thinking, at least about not thinking about anything. From sensory cognition, from the establishment of facts, the dialectical path of cognition leads to logical thinking. Thinking is a purposeful, mediated and generalized reflection by a person of the essential properties and relations of things. Creative thinking is aimed at obtaining new results in practice, science, and technology. Thinking is an active process of posing problems and solving them. Inquisitiveness is an essential sign of a thinking person. The transition from sensation to thought has its objective basis in the bifurcation of the object of knowledge into internal and external, essence and its manifestation, into separate and general.

The special structure of our sense organs and their small number, therefore, do not put an absolute limit on our knowledge, because the activity of theoretical thinking joins them. “The eye sees far, but the mind sees even further,” says the popular saying. Our thought, overcoming the appearance of phenomena, their external appearance, penetrates into the depth of the object, into its essence. Based on the data of sensory and empirical experience, thinking can actively correlate the readings of the sense organs with all the knowledge already available in the head of each individual, moreover, with the total experience, knowledge of mankind, and to the extent that they have become the property of a given person, and solve practical and theoretical problems, penetrating through phenomena into essences of a deeper and deeper order.

Logical - this means subordinate to the rules, principles and laws by which thought moves to the truth, from one truth to another, deeper. Rules, laws of thinking constitute the content of logic as a science. These rules and laws are not something immanent in thought itself. Logical laws are a generalized reflection of the objective relations of things based on practice. The degree of perfection of human thinking is determined by the extent to which its content corresponds to the content of objective reality. Our mind is disciplined by the logic of things, reproduced in the logic of practical actions and all by the system of spiritual culture. The real process of thinking unfolds not only in the head of an individual, but also in the bosom of the entire history of culture. The logicality of thought with the reliability of the initial provisions is, to a certain extent, a guarantee not only of its correctness, but also of its truth. This is the great power of logical thinking.

The first essential feature of thinking is that it is a process of mediated cognition of objects. This mediation can be very complex, multi-stage. Thinking is mediated, first of all, by the sensual form of cognition, often by the symbolic content of images, by language. On the basis of the visible, audible and tangible, people penetrate into the unknown, inaudible and intangible. It is on this mediated knowledge that science is built.

What is the basis for mediated cognition? The objective basis of the mediated process of cognition is the presence of mediated connections in the world. For example, cause-and-effect relationships make it possible, based on the perception of the effect, to draw a conclusion about the cause, and on the basis of knowledge of the cause, to foresee the effect. The mediated nature of thinking also lies in the fact that a person cognizes reality not only on the basis of his personal experience, but also takes into account the historically accumulated experience of all mankind.

In the process of thinking, a person draws threads from the canvas of the general stock of knowledge available in his head about a wide variety of things, from all the experience accumulated by life, into the stream of his thoughts. And often the most incredible comparisons, analogies and associations can lead to the solution of an important practical and theoretical problem. Theorists can successfully extract scientific results about things they may never have seen.

In life, not only "theorists" think, but also practitioners. Practical thinking is aimed at solving particular specific problems, while theoretical thinking is aimed at finding general patterns, if theoretical thinking is focused mainly on the transition from sensation to thought, idea, theory, then practical thinking is aimed primarily at the implementation of thoughts, ideas, and theories. in life. Practical thinking is directly included in practice and is constantly subjected to its controlling influence. Theoretical thinking is subjected to practical verification not in every link, but only in the final results. The rational content of the thinking process is clothed in historically elaborated logical forms. The main forms in which thinking arose, develops and is carried out are concepts, judgments and inference.

A concept is a thought that reflects the general, essential properties, connections of objects and phenomena. Concepts not only reflect the general, but also dismember things, group them, classify them in accordance with their differences. Unlike sensations, perceptions and representations, concepts are devoid of visualization or sensibility. The concept arises and exists in the human head only in a certain connection, in the form of judgments. To think means to judge something, to identify certain connections and relationships between various aspects of an object and between objects.

Judgment is such a form of thought, which, through the connection of concepts, confirms (or denies) something, about something. Judgment is there where we find affirmation or negation, falsity or truth, as well as something conjectural.

Thinking is not mere judgment. In the real process of thinking, concepts or judgments do not stand alone. They are like links included in the chain of more complex mental actions - in reasoning. A relatively complete unit of reasoning is inference. From existing judgments, it forms a new conclusion. From existing judgments, it forms a new one - a conclusion. It is the derivation of new judgments that is characteristic of inference as a logical operation. The propositions from which the conclusion is drawn are the premises. Inference is an operation of thinking, during which a new judgment is derived from a comparison of a number of premises.

The disclosure of relationships, connections between objects is an essential task of thinking: this determines the specific path of thinking to an ever deeper knowledge of being.

The task of thinking is to identify essential, necessary connections, based on real dependencies, separating them from random coincidences.

In a detailed process of thinking in the course of solving a complex problem that cannot be determined by an unambiguous algorithm, several main stages or phases can be distinguished. The beginning of the thought process is seen in the creation of a problem situation. Already this stage is not for everyone - those who are not used to thinking take the world around them for granted. The more knowledge, the more problems a person sees. It is necessary to have I. Newton's thinking in order to see a problem in an apple falling to the ground. A problem situation, as a rule, contains a contradiction and does not have an unambiguous solution.

The main mental operations are analysis, synthesis, comparison, abstraction, concretization, generalization.

Analysis- this is a mental decomposition of the whole into parts or a mental selection of the whole of its sides, actions, relations. In its elementary form, analysis is expressed in the practical decomposition of objects into their component parts.

Synthesis - it is a mental union of parts, properties, actions into a single whole. The operation of synthesis is the opposite of analysis. In its process, the relation of individual objects or phenomena as elements or parts to their complex whole, object or phenomenon is established. Synthesis is not a mechanical connection of parts and therefore is not reduced to their sum.

Comparison- establishing similarities or differences between objects and phenomena or their individual features. In practice, the comparison can be one-sided (incomplete in one feature), and multilateral (complete, in all features); superficial and deep; unmediated and indirect.

Abstraction- consists in the fact that the subject, isolating any properties, signs of the object under study, is distracted from the rest. Abstraction is usually carried out as a result of analysis. It was through abstraction that abstract, abstract concepts of length, breadth, quantity, equality, value, etc. were created. Abstraction is a complex process that depends on the originality of the object under study and the goals of the study. Thanks to abstraction, a person can be distracted from the single, concrete.

Specification- involves the return of thought from the general and abstract to the concrete in order to reveal the content. Concretization is addressed in the event that the expressed thought turns out to be incomprehensible or it is necessary to show the manifestation of the general in the individual.

Generalization- a mental union of objects and phenomena according to their essential and common features.

All of these operations cannot occur in isolation, without connection with each other. On their basis, more complex operations arise, such as classification, systematization, and so on. Human thinking not only includes various operations, but also proceeds on the totality and allows us to speak about the existence of different types of thinking.

It is possible to single out creative (productive), reproducing (reproductive), theoretical, practical, objective-effective, visual-figurative, verbal-logical thinking.

Creative thinking is aimed at creating new ideas, its result is the discovery of a new one or the improvement of the solution of a particular problem.

It is necessary to distinguish between the creation of an objectively new, i.e., something that has not yet been created, and a subjectively new one for a given particular person.

Unlike creative thinking, reproductive thinking is the application of ready-made knowledge and skills.

Features of subject-effective thinking are manifested in the fact that tasks are solved with the help of a real, physical transformation of the situation, testing the properties of objects. This form of thinking is most typical for children under 3 years old.

Visually - figurative thinking is associated with operating images. This type of thinking is spoken about when a person, solving a problem, analyzes, compares, generalizes various images, ideas about phenomena and objects. Visually - figurative thinking most fully recreates the whole variety of various actual characteristics of the subject. The vision of an object from several points of view can be simultaneously fixed in the image. In this capacity, visual-figurative thinking is practically inseparable from imagination.

Verbal-logical thinking functions on the basis of linguistic means and represents the latest stage of the historical and ontogenetic development of thinking. For verbal - logical thinking is characterized by the use of concepts, logical constructions that do not have a direct figurative expression (for example, cost).

It should be noted that all types of thinking are closely interconnected. Separate types of thinking constantly flow into each other. So, it is practically impossible to separate visually - figurative and verbally - logical thinking, when the content of the task is diagrams and graphs. Practically effective thinking can be both intuitive and creative at the same time. Therefore, when trying to determine the type of thinking, one should remember that this process is always relative and conditional.

Thus, logical thinking is the ability to operate with abstract concepts, this is controlled thinking, this is thinking by reasoning, this is strict adherence to the laws of inexorable logic, this is the impeccable construction of cause-and-effect relationships.

Features of the logical thinking of a younger student

By the beginning of primary school age, the mental development of the child reaches a fairly high level. All mental processes: perception, memory, thinking, imagination, speech - have already passed quite a long way of development, since the child's curiosity is constantly aimed at knowing the world around and building the world around. The child, playing, experiments, tries to establish cause-and-effect relationships. He himself, for example, can find out which objects sink and which will float.

Various cognitive processes that provide a variety of activities of the child do not function in isolation from each other, but represent a complex system, each of them is connected with all the others. This relationship does not remain unchanged throughout childhood: at different periods, one of the processes acquires leading importance for the overall mental development.

Depending on the extent to which the thought process is based on perception, representation or concept, there are three main types of thinking:

1. Subject-effective (visual-effective).

2. Visual-figurative.

3. Abstract (verbal-logical).

Object-effective thinking - thinking associated with practical, direct actions with the subject; visual-figurative thinking - thinking that is based on perception or representation (typical for young children). An example is the game "Postman", used in a math lesson: Three students participate in the game - the postman. Each of them needs to deliver a letter to three houses. Each house depicts one of the geometric shapes. The postman's bag contains letters - 10 geometric shapes cut out of cardboard. On a signal from the teacher, the postman looks for the letter and takes it to the appropriate house. The winner is the one who quickly delivers all the letters to the houses - decomposes geometric shapes.

Visual-figurative thinking makes it possible to solve problems in a directly given, visual field. The further way of development of thinking lies in the transition to verbal-logical thinking - this is thinking in terms that are devoid of direct visibility inherent in perception and representation. The transition to this new form of thinking is associated with a change in the content of thinking: now these are no longer specific ideas that have a visual basis and reflect the external signs of objects, but concepts that reflect the most essential properties of objects and phenomena and the relationship between them. This new content of thinking in primary school age is set by the content of the leading educational activity. For example, you can use tasks such as: make 2 squares out of 7 sticks; continue the pattern and others.

Verbal-logical, conceptual thinking is formed gradually during primary school age. At the beginning of this age period, visual-figurative thinking is dominant, therefore, if in the first two years of education children work a lot with visual samples, then in the next classes the volume of this kind of activity is reduced. As he masters educational activities and assimilates the basics of scientific knowledge, the student gradually joins the system of scientific concepts, his mental operations become less connected with specific practical activities or visual support. Verbal-logical thinking allows the student to solve problems and draw conclusions, focusing not on the visual signs of objects, but on internal, essential properties and relationships. In the course of training, children master the methods of mental activity, acquire the ability to act "in the mind" and analyze the process of their own reasoning. The child has logically correct reasoning: when reasoning, he uses the operations of analysis, synthesis, comparison, classification, generalization. Developing verbal-logical thinking through the solution of logical problems, it is necessary to select such tasks that would require inductive (from the singular to the general), deductive (from the general to the singular) and traductive (from the singular to the singular or from the general to the general, when the premises and conclusion are judgments of the same generality) inferences. Traductive reasoning can be used as the first step in learning to solve logical problems. These are tasks in which, based on the absence or presence of one of the two possible features in one of the two objects under discussion, a conclusion follows about the presence or absence of this feature in the other object, respectively. For example, "Natasha's dog is small and fluffy, Ira's is big and fluffy. What is the same about these dogs? What is different?"

As a result of studying at school, when it is necessary to regularly perform tasks without fail, younger students learn to control their thinking, to think when necessary.

In many ways, the formation of such arbitrary, controlled thinking is facilitated by the tasks of the teacher in the lesson, which encourage children to think.

When communicating in primary school, children develop conscious critical thinking. This is due to the fact that the class discusses ways to solve problems, considers various solutions, the teacher constantly asks students to justify, tell, prove the correctness of their judgment. The younger student regularly becomes part of the system when he needs to reason, compare different judgments, and carry out conclusions.

In the process of solving educational problems in children, such operations of logical thinking as analysis, synthesis, comparison, generalization and classification are formed.

Recall that analysis as a mental action involves the decomposition of the whole into parts, the selection by comparing the general and the particular, the distinction between the essential and the non-essential in objects and phenomena.

Mastering analysis begins with the child's ability to distinguish various properties and signs in objects and phenomena. As you know, any subject can be viewed from different points of view. Depending on this, one or another feature, the properties of the object, come to the fore. The ability to isolate properties is given to younger students with great difficulty. And this is understandable, because the concrete thinking of the child must do the complex work of abstracting the property from the object. As a rule, out of an infinite set of properties of any subject, first-graders can single out only two or three. As children develop, expand their horizons and get acquainted with various aspects of reality, this ability, of course, improves. However, this does not exclude the need to specifically teach younger students to see their different aspects in objects and phenomena, to single out many properties.

In parallel with mastering the technique of highlighting properties by comparing various objects (phenomena), it is necessary to derive the concept of common and distinctive (private), essential and non-essential features, while using such operations of thinking as analysis, synthesis, comparison and generalization. The inability to single out the general and the essential can seriously impede the learning process. In this case, typical material: subsuming a mathematical problem under an already known class. The ability to highlight the essential contributes to the formation of another skill - to be distracted from unimportant details. This action is given to younger students with no less difficulty than highlighting the essential.

In the process of learning, tasks become more complex: as a result of highlighting the distinctive and common features of several objects, children try to break them into groups. Here such operation of thinking as classification is necessary. In elementary school, the need to classify is used in most lessons, both when introducing a new concept and at the stage of consolidation.

In the process of classification, children analyze the proposed situation, identify the most significant components in it, using the operations of analysis and synthesis, and generalize for each group of objects included in the class. As a result, there is a classification of objects according to an essential feature.

As can be seen from the above facts, all operations of logical thinking are closely interconnected and their full-fledged formation is possible only in combination. Only their interdependent development contributes to the development of logical thinking as a whole. Methods of logical analysis, synthesis, comparison, generalization and classification are necessary for students already in the 1st grade, without mastering them there is no full assimilation of educational material.

These data show that it is at primary school age that it is necessary to carry out purposeful work to teach children the basic methods of mental activity.

Text tasks as a means of developing logical thinking

The term "task" in terms of frequency of use is one of the most common in science and educational practice.

The cognitive task is the subject of research in many scientific fields, therefore, the definition of this concept reflects the specifics of each of them.

In psychology, the term "task" is used to designate objects related to three different criteria: 1) to the goal of the subject's actions, to the requirements set for the subject; 2) to a situation that includes, along with the goal, the conditions in which it must be achieved; 3) to the verbal formulation of this situation.

Some authors consider the concept of "task" as indefinable and in the broadest sense meaning that which requires the execution of a decision. There are attempts to clarify the content of the task through the generic concept of "the phenomenon of learning" and specific differences: to be a way of organizing and managing educational and cognitive activities; the carrier of actions adequate to the content of training; a means of purposeful formation of knowledge, skills; act as a form of teaching methods; serve as a link between theory and practice.

The latter interpretation covers the whole range of subject problems presented in textbooks, as well as those that can take their place in them. These are research tasks that are non-standard in their formulation.

Numerous points of view on the content of the concept of "task", their classification, the priority of one or another of their types is due to the dynamics of the change in the role and place of tasks in teaching students. The study of this phenomenon leads to the conclusion that the attitude to tasks depended on the status of education, teaching methods, various pedagogical concepts, in particular the concepts of the content of education, etc.

In the history of the use of tasks, the following stages can be distinguished:

the study of theory is carried out with the aim of teaching problem solving;

teaching the subject is accompanied by problem solving;

learning through problem solving;

problem solving as the basis of the educational process

The peculiarity of the first stage is clearly visible from the preface to "Arithmetic" by LF Magnitsky, where it was stated that mathematics should be "corrected" for solving problems.

Today, methodologists are looking for didactic techniques, the use of which contributes to the mastery of schoolchildren with the ability to apply knowledge to solving problems of a certain type.

The second stage, at which teaching the subject is accompanied by solving problems, is due to the fact that one of the main goals of teaching is the formation of skills to apply theoretical material. The assimilation of the theory is reduced to its memorization and reproduction in solving problems. In the bowels of this stage, the idea of ​​expanding the functions of tasks is born. So, S.I. Shokhor-Troitsky in his work "The Purpose and Means of Teaching Lower Mathematics from the Point of View of the Requirements of General Education" noted that tasks should serve as a point of departure for teaching, and not as a means of training students in a certain direction.

This view of the role of tasks formed the content of the new (III) stage: teaching the subject by solving problems. These thoughts are reflected in official documents. Thus, the resolution of the International Congress of Mathematicians (Moscow, 1966) emphasizes that problem solving is the most effective form of not only the development of mathematical activity, but also the assimilation of knowledge, skills, methods and applications of mathematics.

However, despite such documented claims, the role of tasks in learning is reduced to using them as a means of developing and applying theory. This can be confirmed by the training scheme presented, for example, in the book "Pedagogy of Mathematics" by A.A. Stolyar: "Tasks - theory - tasks" (Moscow, 1986)

In this scheme, the role of tasks in the assimilation of the theory continues to be correlated with its memorization and reproduction. Knowledge is still identified with educational information.

Since the second half of the 20th century, publications have appeared that deal with extended functions of tasks. For example, K.I. Neshkov and A.D. Samushin distinguishes the following groups of tasks:

with didactic functions;

with cognitive functions;

with development features.

The tasks of the first group are designed to master the theoretical material, in the process of solving problems of the second type, students deepen their knowledge of the theory and methods of solving them. The content of tasks of the third type can "deviate" from the main course, complicate as much as possible some of the previously studied questions of the course. Of course, it is expedient to widely use tasks in training, but one cannot agree that developing functions are inherent only in tasks whose content "departs" from the compulsory course, expanding it.

Research on the function of tasks contributed to understanding their role and place in learning. All scientists are unanimous that the tasks serve both the assimilation of knowledge and skills, and the formation of a certain style of thinking (logical thinking). It is already becoming clear that the formation of knowledge (concepts, judgments, theories) cannot be carried out outside of activity.

Teachers' research has led to a new understanding of the content of education. If earlier the content was composed of subject knowledge, now, in addition to them, methods of activity are included in the form of various actions included in the content of learning through tasks. This is a completely new turn: from a means of forming skills, tasks begin to turn into a multidimensional learning phenomenon. They become the bearer of actions that are adequate to the content of training; a means of purposeful formation of knowledge, skills; the way of organizing and managing the educational and cognitive activities of students; one of the forms of implementation of teaching methods; link between theory and practice.

Problem solving should ensure the mastery of the following skills: to recognize objects belonging to the concept; to deduce consequences from the belonging of an object to a concept, to move from the definition of a concept to its features; rethink objects in terms of different concepts, etc.

With the change in the role and place of tasks in training, the very content of tasks is also updated. If earlier the requirement of the problem was expressed by the words: "find", "construct", "calculate", "prove", now - "explain", "choose the most optimal solution from various methods", "predict various solutions", "is it true solution?", "explore".

Some scholars have attempted to define a criteria basis for selecting an aesthetically pleasing task.

For example, E.T. Bell, performing similar studies on a mathematical object, highlights the following signs of attraction:

universality of use in various branches of mathematics;

productivity or the possibility of stimulating influence on further progress in this area on the basis of abstraction and generalization;

the maximum coverage capacity of objects of the type in question.

That is, now a new stage in the use of tasks, when they serve as the basis for the education, development and upbringing of students. Tasks are needed, the solution of which requires students to integrate knowledge from various educational areas.

In fact, everyday human activity consists of solving problems in all the variety of their content.

In the course of the theoretical foundations of mathematics and in teaching mathematics to younger students, text and plot tasks predominate. These tasks are formulated in natural language (that is why they are called text tasks); they usually describe the quantitative side of some phenomena, events (therefore they are often called plot). They are tasks to find what you are looking for and come down to calculating the unknown value of a certain quantity (which is why they are sometimes called computational). By tasks (in a school course) we mean both equations, and finding the value of a numerical expression, etc., because by structure (there is a condition - known, there is a requirement - sought), therefore, these are tasks. Moreover, “data” is a sufficient condition, “sought” is a necessary one, i.e. on the face of logical following, and this is shown that the problem is being solved.

That is, text tasks in the course of mathematics, like the entire course of mathematics, develop the logical thinking of students of any age. For this development to be successful, one must start from the first grade, but for this, primary school teachers must know the essence of logical reasoning themselves, be able to teach their students to think logically.

ChapterII. A set of tasks for the development of logical thinking of younger students

2.1. Tasks - jokes, smart

There were 40 magpies on one tree. A hunter passed, shot and killed 6 magpies. How many magpies are left on the tree? (None (the magpies got scared of the shot and flew away)).

How many ends does a stick have? - Two. How many ends do two and a half sticks have? (Six)

The two went to the river. There is only one boat on the shore. How can they cross to the other side if the boat can only take one person? (Travelers approached opposite banks of the river).

How many ends do thirty and a half sticks have? (62 ends)

One fifth-grader wrote about himself like this: "I have twenty-five fingers on one hand, the same number on the other, and on both legs 10." How it is? It is necessary to correctly punctuate: "I have twenty fingers: five on one hand, the same number on the other, but on both legs 10."

The shepherd chased the geese. One goes ahead of three, one drives three and two go in the middle. How many geese did he have? (Four)

The shepherd was asked how many geese he had. He replied: "One goes ahead of the two, one pushes the two, one goes in the middle." How many geese did the shepherd feed? (Three)

There are months that end with the number 30 or 31. And in which months does the number 28 occur? (In all)

A team of three horses traveled 60 km. How many kilometers did each horse ride? (60 km)

An airplane flies the distance from city A to city B in 1 hour and 20 minutes. However, he makes the return flight in 80 minutes. How do you explain it? (80 min = 1 hour 20 min)

Two trains left Leningrad and Moscow at the same time. The speed of the Leningrad one is 2 times that of the Moscow one. Which train will be further from Moscow when they meet? (Both trains will be at the same distance from Moscow).

When can a person race at the speed of a racing car? (When he's in that car)

Is it possible to throw a ball in such a way that, after flying for some time, it stops and starts moving in the opposite direction? (The ball must be thrown up)

Two fathers and two sons shared three oranges among themselves so that each got one orange. How could this happen? (They were grandfather, father and grandson)

A boy has as many sisters as brothers, and his sister has half as many sisters as brothers. How many brothers and sisters are in this family? (1 sister and 2 brothers)

How many ends does 72 and a half sticks have? (146 ends)

A cyclist traveled from a city to a village 32 km apart at a speed of 12 km/h. A pedestrian left the village for the city at the same time with a speed of 4 km/h. Which of them will be further from the city in 2 hours? (In 2 hours they will be at the same distance from the city)

Someone decided to enter the protected area and for this he began to observe the gatekeeper. The first visitor was asked the question: "Twenty-two?" He answered: "Eleven," and was let through the gate. The second was asked: "Twenty-eight?" After the answer: "Fourteen" and they missed him. "How simple," - someone thought and went to the gate. He was asked: "Forty-eight?" He said, "Twenty-four," and was arrested.
How was he supposed to answer to be let through? (He should answer: "Eleven", since the answer password was the number of letters in the number that the gatekeeper asked).

2.1. Tasks in verse, simple - compound

Tasks in verse

Apples fell from the branch to the ground.

Crying, crying, tears shed
Tanya collected them in a basket.
Brought as a gift to my friends
Two Seryozhka, three Antoshka,
Katerina and Marina
Olya, Sveta and Oksana,
The biggest one is for mom.
Speak quickly
How many Tanya's friends? (7 friends)

P growing tasks:

The turtle crawled for 3 minutes at a speed of X m/min. Which way did she crawl?

What values ​​can X take?

Maybe 1000m?

More or less? (less than 5 m)

What path will she crawl if X = 5 m/min?

5 ∙ 3 \u003d 15 (m.)

Answer: 15 m.

There were 18 sweets, ate 2/9. How many sweets did you eat?

18: 9 ∙ 2 \u003d 4 (k)

Answer: ate 4 candies.

For 6 kg of apples they paid d rubles. What is the price of apples?

What values ​​does the variable d take?

d = 60, 120, 66, 72.

At what values ​​of d will the price be expressed in kopecks? (77, 62, 123, 67).

Two flies compete in running. They run from the floor to the ceiling and back. The first fly runs in both directions at the same speed. The second runs down twice as fast as the first, and up twice as slow as the first. Which fly will win?

Answer: The first fly reaches the ceiling when the second fly is halfway there; the first returns to the floor when the second reaches the ceiling. The first one wins.

Composite tasks:

Four hobbits traveled along the great road. Each was carrying 24 kg of provisions. How many days will this provision last if the hobbits eat 6 kg every day?

(24 ∙ 4) : 6 = 16 (d.)

Answer: the provisions will last for 16 days.

A family of crocodiles walked down the street: a grandfather, two fathers and two sons. All together were 90 years old. How many crocodiles were walking down the street? How old is each if each father is 25 years older than his son?

1) 90 - 25 - 25 - 25 \u003d 15 (l.) - three parts

2) 15: 3 = 5 (l.) - to the grandson

3) 5 + 25 = 30 (l.) - dad

4) 30 + 25 = 55 (l.) - grandfather

Answer: 5 years old grandson, 30 years old father, 55 years old grandfather.

Robinson and Friday have 11 nuts together. Robinson and his Parrot have 13 nuts. Parrot and Friday have 12 nuts. How many nuts do Robinson, Friday and Parrot have in total?

At the Parrot - 7 op.

At Friday - 5 op.

Robinson has 6 op.

P + Fri = 11

Pop + Fri = 12

2R + 2Fri + 2Pop = 36

R + Fri + Pop \u003d 18 (op.) - total

Answer: they all have 18 nuts together.

“Ah - ah, from the Earth to the Moon, only 384,400 km!” - exclaimed the Hare. He loaded 15800 kg of equipment onto the spacecraft and began flying to the moon. "Wait for it!" Wolf said. He loaded onto the spacecraft 6480 kg of equipment less than a hare, and flew in pursuit. He caught up with the hare at a distance of 105,600 km from the Earth. Which of the following questions can be answered by the condition of the problem?

How many kilograms does the hare weigh?

How many kilograms of equipment did Wolf load onto the spacecraft?

At what distance from the Moon did the Wolf catch up with the Hare?

How many kilometers from the moon to the earth?

2) 15800 - 6480 = 9320 (kg.) - Loaded by Wolf

4) 384400 - 105600 = 278800 (km.) - from the Moon

The average age of the eight people in the room was 12 years. When 1 person left the room, the average age became 11 years old. How old was the person who left the room?

12 ∙ 8 \u003d 96 (l.) - was everything

11 ∙ 7 \u003d 77 (l.) - became the remaining 7

96 - 77 \u003d 19 (l.) - was released.

Answer: 19 years old was released.

2.3. Historical tasks

On October 4, 1956, the first artificial Earth satellite with a mass of 84 kg was launched in the Soviet Union. Calculate the mass of the second satellite of the Earth, together with the equipment and the dog Laika (which was launched in the USSR on November 3, 1957), if its mass was 425 kg more than the mass of the first satellite. How many full years, months and days have passed since the launch of the first satellite in the Soviet Union to the present day? (until March 20, 2004)

84 + 425 = 509 (kg.) - mass of the second satellite

1956 9 months 3 days

46 l. 5 months 16 days

Orenburg was founded on April 30, 1733. How many years, months and days does the city of Orenburg exist (as of March 20, 2004)

2003 2 months 19 days

1742 3 months 29 days

260 l. 10 months 19 days

The peasant needs to be transported across the river wolf, goat and cabbage. The boat is small: a peasant can fit in it, and with him only a goat, or only a wolf, or only a cabbage. But if you leave the wolf with the goat, then the wolf will eat the goat, and if you leave the goat with the cabbage, then the goat will eat the cabbage. How did the peasant transport his cargo?

Answer: We'll have to start with a goat. The peasant, having transported the goat, returns and takes the wolf, which he transports to the other side, where he leaves him, but then he takes and carries the goat back to the first bank. Here he leaves her and transports the cabbage to the wolf. Following this, returning, he carries a goat, and the crossing ends safely.

It is said that two fathers and two sons found three rupees (silver coins) on the road leading to Bombay and quickly divided them among themselves, and each got a coin. How did they manage to cope with the task?

Answer: The travelers were able to share the find equally, because there were three of them: grandfather, father and son (or in other words: two fathers, two sons).

While passing through a small town, one merchant went to have a bite to eat at a restaurant, and then decided to get a haircut. There were only two hairdressers in the town, and in each there was only one master, who is also the owner. In one, the hairdresser was unkemptly shaved and had a bad cut, and in the other, he was clean-shaven and had a great haircut. The merchant decided to have his hair cut at the first barbershop. Do you think he made the right choice?

Answer: The merchant correctly judged that since there are only two hairdressers in the city, they certainly cut each other's hair. So, you need to go get a haircut to someone who has a bad haircut.

A peasant woman came to the market to sell eggs. The first customer bought half of all the eggs from her and another half an egg. The second customer bought half the remaining eggs and another half an egg. The third bought only one egg. After that, the peasant woman had nothing left. How many eggs did she bring to the market?

Answer: After the second customer bought half of the remaining eggs and another half an egg, the peasant woman had only one egg left. This means that one and a half eggs make up the second half of what is left after the first sale. It is clear that the total remainder is three eggs. By adding half an egg, we get half of what the peasant woman originally had. So, the number of eggs she brought to the market is seven.

2.4. Rebuses, crossword puzzles, charades

puzzles

Guess 4 names:

(Seva, Seryozha, Nastya, Vova)

What closed the question?

(Number 1, because the top fish is the minuend, the bottom ones are the subtrahend, and the number is the difference between the numbers obtained)

Crosswords

To crossword number 1

Vertically:

1. The division action component. (Dividend)

2. The largest remainder when divided by five. (Four)

3. To find out how many times one number is greater than another, you need to perform the action ...? (Subtraction)

4. Multiplication action component. (Factor)

Horizontally:

5. Divisible, which is completely divisible by some number.

To crossword number 2

Horizontally:

There are ten in one meter ... (Decimeter)

This unit of mass measures the weight of a person. (Kilogram)

There are ten in one decimeter ... (Centimeter)

A record made up of numbers, letters, and arithmetic symbols. (Expression)

A device made of transparent material with which you can measure the area of ​​​​a figure. (Palette)

Vertically :

Read the keyword. What does it mean? (Ton - the name of various units of mass).

Charades

You measure the area
Remember first -
Its you at school,
Undoubtedly studied.
five letters,
Those who follow are inspired,
They can't live
Without dance, music and stage.
For exhibits
weapon eyes,
You will find the answer
In the historical museum. (Ar - ballet)

Number and note next to it,

Yes, write a consonant

But in general - there is one master,

He makes great furniture. (One hundred - la - r)

He is of high rank and rank.

And the whole word is a designation,

Dose-breaking training. (Couple - Count)

In the dance you will find the first syllable,

And make a suggestion.

In general, the one who protects

Glory, honor of the native country,

He knows no fear in battle

And in labor - labor hero. (Pa - three - from).

2.5. Geometric problems

"My friend! You are given a figure of 5 squares: 4 small and one large. You need to remove a few matches so that 2 squares (of any size) remain." What do you think, how many matches, at the very least, should be removed so that instead of five squares there are two? (2 matches will need to be removed).

Five Little Cooks decided to share a large rectangular chocolate bar among themselves.

But she fell to the floor and when they unrolled her, they saw that the chocolate bar had broken into 7 pieces. Nikolay ate the biggest piece. Sveta and Masha ate the same amount of chocolate, but Sveta ate three pieces and Masha only one piece. Bella ate 1/7 of the whole chocolate bar and Katya ate the rest. What piece of chocolate did Katya get? (Nikolay ate the sixth. Sveta ate 7, 5, 4, and Masha ate the third. Bella ate the first. So Katya ate the second.)

Conclusion

The development of logical thinking as a pedagogical process must be carried out in accordance with the laws of the development of the child's body, in unity and harmony with the intellectual development of the child.

Since logical thinking can be considered as a new priority direction of pedagogical theory and practice, its content today is at the stage of formation, revision of the object of study, definition of methodological approaches, that is, the problem is relevant.

The study of this problem was carried out by: G. Eysenck, F. Galton, J. Ketell, K. Meili, J. Piaget, Ch. According to these researchers, logical thinking is a purposeful, mediated and generalized reflection by a person of the essential properties and relationships of things aimed at obtaining new results in practice, science, and technology.

Having determined the main tasks of developing the logical thinking of younger schoolchildren, it is necessary to think on what general grounds and principles its content should be built. For they largely determine the effectiveness of training, education and development of schoolchildren in intellectual development. The formation of initial logical techniques in mathematics lessons is carried out through the operations of logical thinking:

Allocation in the studied objects of the basis, properties, and their comparison

Acquaintance with the signs of necessary and sufficient

Classification of objects and concepts

Analysis and synthesis of tasks and assignments

Generalization, i.e. logical conclusion.

The lesson of mathematics provides a unique opportunity to ensure the relationship of the pedagogical process with the process of mastering non-standard tasks by the child, acting, at the same time, with the basic concepts of mathematics.

The system of classes conducted in mathematics lessons, by solving problems, is the optimal form of work with younger students on the formation of logical thinking.

One of the most important tasks facing the primary school teacher is the development of an independent logic of thinking, which would allow children to draw conclusions, provide evidence, make judgments that are logically related to each other, substantiate their judgments, draw conclusions, and, ultimately self-acquire knowledge. Logical thinking is not innate, so it can and should be developed. Solving logical problems in elementary school is just one of the methods for developing thinking. In many ways, the role of teaching mathematics in the development of thinking is due to modern developments in the field of modeling and design techniques, especially in objectively oriented modeling and design, based on inherently human conceptual thinking.

Of course, the problem raised is quite deep and voluminous and requires more than one year of painstaking work.

Literature

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Ministry of Education and Science of the KChR, Zelenchuksky district

MOU "Secondary School N. Arkhyz"

The development of logical thinking in younger students

Nizhny Arkhyz

I. Significance of the development of logical thinking in children.

II. Types of exercises for the development of logical thinking.

a) Choose two words

b) "What's wrong?"

c) What do they have in common?

d) "Choose the words"

III. Intersubject communications.

IV. The development of verbal-logical memory.

a) Tasks for determining the truth and falsity of judgments;

b) Tasks with linking words.

V. "Mathematics is the gymnastics of the mind."

a) Development of cognitive interests;

b) Logical tasks in mathematics lessons;

c) "Compare and draw a conclusion";

d) Logical tasks of three levels;

e) Finding patterns;

e) "Continue the row";

g) Non-standard tasks.

VI. And what is the result?

The development of logical thinking in children is one of the important tasks of primary education. The ability to think logically, to make conclusions without visual support, to compare judgments according to certain rules is a necessary condition for the successful assimilation of educational material.

Thinking should be developed from the first days of a child's life: at home, in kindergarten and school.

In parallel with the development of thinking, the child also develops speech, which organizes and clarifies the thought, allows you to express it in a generalized way, separating the important from the secondary.

The development of thinking affects the upbringing of a person. The child develops positive character traits and the need to develop good qualities in himself, efficiency, the ability to think and reach the truth on his own, plan activities, as well as self-control and conviction, love and interest in the subject, the desire to learn and know a lot.

Sufficient preparedness of mental activity removes psychological stress in learning, prevents academic failure, preserves health.

No one will argue with the fact that every teacher must develop the logical thinking of students. This is stated in the explanatory notes to the curricula, this is written in the methodological literature for teachers. However, the teacher does not always know how to do this. Often this leads to the fact that the development of logical thinking is largely spontaneous, so the majority of students, even in high school, do not master the initial methods of logical thinking, and these methods must be taught to younger students.

First of all, from lesson to lesson, it is necessary to develop the child's ability to analyze and synthesize. The sharpness of the analytical mind allows you to understand complex issues. The ability to synthesize helps to simultaneously keep complex situations in view, to find causal relationships between phenomena, to master a long chain of inferences, to discover connections between single factors and general patterns. The critical orientation of the mind warns against hasty generalizations and decisions. It is important to develop productive thinking in a child, that is, the ability to create new ideas, the ability to establish connections between facts and groups of facts, to compare a new fact with a previously known one.

The psychologist noted the intensive development of the intellect of children at primary school age. The development of thinking leads, in turn, to a qualitative restructuring of perception and memory, their transformation into regulated, arbitrary processes.

A child, starting to study at school, must have a sufficiently developed concrete thinking. In order to form a scientific concept in him, it is necessary to teach him to approach the attributes of objects in a differentiated way. It must be shown that there are essential features, without which an object cannot be brought under this concept. The criterion for mastering a particular concept is the ability to operate with it. If students in grades 1-2 distinguish, first of all, the most obvious external signs that characterize the action of an object (what it does) or its purpose (what it is for), then by the third grade, students already rely more on knowledge, ideas that have developed in the learning process .

The following exercises contribute to this:

Select two words that are most significant for the word in front of the brackets:

Reading (eyes , notebook, book, pencil, glasses)

Garden (plant, dog, fence, shovel , Earth)

Forest (sheet, trees, apple tree, hunter, bush)

What is superfluous?

ONUAI

135А48

"What do they have in common?"

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Ask your child how one word can describe what you read.

1. Perch, crucian - ...

2. Cucumber tomato - …

3. Wardrobe, sofa - …

4. June July - …

5. Elephant, ant -…

A more complex version of the exercise contains only two words for which you need to find a common concept.

"Find what the following words have in common: a) bread and butter (food)
b) nose and eyes (parts of the face, sense organs)
c) apple and strawberry (fruits)
d) clock and thermometer (measuring instruments)
e) whale and lion (animals)
f) echo and mirror (reflection)"

An exercise. "Choose the words."

1) "Pick up as many words as possible that can be attributed to the group of wild animals (pets, fish, flowers, weather phenomena, seasons, tools, etc.)".

2) Another version of the same task.
Connect with arrows the words that fit the meaning:

ball furniture
poplar flower
cupboard insects
plate wood
coat clothes
ant tableware
pike toy
rose fish"
Such tasks develop the child's ability to distinguish generic and specific concepts, form inductive speech thinking.

Working on the development of logical thinking, I rely on my faith in the potential of children. Some guys can think quickly, are capable of improvisation, others are slow. We often rush the student with the answer, get angry if he hesitates. We demand speed of reaction from the child, but we often achieve that the student either gets used to expressing hasty, but unfounded judgments, or withdraws into himself.

Already in elementary school, when constructing the content of education, it is necessary to provide a system of necessary logical methods of thinking. And although logical techniques were formed in the study of mathematics, they can later be widely used as cognitive ready-made means in mastering the material of other academic subjects. Therefore, when selecting logical techniques that should be formed in the study of a certain subject, one should take into account interdisciplinary connections.

Taking into account subject relations, I use the following tasks:

1. Find an unknown number:

Herring Ice

Soloist List

72350 ?

Answer: 3

In the words of the first column, the first two and the last two letters are excluded. This means that in the number it is necessary to exclude the first two and last two digits, respectively. We get the number 3.

2. Find an unknown number:

Aircraft Scrap

Starling Ditch

350291 ?

Answer: 20

Children notice that in the words plane and starling, two extreme letters are excluded, and the rest are read in reverse order. Therefore, eliminating the two extreme digits and rearranging the rest, we get the number 20.

3. Find an unknown number:

Machine 12

Tier 6

School?

Answer: 10

Analyzing words and numbers, we notice that in the word the car- 6 letters, and the number is 2 times more, in a word shooting range- 3 letters, the number is 2 times larger, in a word school- 5 letters, the number is 2 times more - 10.

4. Find an unknown number:

Wood + earth = 11

Tourist X sport = ?

Answer: 30

In the word wood- 6 letters, in a word Earth- 5 letters, adding these numbers, we get the number 11. In the word tourist- 6 letters, in a word sport- 5 letters, multiplying these numbers, we get the number 30.

In connection with the relative predominance of the activity of the first signal system, visual-figurative memory is more developed in younger students. Children better remember specific information, faces, objects, facts than definitions and explanations. They often memorize verbatim. This is explained by. That mechanical memory is well developed in them and the younger schoolchild still does not know how to differentiate the tasks of memorization (what needs to be remembered verbatim and what in general terms), the child still has a poor command of speech, it is easier for him to memorize everything than to reproduce in his own words. Children still do not know how to organize semantic memorization: they do not know how to break the material into semantic groups, highlight strong points for memorization, and draw up a logical plan of the text.

Under the influence of learning, memory in children at primary school age develops in two directions:

The role and share of verbal-logical memorization is increasing (in comparison with visual-figurative memorization);

The ability to consciously control one's memory and regulate its manifestation (memorization, reproduction, recall) is formed.

The development of verbal-logical memory occurs as a result of the development of logical thinking.

Tasks for determining the truth or falsity of judgments

1. There are two drawings on the board. One depicts a monkey, a cat, a squirrel, the other a snake, a bear, a mouse. Children are given cards on which various statements are written:

All the animals in the picture can climb trees.

All the animals in the picture have fur.

None of the animals in this picture can fly.

Some of the animals in the picture have paws.

Some of the animals shown in the picture live in burrows.

All the animals in this picture have claws.

Some of the animals in the picture hibernate.

In this picture, there is not a single animal without a mustache.

All animals drawn in the picture are mammals.

None of the animals in the picture lay eggs.

Students need to determine for which picture the statement is true, and for which it is false.

You can invite the children on their own sheets opposite each statement to indicate the number of the picture for which this statement is true.

This task can be made more difficult by inviting the children, looking at these pictures, to come up with their own true and false statements, using the words: all, some, none.

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I use special tasks and tasks in mathematics lessons aimed at developing the cognitive abilities and abilities of children. Non-standard tasks require increased attention to the analysis of the condition and the construction of a chain of interrelated logical reasoning.

I will give examples of such tasks, the answer to which must be logically substantiated:

1. There are 5 pencils in the box, 2 blue and 3 red. How many pencils must be taken from the box without looking into it so that there is at least one red pencil among them?

2. The loaf was cut into 3 parts. How many incisions were made?

3. The bagel was cut into 4 parts. How many incisions were made?

4. Four boys bought 6 notebooks. Each boy received at least one notebook. Could any boy buy three notebooks?

I introduce non-standard tasks already in the first grade. The use of such tasks expands the mathematical horizons of younger students, promotes mathematical development and improves the quality of mathematical preparedness.

The use of the classification method in mathematics lessons allows you to expand the methods of work available in practice, contributes to the formation of positive motives in educational activities, since such work contains elements of the game and elements of search activity, which increases the activity of students and ensures independent work. For example:

Divide into two groups:

8 – 6 8 – 5 7 – 2 1 + 7 2 + 5

8 – 4 7 – 3 6 – 2 4 + 3 3 + 5

Write down all the numbers written with two different digits:

22, 56, 80, 66, 74, 47, 88, 31, 94, 44

But especially effective for the development of logical thinking of students are tasks in which the basis for classification is chosen by the children themselves.

The system of work on the development of logical thinking of students is aimed at the formation of mental actions of children. They learn to identify mathematical patterns and relationships, make feasible generalizations, and learn to draw conclusions. The use of reference diagrams and tables in mathematics lessons contributes to a better assimilation of the material, encourages children to think more actively.

As a result of systematic work on the development of logical thinking, the educational activity of students is activated, the quality of their knowledge is noticeably improved.

In conclusion, I would like to advise teachers working on the development of logical thinking in younger students not to forget that it is necessary to take into account the level of ability of the children in your class. Difficulties must be overcome.

List of used literature.

1., Sideleva in primary school: Psychological and pedagogical practice. Teaching aid. – M.: TsGL, 2003. – 208 p.

2. Kostromina to overcome difficulties in teaching children: Psychodiagnostic tables. Psychodiagnostic methods. corrective exercises. - M.: Os - 89, 2001. - 272 p.

3. Artemov A. K., Istomina basics of teaching mathematics in primary school: A manual for students of the faculty of training teachers of primary classes of the correspondence department. - M.: Institute of Practical Psychology, Voronezh: NPO "MODEK", 1996. – 224 p.

4. Vinokurov's abilities of children: Grade 2. – M.: Rosmen-Press, 2002. – 79 p.

5., Parishioners: A textbook for students of secondary pedagogical educational institutions. / Ed. . - M .: Publishing Center "Academy", 1999. - 464 p.

6., Kostenkova activities with children:

Materials for independent work of students on the course "Psychological - pedagogical diagnostics and counseling". – M.: V. Sekachev, 2001. – 80 s.

8. Istomina. Grade 2: A textbook for a four-year elementary school. - Smolensk: Association XXI century, 2000. - 176 p.